Units of Measure PDF

Length Meter m Mass...

Length Meter m Mass Kilogram kg Units of Measure Time Second s Any meaningful quantitative laboratory result consists of two components: the first component Electric current Ampere A represents the number related to the actual test value, and the second is a label identifying the units. The unit defines the physical quantity or dimension, such as mass, length, time, or Thermodynamic temperature Kelvin K volume.1 There are a few laboratory tests that do not have units, but whenever possible, units should be used. Amount of substance Mole mol The Système International d’Unités (SI) was adopted in 1960. It is preferred in scientific Luminous intensity Candela cd literature and clinical laboratories and is the only system employed in many countries. This system was devised to provide the global scientific community with a uniform method of Selected Derived describing physical quantities. The SI system units (referred to as SI units) are based on the metric system. Several subclassifications exist within the SI system, one of which is the basic Frequency Hertz Hz unit. There are seven basic units (Table 1.1), with length (meter), mass (kilogram), and Force Newton N quantity of a substance (mole) being the units most frequently encountered. Derived units are another subclassification of the SI system. A derived unit is a mathematical function describing Celsius temperature Degree Celsius °C one of the basic units. An example of an SI-derived unit is meters per second (m/s), which is used to express velocity. Some non-SI units are so widely used that they have become Catalytic activity Katal kat acceptable for use within the SI system (Table 1.1). These include units such as hour, minute, day, gram, liter, and plane angles expressed as degrees. The SI system uses standard Selected Accepted Non-SI prefixes to indicate a decimal fraction or multiples of that basic unit (Table 1.2).1 For example, Minute (time) (60 s) min 0.001 liter can be expressed using the prefix milli, or 10–3, and since it requires moving the decimal point three places to the right, it can then be written as 1 milliliter, or abbreviated as 1 Hour (3600 s) h mL. It may also be written in scientific notation as 1 × 10–3 L. Likewise, 1000 liters would use Day (86,400 s) d the prefix of kilo (103) and could be written as 1 kiloliter or expressed in scientific notation as 1 × 103 L. Table 1.2 indicates prefixes that are frequently used in clinical laboratories. Prefixes Liter (volume) (1 dm 3 = 10–3 m 3) L smaller than the basic unit have a negative exponent (deci: 10–1), and prefixes larger than the base unit have a positive exponent (kilo: 103). When converting between prefixes, note the Angstrom (0.1 nm = 10–10 m) Å relationship between the two prefixes based on whether you are changing to a smaller or larger prefix. When converting from a larger to smaller, the decimal will move to the right. For © Jones & Bartlett Learning. example, converting one liter (1.0 × 100 or 1.0) to milliliters (1.0 × 10−3 or 0.001), the starting unit (L) is larger than milliliters, by a factor of 1000, or 103. This means that the decimal place moves to the right three places, so 1.0 liter (L) equals 1000 milliliters (mL). The opposite is also TABLE 1.2 Prefixes Used with SI Units true. When converting to a larger unit, the decimal place moves to the left. For example, converting 1000 milliliters (mL) to 1.0 liter (L), the decimal point moves to the left three places to become 1.0 L. Note that the SI term for mass is kilogram, which is the only basic unit that contains a prefix as part of its name. Generally, the clinical laboratory uses the term gram for mass rather than kilogram. TABLE 1.1 SI Units Base Quantity Name Symbol  1.0 L (1 × 100) μL (micro = 10–6) The difference between the exponents = 6. The conversion is from a larger unit to a smaller unit, so the decimal will move 6 places to the right. 1.0 L = 1,000,000 μL Example 2: Convert 5 mL to μL 5 mL (milli = 10−3) μL (micro = 10−6) The difference between the exponents = 3. The conversion is from a larger unit to a smaller unit, so the decimal will move 3 places to the right. 5 mL = 5000 μL Example 3: Convert 5.3 mL to dL 5.3 mL (milli = 10−3) dL (deci = 10−1) The conversion is moving from a smaller unit to a larger unit, so the decimal place will move two places to the left. 5.3 mL = 0.053 dL Reporting of laboratory results is often expressed in terms of substance concentration (e.g., moles) or the mass of a substance (e.g., mg/dL, g/dL, g/L, mmol/L, and IU) rather than in SI units. These traditional units can cause confusion during interpretation and conversion to SI units: examples of conversions can be found later in the chapter. As with other areas of industry, the laboratory and the rest of medicine are moving toward adopting universal standards promoted by the International Organization for Standardization, often referred to as ISO. This group develops standards of practice, definitions, and guidelines that can be adopted by everyone in a given field, providing for more uniform terminology. Many national initiatives Description have recommended common units for laboratory test results, but none have been widely adopted.2 As with any transition, the clinical laboratorian should be familiar with all the terms currently used in their field and how to convert these to SI units. SI CONVERSIONS To convert between SI units, move the decimal the difference between the exponents represented by the prefix of the base unit. When moving from a larger unit to a smaller unit, the decimal will move to the right. When converting from a smaller unit to a larger unit, the decimal will move to the left. If converting from smaller unit to larger unit, then move decimal to the left the exponent difference. If converting from larger unit to smaller unit, then move decimal to the right the exponent difference. Example 1: Convert 1.0 L to μL  manufacturers to indicate any physical or biologic health hazards and precautions needed for the safe use, storage, and disposal of any chemical. Manufacturers are required to provide a Reagents Safety Data Sheet (SDS). A copy of the SDS must be readily available to ensure the safety of laboratorians. In today’s highly automated laboratory, there is little need for reagent preparation by the laboratorian. Most instrument manufacturers make the reagents in a ready-to-use form or “kit” Reference Materials in which all necessary reagents and respective storage containers are prepackaged as a unit, requiring only the addition of water or buffer for reconstitution. A heightened awareness of the Unlike other areas of chemistry, clinical chemistry is involved in the analysis of biochemical by- hazards of certain chemicals and the numerous regulatory agency requirements has caused products found in biological fluids, such as serum, plasma, or urine. For this reason, clinical chemistry laboratories to eliminate massive stocks of chemicals and opt instead for the traditionally defined standards used in analytical chemistry do not readily apply in clinical ease of using prepared reagents. Periodically, the laboratorian may still need to prepare chemistry. reagents or solutions, especially in hospital laboratories involved in research and development, A primary standard is a highly purified chemical that can be measured directly to have an biotechnology applications, specialized analyses, or method validation. exact known concentration and purity. The ACS has purity tolerances for primary standards; because most biologic constituents are unavailable within these tolerance limitations, the National Institute of Standards and Technology (NIST) has certified standard reference Chemicals materials (SRMs) that are used in place of ACS primary standard materials.5–7 Analytic chemicals exist in varying grades of purity: Reagent grade or analytic reagent (AR); These SRMs are assigned a value after analysis using state-of-the-art methods and ultrapure, chemically pure (CP); United States Pharmacopeia (USP); National Formulary (NF); equipment. The chemical composition of these substances is then certified; however, they may and technical or commercial grade.3 Chemicals with AR designation are suitable for use in most not have the purity of a primary standard. Because each substance has been characterized for analytic laboratory procedures. A committee of the American Chemical Society (ACS) certain chemical or physical properties, it can be used in place of an ACS primary standard in established specifications for AR grade chemicals, and chemical manufacturers must either clinical work and is often used to verify calibration or accuracy/bias assessments. Many meet or exceed these requirements. The labels on reagents should clearly state the actual manufacturers use a NIST SRM when producing calibrator and standard materials. These impurities for each chemical lot or list the maximum allowable impurities. The label should also materials are considered “traceable to NIST” and may meet certain accreditation requirements. include one of the following designations: AR or ACS or For laboratory use or ACS Standard- Standard reference materials are used for linearity studies to determine the relationship Grade Reference Materials. Ultrapure chemicals have additional purification steps for use in between the standard’s concentration and the instrument result. Linearity studies are required specific procedures such as chromatography, immunoassays, molecular diagnostics, when a new test or new test methodology is introduced. There are SRMs for a number of standardization, or other techniques that require extremely pure chemicals. These reagents routine analytes, hormones, drugs, and blood gases, with others being added.5 Calibration of may have designations of HPLC (high-performance liquid chromatography) or chromatographic an instrument is a process that pairs an analytical signal with a concentration value of an on their labels. analyte. When performing a calibration, a series of calibrators with known concentrations of a Because USP- and NF-grade chemicals are used to manufacture drugs, the limitations specific analyte are used. The instrument is programmed with the known concentrations and established for this group of chemicals are based only on the criterion of not being injurious to will adjust the analytic signal to match the given concentration. Calibrators can be purchased as individuals. Chemicals in this group may be pure enough for use in most chemical procedures, a kit or made by diluting a known stock solution. but the purity standards they meet are not based on the needs of the laboratory and may or may not meet all assay requirements. Water Specifications8 Reagent designations of CP or ultrapure grade indicate that the impurity limitations are not stated, and preparation of these chemicals is not uniform. It is not recommended that clinical Water is the most frequently used reagent in the laboratory. Tap water is unsuitable for laboratories use these chemicals for reagent preparation unless further purification or a reagent laboratory applications. Most procedures, including reagent and control preparation, require blank is included. Technical or commercial grade reagents are used primarily in manufacturing water that has been substantially purified, known as reagent-grade water. There are various and should never be used in the clinical laboratory. water purification methods including distillation, ion exchange, reverse osmosis, ultrafiltration, Organic reagents also have varying grades of purity that differ from those used to classify ultraviolet light, sterilization, and ozone treatment. According to the Clinical and Laboratory inorganic reagents. These grades include a practical grade with some impurities; CP, which Standards Institute (CLSI), reagent-grade water is classified into one of six categories based approaches the purity level of reagent-grade chemicals; spectroscopic (spectrally pure) and on the specifications needed for its use rather than the method of purification or preparation.9 chromatographic grade organic reagents; and reagent grade (ACS), which is certified to These categories include clinical laboratory reagent water (CLRW), special reagent water contain impurities below established ACS levels. Other than the purity aspects of the chemicals, (SRW), instrument feed water, water supplied by method manufacturer, autoclave and wash laws related to the Occupational Safety and Health Administration (OSHA)4 require water, and commercially bottled purified water. Each category has a specific acceptable limit. The College of American Pathologists requires laboratories to define the specific type of water used in reagent preparation. Resistance is measured because pure water, devoid of ions, is a required for each of its testing procedures and requires water quality testing at least annually. poor conductor of electricity and has increased resistance. The relationship of water purity to Water quality testing routinely includes monitoring microbial colony-forming units/mL and may resistance is linear; generally, as purity increases, so does resistance. This one measurement also include other parameters. does not suffice for determination of true water purity because a nonionic contaminant may be Distilled water has been purified to remove almost all organic materials, using a technique of present that will have little effect on resistance. Reagent water meeting specifications from distillation where water is boiled and vaporized. Many impurities do not rise in the water vapor other organizations, such as the American Society for Testing and Materials (ASTM), may not and will remain in the boiling apparatus so that the water collected after condensation has less be equivalent to those established by the CLSI, so care should be taken to meet the assay contamination. Water may be distilled more than once, with each distillation cycle removing procedural requirements for water type. additional impurities. Ultrafiltration and nanofiltration, like distillation, are excellent in removing particulate matter, microorganisms, and any pyrogens or endotoxins. Solution Properties Deionized water has some or all ions removed, although organic material may still be present, so it is neither pure nor sterile. Generally, deionized water is purified from previously In clinical chemistry, substances found in biologic fluids, including serum, plasma, urine, and treated water, such as prefiltered or distilled water. Deionized water is produced using either an spinal fluid, are quantified. A substance that is dissolved in a liquid is called a solute; a biologic anion- or a cation-exchange resin, followed by replacement of the removed ions with hydroxyl solute is also known as an analyte. The liquid in which the solute is dissolved—for example, a or hydrogen ions. A combination of several ion-exchange resins will produce different grades of biologic fluid—is the solvent. Together, solute and solvent represent a solution. Any chemical deionized water. A two-bed system uses an anion resin followed by a cation resin. The different or biologic solution can be described by its basic properties, including concentration, saturation, resins may be in separate columns or in the same column. This process is excellent at removing colligative properties, redox potential, conductivity, density, pH, and ionic strength. dissolved ionized solids and dissolved gases. Reverse osmosis is a process that uses pressure to force water through a semipermeable Concentration membrane, producing a filtered product. Reverse osmosis may be used for the pretreatment of The analyte concentration in solution can be expressed in many ways. Concentration is water, however, it does not remove dissolved gases. commonly expressed as percent solution, molarity, molality, or normality. These are non-SI Filtration can remove particulate matter from municipal water supplies before any additional units, however; the SI unit for the amount of a substance is the mole. Examples of treatments. Filtration cartridges can be composed of glass, cotton, or activated charcoal, which concentration calculations are provided later in this chapter. removes organic materials and chlorine. Some have submicron filters (≤0.2 µm), which remove Percent solution is expressed as the amount of solute per 100 total units of solution. Three any substances larger than the filter’s pores, including bacteria. The use of these filters expressions of percent solutions are weight per weight (w/w), volume per volume (v/v), and depends on the quality of the municipal water and the other purification methods used. For weight per volume (w/v). Weight per weight (% w/w) refers to the number of grams of solute example, hard water (containing calcium, iron, and other dissolved elements) may require per 100 g of solution. Volume per volume (% v/v) is used for liquid solutes and gives the prefiltration with a glass or cotton filter rather than activated charcoal or submicron filters, which milliliters of solute in 100 mL of solution. For v/v solutions, it is recommended that grams per quickly become clogged and are expensive to use. The submicron filter may be better suited deciliter (g/dL) be used instead of % v/v. Weight per volume (% w/v) is the most commonly after distillation, deionization, or reverse osmosis treatment. used percent solution in the clinical laboratory and is defined as the number of grams of solute Ultraviolet oxidation, which removes some trace organic material or sterilization processes at in 100 mL of solution. Weight per volume is not the same as molarity, and care must be taken specific wavelengths, can destroy bacteria when used as part of a system but may leave to not confuse the two. Examples of percent solution calculations can be found later in this behind some residual products. This technique is often followed by other purification processes. chapter. Reagent-grade water can be obtained by initially filtering to remove particulate matter, Molarity (M) is expressed as the number of moles per 1 L of solution. One mole of a followed by reverse osmosis, deionization, and a 0.2-µm filter or more restrictive filtration substance equals its gram molecular weight (gmw), so the customary units of molarity (M) are process. Autoclave wash water is acceptable for glassware washing but not for analysis or moles/liter. The SI representation for the traditional molar concentration is moles of solute per reagent preparation. SRW is used for specific techniques like the HPLC, molecular diagnostics, volume of solution, with the volume of the solution given in liters. The SI expression for or mass spectrophotometry, which may require specific parameters for the analysis. All SRW concentration should be represented as moles per liter (mol/L), millimoles per liter (mmol/L), should meet CLRW standards and, depending on the application, CLRW should be stored in a micromoles per liter (μmol/L), or nanomoles per liter (nmol/L). The common concentration term manner that reduces any chemical or bacterial contamination and for short periods. molarity is not an SI unit for concentration. Molarity depends on volume, and any significant Testing procedures to determine the quality of reagent-grade water include measurements of physical changes that influence volume, such as changes in temperature and pressure, will also resistance, pH, colony counts on selective and nonselective media for the detection of bacterial influence molarity. Calculations can be found in the Laboratory Mathematics and Calculations contamination, chlorine, ammonia, nitrate or nitrite, iron, hardness, phosphate, sodium, silica, section of this chapter. carbon dioxide, chemical oxygen demand, and metal detection. Some accreditation agencies10 Molality (m) represents the amount of solute per 1 kg of solvent. Molality is sometimes recommend that laboratories document culture growth, pH, and specific resistance on water confused with molarity; however, it can be easily distinguished because molality is always atmospheric pressure (usually 1 atmosphere). expressed in terms of moles per kilogram (weight per weight) and describes moles per 1000 g The osmotic pressure of a dilute solution is directly proportional to the concentration of the (1 kg) of solvent. Note that the common abbreviation (m) for molality is a lowercase “m,” while molecules in solution. The expression for concentration is the osmole. One osmole of a the uppercase “M” refers to molarity. Molality is not influenced by temperature or pressure substance equals the molarity or molality multiplied by the number of particles, not the kind of because it is based on mass rather than volume. particle, at dissociation. If molarity is used, the resulting expression would be termed Normality is the least likely of the four concentration expressions to be encountered in osmolarity; if molality is used, the expression changes to osmolality. Osmolality is preferred clinical laboratories, but it is often used in chemical titrations and chemical reagent since it depends on the weight rather than volume and is not readily influenced by temperature classification. It is defined as the number of gram equivalent weights per 1 L of solution. An and pressure changes. When a solute is dissolved in a solvent, the colligative properties change equivalent weight is equal to the gmw of a substance divided by its valence. The valence is in a predictable manner for each osmole of substance present. In the clinical setting, freezing the number of units that can combine with or replace 1 mole of hydrogen ions for acids and point and vapor pressure depression can be measured as a function of osmolality. Freezing hydroxyl ions for bases and the number of electrons exchanged in oxidation–reduction point is preferred since vapor pressure measurements can give inaccurate readings when some reactions. Normality is always equal to or greater than the molarity of the compound. substances, such as alcohols, are present in the samples. Calculations can be found later in this chapter. Normality was previously used for reporting electrolyte values, expressed as milliequivalents per liter (mEq/L); however, this convention has Redox Potential been replaced with millimoles per liter (mmol/L). The College of American Pathologists (CAP) currently requires chloride to be reported in mmol/L. Because the four main electrolytes, Na+, Redox potential, or oxidation–reduction potential, is a measure of the ability of a solution to K+, CO2– (HCO3–), and Cl–, all have a valence of 1, the concentration reported will remain the accept or donate electrons. Substances that donate electrons are called reducing agents; same whether the unit is mEq/L or mmol/L. those that accept electrons are considered oxidizing agents. The mnemonic—LEO (lose Solution saturation gives little specific information about the concentration of solutes in a electrons oxidized) the lion says GER (gain electrons reduced)—may prove useful when trying solution. A solution is considered saturated when no more solvent can be dissolved in the to recall the relationship between reducing/oxidizing agents. solution. Temperature, as well as the presence of other ions, can influence the solubility constant for a solute in a given solution and thus affect the saturation. Routine terms in the Conductivity clinical laboratory that describe the extent of saturation are dilute, concentrated, saturated, and Conductivity is a measure of how well electricity passes through a solution. A solution’s supersaturated. A dilute solution is one in which there is relatively little solute or one that has a conductivity quality depends principally on the number of respective charges of the ions lower solute concentration per volume of solvent than the original, such as when making a present. Resistivity, the reciprocal of conductivity, is a measure of a substance’s resistance to dilution. In contrast, a concentrated solution has a large quantity of solute in solution. A solution the passage of electrical current. The primary application of resistivity in the clinical laboratory in which there is an excess of undissolved solute particles can be referred to as a saturated is for assessing the purity of water. Resistivity (resistance) is expressed as ohms and solution. As the name implies, a supersaturated solution has an even greater concentration of conductivity is expressed as ohms−1. undissolved solute particles than a saturated solution of the same substance. Because of the greater concentration of solute particles, a supersaturated solution is thermodynamically unstable. The addition of a crystal of solute or mechanical agitation disturbs the supersaturated pH and Buffers solution, resulting in crystallization of any excess material out of solution. An example is when Buffers are weak acids or bases and their related salts that minimize changes in the hydrogen measuring serum osmolality by freezing point depression. ion concentration. Hydrogen ion concentration is often expressed as pH. A lowercase p in front of certain letters or abbreviations operationally means the “negative logarithm of” or “inverse log Colligative Properties of” that substance. In keeping with this convention, the term pH represents the negative or inverse log of the hydrogen ion concentration. Mathematically, pH is expressed as Colligative properties are those properties related to the number of solute particles per solvent molecules, not on the type of particles present. The behavior of particles or solutes in solution demonstrates four properties: osmotic pressure, vapor pressure, freezing point, and boiling point. These are called colligative properties. Osmotic pressure is the pressure that opposes osmosis when a solvent flows through a semipermeable membrane to establish equilibrium (Eq. 1.1) between compartments of differing concentration. Vapor pressure is the pressure exerted by the vapor when the liquid solvent is in equilibrium with the vapor. Freezing point is the temperature at which the first crystal (solid) of solvent forms in equilibrium with the solution. where [H+] equals the concentration of hydrogen ions in moles per liter (M). The pH scale Boiling point is the temperature at which the vapor pressure of the solvent reaches ranges from 0 to 14 and is a convenient way to express hydrogen ion concentration. Eliminating the minus sign in front of the log of the quantity results in an equation known as Unlike a strong acid or base, which dissociates almost completely, the dissociation constant for a weak acid or base solution (like a buffer) tends to be very small, meaning little the Henderson-Hasselbalch equation, which mathematically describes the dissociation dissociation occurs. characteristics of weak acids (pKa) and bases (pKb) and the effect on pH: The dissociation of acetic acid (CH3COOH), a weak acid, can be illustrated as follows: (Eq. 1.7) (Eq. 1.2) When the ratio of [A−] to [HA] is 1, the pH equals the pK and the buffer has its greatest Description buffering capacity. The dissociation constant Ka, and therefore the pKa, remains the same for a given substance. Any changes in pH are solely due to the ratio of conjugate base [A−] − + HA = weak acid, A = conjugate base, H = hydrogen ions, [] = concentration of item in the concentration to weak acid [HA] concentration. Refer to Chapter 12, Blood Gases, pH, and bracket. Buffer Systems, for more information. Sometimes, the conjugate base (A−) will be referred to as a “salt” since, physiologically, it will Ionic strength is another important aspect of buffers, particularly in separation techniques. be associated with some type of cation, such as sodium (Na+). Ionic strength is the concentration or activity of ions in a solution or buffer. Increasing ionic The dissociation constant, Ka, for a weak acid may be calculated using the following strength increases the ionic cloud surrounding a compound and decreases the rate of particle equation: migration. It can also promote compound dissociation into ions effectively increasing the solubility of some salts, along with changes in current, which can also affect electrophoretic separation. (Eq. 1.3) Rearrangement of this equation reveals (Eq. 1.4) Taking the log of each quantity and then multiplying by minus 1 (−1), the equation can be rewritten as (Eq. 1.5) By convention, lowercase p means “negative log of”; therefore, –log[H+] may be written as pH, and −Ka may be written as pKa. The equation now becomes (Eq. 1.6)  calibration points (0°C, 25°C, 30°C, and 37°C) for use with liquid-in-glass thermometers. Gallium, another SRM, has a known melting point and can also be used for thermometer Laboratory Equipment verification. As automation advances and miniaturizes, the need for an accurate, fast-reading electronic In today’s clinical chemistry laboratory, there are many different types of equipment in use. thermometer (thermistor) has increased and is now routinely incorporated in many devices. The Most manual techniques have been replaced by automation, but it is still necessary for the advantages of a thermistor over the more traditional liquid-in-glass thermometers are size and laboratorian to be knowledgeable in the operation and use of common laboratory equipment. millisecond response time. Similar to the liquid-in-glass thermometers, the thermistor can be The following is a brief discussion of the composition and general use of common equipment calibrated against an SRM thermometer. found in a clinical chemistry laboratory, including heating units, thermometers, pipettes, flasks, beakers, balances, and centrifuges. Glassware and Plasticware Until recently, laboratory supplies (e.g., pipettes, flasks, beakers) consisted of some type of Heating Units glass and could be correctly termed glassware. As plastic material was refined and made Heat blocks and water baths are common heating units within the laboratory. The temperature available to manufacturers, plastic has been increasingly used to make laboratory supplies. A of these heating units must be monitored daily when in use. The predominant practice for brief summary of the types and uses of glass and plastic commonly seen today in laboratories temperature measurement uses the Celsius (°C) scale; however, Fahrenheit (°F) and Kelvin can be found in the Navigate 2 digital component. Regardless of design, most laboratory (°K) scales are also used.11 The SI designation for temperature is the Kelvin scale. Table 1.3 supplies must satisfy certain tolerances of accuracy and fall into two classes of precision gives the conversion formulas between Fahrenheit and Celsius scales, and Appendix C (found tolerance, either Class A or Class B as given by ASTM.12,13 Those that satisfy Class A ASTM in the Navigate 2 digital component) lists the various conversion formulas. precision criteria are stamped with the letter “A” on the glassware and are preferred for laboratory applications. Class B glassware generally have twice the tolerance limits of Class A, even if they appear identical, and are often found in student laboratories where durability is TABLE 1.3 Common Temperature Conversions needed. Vessels holding or transferring liquid are designed either to contain (TC) or to deliver (TD) a specified volume. The major difference is that TC devices do not deliver the volume Celsius (Centigrade) to Fahrenheit °C (9/5) + 32 (multiply Celsius temperature by 9; divide the answer by 5, then add 32) measured when the liquid is transferred into a container, whereas the TD designation means that the labware will deliver the amount measured. Fahrenheit to Celsius (Centigrade) (°F − 32)5/9 (subtract 32 and divide the answer by 9; then multiply that answer by 5) Glassware used in the clinical laboratory usually fall into one of the following categories: Kimax/Pyrex (borosilicate), Corex (aluminosilicate), high silica, Vycor (acid and alkali resistant), © Jones & Bartlett Learning. low actinic (amber colored), or flint (soda lime) glass used for disposable material.14 Glassware routinely used in clinical chemistry should consist of high thermal borosilicate or aluminosilicate All analytic reactions occur at an optimal temperature. Some laboratory procedures, such as glass. The manufacturer is the best source of information about specific uses, limitations, and enzyme determinations, require precise temperature control, whereas others work well over a accuracy specifications for glassware. wide range of temperatures. Reactions that are temperature dependent use some type of Plasticware is beginning to replace glassware in the laboratory setting; high resistance to heating/cooling cell, heating/cooling block, or water/ice bath to provide the correct temperature corrosion and breakage, as well as varying flexibility, has made plasticware appealing. environment. Laboratory refrigerator temperatures are often critical and need periodic Relatively inexpensive, it allows most items to be completely disposable after each use. The verification. Thermometers can be an integral part of an instrument or need to be placed in the major types of resins frequently used in the clinical chemistry laboratory are polystyrene, device for temperature maintenance and monitoring. Several types of temperature devices are polyethylene, polypropylene, Tygon, Teflon, polycarbonate, and polyvinyl chloride. Again, the currently used in the clinical laboratory, including liquid-in-glass and electronic (thermistor) individual manufacturer is the best source of information concerning the proper use and devices. Regardless of which type is being used, all temperature-reading devices must be limitations of any plastic material. calibrated for accuracy. Liquid-in-glass thermometers use a colored liquid (red or other colored In most laboratories, glass or plastic that is in direct contact with biohazardous material is material), encased in plastic or glass, measuring temperatures between 20°C and 400°C. usually disposable. If not, it must be decontaminated according to appropriate protocols. Visual inspection of the liquid-in-glass thermometer should reveal a continuous line of liquid, free Should the need arise, cleaning of glass or plastic may require special techniques. Immediately from separation or bubbles. If separation or bubbles are present, then replace the rinsing glass or plastic supplies after use, followed by washing with a detergent designed for thermometer. cleaning laboratory supplies and several distilled water rinses, may be sufficient. Presoaking Liquid-in-glass thermometers should be calibrated against a NIST-certified or NIST-traceable glassware in soapy water is highly recommended whenever immediate cleaning is impractical. thermometer for critical laboratory applications.11 NIST has an SRM thermometer with various Many laboratories use automatic dishwashers and dryers for cleaning. Detergents and temperature levels should be compatible with the material and the manufacturer’s possible to maximize accuracy and precision and thus decrease calibration time (Figure 1.1 recommendations. To ensure that all detergent has been removed from the labware, multiple illustrates representative laboratory glassware). rinses with appropriate grade water is recommended. Check the pH of the final rinse water and compare it with the initial pH of the prerinse water. Detergent-contaminated water will have a more alkaline pH as compared with the pH of the prerinse water. Visual inspection should reveal spotless vessel walls. Any biologically contaminated labware should be disposed of according to the precautions followed by the laboratory. Some determinations, such as those used in assessing heavy metals or assays associated with molecular testing, require scrupulously clean or disposable glassware. Other applications may require plastic rather than glass because glass can absorb metal ions. It is suggested that disposable glass and plastic be used whenever possible. Dirty reusable pipettes should be placed, with the pipette tips up, immediately in a specific pipette soaking/washing/drying container. This container should have soapy water high enough to cover the entire pipette. For each final water rinse, fresh reagent-grade water should be used; if possible, designate a pipette container for final rinses only. Cleaning brushes are available to fit almost any size glassware and are recommended for any articles that are washed routinely. Although plastic material is often easier to clean because of its nonwettable surface, it may not be appropriate for some applications involving organic solvents or autoclaving. Brushes or harsh abrasive cleaners should not be used on plasticware. Many initial cleaning procedures, described in Appendix J (found in the Navigate 2 digital component), can be adapted for plasticware. Ultrasonic cleaners can help remove debris coating the surfaces of glass or plasticware. Properly cleaned laboratory glass and plasticware should be completely dried before using. Laboratory Glassware Flasks, beakers, and graduated cylinders are used to hold solutions. Volumetric and Erlenmeyer flasks are two types of containers in general use in the clinical laboratory. A volumetric flask is calibrated to hold one exact volume of liquid (TC). The flask has a round, lower portion with a flat bottom and a long, thin neck with an etched calibration line. Figure 1.1 Laboratory glassware. Volumetric flasks are used to bring a given reagent to its final volume with the recommended © Wolters Kluwer. diluent. When bringing the bottom of the meniscus to the calibration mark, a pipette should be used for adding the final drops of diluent to ensure maximum control is maintained and the Pipettes calibration line is not missed. Erlenmeyer flasks and Griffin beakers are designed to hold different volumes rather than Pipettes are a type of laboratory equipment used to transfer liquids; they may be reusable or one exact amount. Because Erlenmeyer flasks and Griffin beakers are often used in reagent disposable. Although pipettes may transfer any volume, they are usually used for volumes of 20 preparation, flask size, chemical inertness, and thermal stability should be considered. The mL or less; larger volumes are usually transferred or dispensed using automated pipetting Erlenmeyer flask has a wide bottom that gradually evolves into a smaller, short neck. The devices. Table 1.4 outlines the pipette classification. Griffin beaker has a flat bottom, straight sides, and an opening as wide as the flat base, with a small spout in the lip. TABLE 1.4 Pipette Classification Graduated cylinders are long, cylindrical tubes usually held upright by an octagonal or circular base. The cylinder has horizontal calibration marks and is used to measure volumes of liquids. Graduated cylinders do not have the accuracy of volumetric labware. The sizes routinely I. Design used are 10, 25, 50, 100, 500, 1000, and 2000 mL. A. To contain (TC) All laboratory glassware used for critical measurements should be Class A whenever  B. To deliver (TD) continuous rings located near the top of the pipette. This means that the last drop of liquid should be expelled into the receiving vessel. Without these markings, a pipette is self-draining, and the user allows the contents of the pipette to drain by gravity. The tip of the pipette should I. Drainage characteristics not be in contact with the accumulating fluid in the receiving vessel during drainage. With the A. Blowout exception of the Mohr pipette, the tip should remain in contact with the side of the vessel for B. Self-draining several seconds after the liquid has drained. The pipette is then removed (Figure 1.2). I. Type A. Measuring or graduated 1. Serologic 2. Mohr 3. Bacteriologic 4. Ball, Kolmer, or Kahn 5. Micropipette B. Transfer 1. Volumetric 2. Ostwald-Folin 3. Pasteur pipettes 4. Automatic macropipettes or micropipettes © Jones & Bartlett Learning. Similar to other laboratory equipment, pipettes are designed to contain (TC) or to deliver (TD) a particular volume of liquid. The major difference is the amount of liquid needed to wet the interior surface of the pipette and the amount of any residual liquid left in the pipette tip. Most manufacturers stamp TC or TD near the top of the pipette to alert the user as to the type of pipette. Like other TC-designated labware, a TC pipette holds or contains a particular volume but does not dispense that exact volume, whereas a TD pipette will dispense the volume indicated. When using either pipette, the tip must be immersed in the intended transfer liquid to a level that will allow the tip to remain in solution after the volume of liquid has entered the pipette— without touching the vessel walls. The pipette is held upright, not at an angle (Figure 1.2). Using a pipette bulb or similar device, a slight suction is applied to the opposite end until the liquid enters the pipette and the meniscus is brought above the desired graduation line (Figure 1.3A), and suction is then stopped. While the meniscus level is held in place, the pipette tip is raised slightly out of the solution and wiped with a laboratory tissue to remove any adhering liquid. The liquid is allowed to drain until the bottom of the meniscus touches the desired calibration mark (Figure 1.3B). With the pipette held in a vertical position and the tip against the side of the receiving vessel, the pipette contents are allowed to drain into the vessel (e.g., test tube, cuvette, or flask). A blowout pipette has a continuous etched ring or two small, close,  Figure 1.2 Correct and incorrect pipette positions. © Wolters Kluwer. Description Figure 1.3 Pipetting technique. (A) Meniscus is brought above the desired graduation line. (B) Liquid is allowed to drain until the bottom of the meniscus touches the desired calibration mark. © Wolters Kluwer. Measuring or graduated pipettes are capable of dispensing several different volumes. Measuring pipettes are used to transfer reagents or make dilutions and can be used to repeatedly transfer a particular solution. The markings at the top of a measuring or graduated pipette indicate the volume(s) it is designed to dispense. Because the graduation lines located on the pipette may vary, the increments will be indicated on the top of each pipette. For example, a 5-mL pipette can be used to measure 5, 4, 3, 2, or 1 mL of liquid, with further graduations between each milliliter. The pipette is designated as 5 in 1/10 increments (Figure 1.4) and could deliver any volume in tenths of a milliliter, up to 5 mL. Another pipette, such as a 1-mL pipette, may be designed to dispense 1 mL and have subdivisions of hundredths of a milliliter. The subgroups of measuring or graduated pipettes are Mohr, serologic, and micropipettes. A Mohr pipette does not have graduations to the tip. It is a self-draining pipette, but the tip should not be allowed to touch the vessel while the pipette is draining. A serologic pipette has graduation marks to the tip and is generally a blowout pipette. A micropipette is a pipette with a total holding volume of less than 1 mL; it may be designed as either a Mohr or a serologic pipette. Figure 1.4 Volume indication of a pipette. © Wolters Kluwer. Figure 1.5 Disposable transfer pipettes. Transfer pipettes are designed to dispense one volume without further subdivisions. Ostwald- © Wolters Kluwer. Folin pipettes are used with biologic fluids having a viscosity greater than that of water. They are blowout pipettes, indicated by two etched, continuous rings at the top. The volumetric pipette is designed to dispense or transfer aqueous solutions and is always self-draining. The The automatic pipette is the most routinely used pipette in today’s clinical chemistry bulb-like enlargement in the pipette stem easily identifies the volumetric pipette. This type of laboratory. Automatic pipettes come in a variety of types including fixed volume, variable pipette usually has the greatest degree of accuracy and precision and should be used when volume, and multichannel. The term automatic, as used here, implies that the mechanism that diluting standards, calibrators, or quality control material. They should only be used once prior draws up and dispenses the liquid is an integral part of the pipette. It may be a fully to cleaning. Disposable transfer pipettes may or may not have calibration marks and are used automated/self-operating, semiautomatic, or completely manually operated device. Automatic to transfer solutions or biologic fluids without consideration of a specific volume. These pipettes and semiautomatic pipettes have many advantages, including safety, stability, ease of use, should not be used in any quantitative analytic techniques (Figure 1.5). increased precision, the ability to save time, and less cleaning required because the pipette tips are disposable. Figure 1.6 illustrates many common automatic pipettes. A pipette associated with only one volume is termed a fixed volume, and models able to select different volumes are termed variable; however, only one volume may be used at a time. The available range of pipette volumes is 1 μL to 5000 mL. A pipette with a capability of less than 1 mL is considered a micropipette, and a pipette that dispenses greater than 1 mL is called an automatic macropipette. Multichannel pipettes are able to attach multiple pipette tips to a single handle and can then be used to dispense a fixed volume of fluid to multiple wells, such as to a multiwell microtiter plate. In addition to classification by volume delivery amounts, automatic pipettes can also be categorized according to their mechanism: air-displacement, positive displacement, and dispenser pipettes. An air-displacement pipette relies on a piston for creating suction to draw the sample into a disposable tip that must be changed after each use. The piston does not come in contact with the liquid. A positive-displacement pipette operates by moving the piston brands can be used for one particular pipette, but they do not necessarily perform in an in the pipette tip or barrel, much like a hypodermic syringe. It does not require a different tip for identical manner. Tips for positive-displacement pipettes are made of straight columns of glass each use. Because of carryover concerns, rinsing and blotting between samples may be or plastic. These tips must fit snugly to avoid carryover and can be used repeatedly without required. Dispensers and dilutor/dispensers are automatic pipettes that obtain the liquid from a being changed after each use. As previously mentioned, these devices may need to be rinsed common reservoir and dispense it repeatedly. The dispensing pipettes may be bottle-top, and dried between samples to minimize carryover. motorized, handheld, or attached to a dilutor. The dilutor often combines sampling and Class A pipettes do not need to be recalibrated by the laboratory. Automatic pipetting dispensing functions. Many automated pipettes use a wash between samples to eliminate devices, as well as non–Class A materials, do need recalibration.15,16 Calibration of pipettes is carryover problems. However, to minimize carryover contamination with manual or done to verify accuracy and precision of the device and may be required by the laboratory’s semiautomatic pipettes, careful wiping of the tip may remove any liquid that adhered to the accrediting agency. A gravimetric method (see the Navigate 2 digital component resources for outside of the tip before dispensing any liquid. Care should be taken to ensure that the orifice of this procedure) can accomplish this task by delivering and weighing a solution of known specific the pipette tip is not blotted, drawing sample from the tip. Another precaution in using manually gravity, such as water. A currently calibrated analytic balance and at least Class 2 weights operated semiautomatic pipettes is to move the plunger in a continuous and steady manner. should be used.17 Deviation from the chosen volume is calculated based on the type of pipette Pipettes should be operated according to the manufacturer’s directions. tested. Pipettes that fall outside of the maximum allowable error will need to be adjusted following the manufacturer’s instructions. Although gravimetric validation is the most desirable method,18,19 pipette calibration may also be accomplished by using photometric methods, particularly for automatic pipetting devices. When a spectrophotometer is used, the molar absorptivity of a compound, such as potassium dichromate, is obtained. After an aliquot of diluent is pipetted, the change in concentration will reflect the volume of the pipette. Another photometric technique used to assess pipette accuracy compares the absorbances of dilutions of potassium dichromate, or another colored liquid with appropriate absorbance spectra, using Class A volumetric labware versus equivalent dilutions made with the pipetting device. These calibration techniques are time consuming and impractical for use in daily checks. It is recommended that pipettes be checked initially and subsequently three or four times per year, or as dictated by the laboratory’s accrediting agency. Many companies offer calibration services; the one chosen should also satisfy any accreditation requirements. A quick, daily check for many larger volume automatic pipetting devices involves the use of volumetric flasks. For example, a bottle-top dispenser that routinely delivers 2.5 mL of reagent may be checked by dispensing four aliquots of the reagent into a 10-mL Class A volumetric flask. The bottom of the meniscus should meet with the calibration line on the volumetric flask. Syringes Syringes are sometimes used for transfer of small volumes (< 500 μL) in blood gas analysis or in separation techniques such as chromatography or electrophoresis (Figure 1.7). The syringes are glass and have fine barrels. The plunger is often made of a fine piece of wire. Tips are not used when syringes are used for injection of sample into a gas chromatographic or high- pressure liquid chromatographic system. In electrophoresis work, however, disposable Teflon tips may be used. Figure 1.6 (A) Adjustable volume pipette. (B) Fixed volume pipette with disposable tips. (C) Multichannel pipette. (D) Multichannel pipette in use. © Wolters Kluwer. Disposable, one-use pipette tips are designed for use with air-displacement pipettes. The laboratorian should ensure that the pipette tip is seated snugly onto the end of the pipette and free from any deformity. Plastic tips used on air-displacement pipettes can vary. Different  Analytic and electronic balances are currently the most popular in the clinical laboratory. Analytic balances (Figure 1.8) are required for the preparation of any primary standard. It has a single pan enclosed by sliding transparent doors, which minimize environmental influences on pan movement, tared weighing vessel, and sample. An optical scale allows the operator to visualize the mass of the substance. The weight range for many analytic balances is from 0.01 mg to 160 g. Figure 1.7 Microliter glass syringe. © Wolters Kluwer. Desiccators and Desiccants Many compounds combine with water molecules to form loose chemical crystals. The compound and the associated water are called a hydrate. When the water of crystallization is removed from the compound, it is said to be anhydrous. Substances that take up water on exposure to atmospheric conditions are called hygroscopic. Materials that are very hygroscopic can remove moisture from the air as well as from other materials. These materials make excellent drying substances and are sometimes used as desiccants (drying agents) to keep other chemicals from becoming hydrated. Closed and sealed containers that include desiccant material are referred to as desiccators and may be used to store more hygroscopic substances. Many sealed packets or shipping containers, often those that require refrigeration, include some type of small packet of desiccant material to prolong storage. Balances A properly operating balance is essential in producing high-quality reagents and standards. However, because many laboratories discontinued in-house reagent preparation, balances may no longer be as widely used. Balances are classified according to their design, number of pans (single or double), and whether they are mechanical or electronic or classified by operating ranges.  Figure 1.8 Analytic balance. © Wolters Kluwer. Electronic balances (Figure 1.9) are single-pan balances that use an electromagnetic force to counterbalance the weighed sample’s mass. Their measurements equal the accuracy and precision of any available mechanical balance, with the advantage of a fast response time (< 10 seconds). Figure 1.9 Electronic top-loading balance. © Wolters Kluwer. Test weights used for calibrating balances should be selected from the appropriate ANSI/ASTM Classes 1 through 4.19 Weighing instruments will need to be calibrated and adjusted periodically due to wear and tear from frequent use. Mechanisms for automatic adjustments are built into many newer instruments. These instruments will test and adjust the sensitivity of the device. Periodic verification is still necessary to assure the performance of that device. The frequency of calibration is dictated by the accreditation/licensing guidelines for a specific laboratory. Balances should be kept clean and be located in an area away from heavy traffic, large pieces of electrical equipment, and open windows to prevent inaccurate readings. The level checkpoint should always be corrected before weighing occurs. Centrifuges Centrifugation is a process in which centrifugal force is used to separate serum or plasma from the blood cells as the blood samples are being processed; to separate a supernatant from a precipitate during an analytic reaction; to separate two immiscible liquids, such as a lipid- laden sample; or to expel air. When samples are not properly centrifuged, small fibrin clots and cells can cause erroneous results during analysis. The centrifuge separates the mixture based on mass and density of the component parts. It consists of a head or rotor, carriers, or shields that are attached to the vertical shaft of a motor or air compressor and enclosed in a metal covering. The centrifuge always has a lid, with new models having a locking lid for safety. Many models include a brake or a built-in tachometer, which indicates speed, and some centrifuges are refrigerated. Centrifugal force depends on three variables: mass, speed, and radius. The speed is expressed in revolutions per minute (rpm), and the centrifugal force generated is expressed in terms of relative centrifugal force (RCF) or gravities (g). The speed of the centrifuge is related to the RCF by the following equation: RCF = 1.118 × 10–5 × r × (rpm)2 where 1.118 × 10−5 is a constant, determined from the angular velocity, and r is the radius in centimeters, measured from the center of the centrifuge axis to the bottom of the test tube shield or bucket. Centrifuge classification is based on several criteria, including benchtop (Figure 1.10A) or floor model; refrigeration; rotor head (e.g., fixed angle, hematocrit, cytocentrifuge, swinging bucket [Figure 1.10B], or angled); or maximum speed attainable (i.e., ultracentrifuge).  Figure 1.10 (A) Benchtop centrifuge. (B) Swinging-bucket rotor. © Wolters Kluwer. Centrifuge maintenance includes daily cleaning of any spills or debris, such as blood or glass, and ensuring that the centrifuge is properly balanced and free from any excessive vibrations. Balancing the centrifuge load is critical (Figure 1.11). Many newer centrifuges will automatically decrease their speed if the load is not evenly distributed, but more often, the centrifuge will shake and vibrate or make more noise than expected. A centrifuge needs to be balanced by equalizing both the volume and weight distribution across the centrifuge head. Many laboratories will have “balance” tubes of routinely used volumes and tube sizes, which can be used to match those from patient samples. A good rule of thumb is one of even placement and “opposition” (Figure 1.12). Exact positioning of tubes depends on the design of the centrifuge holders. Figure 1.11 Properly balanced centrifuge. Colored circles represent counterbalanced positions for sample tubes. © Wolters Kluwer.  © Ariel Skelley/DigitalVision/Getty Images. Figure 1.12 Properly loaded centrifuge. © Wolters Kluwer. The centrifuge cover should remain closed until the centrifuge has come to a complete stop to avoid any aerosol production. It is recommended that the timer, brushes (if present), and speed be periodically checked. The brushes, which are graphite bars attached to a retainer spring, create an electrical contact in the motor. The specific manufacturer’s service manual should be consulted for details on how to change brushes and on lubrication requirements. The speed of a centrifuge is easily checked using a tachometer or strobe light. The hole located in the lid of many centrifuges is designed for speed verification using these devices but may also represent an aerosol biohazard if the hole is uncovered. Accreditation agencies require periodic verification of centrifuge speeds. CASE STUDY 1.2, PART 2 Recall Mía, the new graduate. 1. How should Mía place the chemistry tubes in the centrifuge? 2. If the centrifuge starts vibrating, what is the first troubleshooting step Mía should take? 3. If the rubber cap came off the tube during centrifugation, how should Mía decontaminate the centrifuge?  (Eq. 1.11) Laboratory Mathematics and Calculations where x is the negative exponent base 10 expressed and N is the decimal portion of the Significant Figures scientific notation expression. Significant figures are the minimum number of digits needed to express a particular value in For example, if the hydrogen ion concentration of a solution is 5.4 × 10−6, then x = 6 and N = scientific notation without loss of accuracy. There are several rules in regard to identifying 5.4. Substitute this information into Equation 1.11, and it becomes significant figures: 1. All nonzero numbers are significant (1, 2, 3, 4, 5, 6, 7, 8, 9). (Eq. 1.12) 2. All zeros between nonzero numbers are significant. The logarithm of N (5.4) is equal to 0.7324, or 0.73. The pH becomes 3. All zeros to the right of the decimal are not significant when followed by a nonzero number. 4. All zeros to the left of the decimal are not significant. (Eq. 1.13) The same formula can be applied to obtain the hydrogen ion concentration of a solution when The number 814.2 has four significant figures, because in scientific notation, it is written as only the pH is given. Using a pH of 5.27, the equation becomes 8.142 × 102. The number 0.000641 has three significant figures, because the scientific notation −4 expression for this value is 6.41 × 10. The zeros to the right of the decimal preceding the nonzero digits are merely holding decimal places and are not needed to properly express the (Eq. 1.14) number in scientific notation. However, by convention, zeros following a decimal point are In this instance, the x term is always the next largest whole number. For this example, the next considered significant. For example, 10.00 has four significant figures. The zeros to the right of largest whole number is 6. Substituting for x, the equation becomes the decimal indicate the precision of this value. (Eq. 1.15) Logarithms A shortcut is to simply subtract the pH from x (6 − 5.27 = 0.73) and take the antilog of that Logarithms are the inverse of exponential functions and can be related as such: answer 5.73. The final answer is 5.73 × 10−6. Note that rounding, while allowed, can alter the answer. A more algebraically correct approach follows in Equations 1.16 through 1.18. Multiply x = AB or B = logA (x) all the variables by −1: This is then read as B is the log base A of X, where B must be a positive number, A is a positive number, and A cannot be equal to 1. Calculators with a log function do not require conversion to scientific notation. (Eq. 1.16) To determine the original number from a log value, the process is performed in reverse. This process is termed the antilogarithm or antilog as it is the inverse of the logarithm. Most Solve the equation for the unknown quantity by adding a positive 6 to both sides of the equal calculators require using an inverse or secondary/shift function when entering this value. If given sign, and the equation becomes a log of 3.1525, the resulting value is 1.424 × 103 on the base 10 system. Consult the specific manufacturer’s directions of the calculator to become acquainted with the proper use of these functions. (Eq. 1.17) pH (Negative Logarithms) The result is 0.73, which is the antilogarithm value of N, which is 5.37, or 5.4: In certain circumstances, the laboratorian may work with negative logs. Such is the case with pH or pKa. As previously stated, the pH of a solution is defined as the negative log of the hydrogen ion concentration. The following is a convenient formula to determine the negative (Eq. 1.18) logarithm when working with pH or pKa: The hydrogen ion concentration for a solution with a pH of 5.27 is 5.4 × 10−6. Many scientific calculators have an inverse function that allows for more direct calculation of negative logarithms. Concentration A description of each concentration term is provided at the beginning of this chapter. The (Eq. 1.22) following discussion focuses on the basic mathematical expressions needed to prepare reagents of a stated concentration. Lastly, add 100 g of 10% NaOH to a 1000-mL volumetric Class A flask and add sufficient Percent Solution volume of reagent-grade water to the calibration mark. A percent solution is determined in the same manner regardless of whether weight/weight, volume/volume, or weight/volume units are used. Percent implies “parts per 100,” which is represented as percent (%) and is independent of the molecular weight of a substance. Example 1.3: Volume/Volume (v/v) If both chemicals in a solution are in the liquid form, the volume per unit volume is used to give Example 1.1: Weight/Weight (w/w) the volume of solute present in 100 mL of solution. To make up 50 mL of a 2% (v/v) concentrated hydrochloric acid solution, a similar approach is used. The (v/v) is restated as a To make up 250 g of a 5% aqueous solution of hydrochloric acid (using 12 M HCl), multiply the fraction: total amount by the percent expressed as a decimal. The 5% aqueous solution can be expressed as (Eq. 1.19) Then, the calculation becomes Therefore, the calculation becomes 0.02 × 50 mL = 1 mL or using a ratio (Eq. 1.20) Another way of arriving at the answer is to set up a ratio so that (Eq. 1.23) Therefore, add 40 mL of reagent-grade water to a 50-mL Class A volumetric flask, add 1 mL of (Eq. 1.21) concentrated HCl, mix, and dilute up to the calibration mark with reagent-grade water. Remember, always add acid to water! Molarity Example 1.2: Weight/Volume (w/v) Molarity (M) is routinely expressed in units of moles per liter (mol/L) or sometimes millimoles per milliliter (mmol/mL). Remember that 1 mol of a substance is equal to the gram molecular The most frequently used term for a percent solution is weight per volume, which is often weight (gmw) of that substance. When trying to determine the amount of substance needed to expressed as grams per 100 mL of the diluent. To make up 1000 mL of a 10% (w/v) solution of yield a particular concentration, initially decide what final concentration units are needed. For NaOH, use the preceding approach. Restate the w/v as a fraction: molarity, the final units will be moles per liter (mol/L) or millimoles per milliliter (mmol/mL). The second step is to consider the existing units and the relationship they have to the final desired units. Essentially, try to put as many units as possible into like terms and arrange so that the same units cancel each other out, leaving only those needed in the final answer. To accomplish Next, set up a ratio and solve for x this, it is important to remember what units are used to define each concentration term. It is key to understand the relationship between molarity (moles/liter), moles, and gmw. While molarity is given in these examples, the approach for molality is the same except that one molal is expressed as one mole of solute per kilogram of solvent. For water, one kilogram is proportional to one liter, so molarity and molality are equivalent.  In a 250-mL Class A volumetric flask, add 200 mL of reagent-grade water. Add 43.8 g of HCl Example 1.4 and mix. Dilute up to the calibration mark with reagent-grade water. How many grams are needed to make 1 L of a 2 M solution of HCl? Normality Step 1: What units are needed in the final answer? Answer: Grams per liter (g/L). Normality (N) is expressed as the number of equivalent weights per liter (Eq/L) or Step 2: Assess other mass/volume terms used in the problem. In this case, moles are also needed for the calculation: milliequivalents per milliliter (mmol/mL). Equivalent weight is equal to gmw divided by the How many grams are equal to 1 mole? The gmw of HCl, which can be determined from the periodic table, will be equal to 1 mole. For HCl, the gmw is 36.5g/mol, so the equation may be written as valence (V). Normality has often been used in acid–base calculations because an equivalent weight of a substance is also equal to its combining weight (or the weight that will combine with or displace 1 mole of hydrogen). Another advantage in using equivalent weight is that an equivalent weight of one substance is equal to the equivalent weight of any other chemical. (Eq. 1.24) Cancel out like units, and the final units should be grams per liter. In this example, 73 g HCl per Example 1.7 liter is needed to make a 2 M solution of HCl. Give the equivalent weight, in grams, for each substance listed below. 1. NaCl (gmw = 58 g/mol, valence = 1) Example 1.5 A solution of NaOH is contained within a Class A 1-L volumetric flask filled to the calibration mark. The content label reads 24 g of NaOH. Determine the molarity. (Eq. 1.27) Step 1: What units are needed? Answer: Moles per liter (mol/L). 2. H2SO4 (gmw = 98 g/mol, valence = 2) Step 2: The units that exist are grams and L. NaOH may be expressed as moles and grams. The calculated gmw of NaOH is 40 g/mol. Rearrange the equation so that grams can be canceled, and the remaining units reflect those needed in the answer, which are mole/L. (Eq. 1.28) Step 3: The equation becomes Example 1.8 (Eq. 1.25) What is the normality of a 500 mL solution that contains 7 g of H SO ? 2 4 Step 1: What units are needed? Answer: Normality expressed as equivalents per liter (Eq/L). By canceling out like units and performing the appropriate calculations, the final answer of 0.6 Step 2: Start with what is given: 7 g/500 mL M or 0.6 mol/L. Step 3: Calculate the gmw of H2SO4 (98 g/mol) and determine the valence (2) Step 4: Add a conversion factor to convert mL to L (1000 mL/1 L) Example 1.6 Step 5: Cancel out like terms and calculate the result in Eq/L. Prepare 250 mL of a 4.8 M solution of HCl. This equation is: Step 1: Start with what is given: 4.8 moles/L Step 2: Determine the gmw of HCl ([H = 1] + [Cl = 35.5] = 36.5 g/mol) Step 3: Set up the equation, cancel out like units, and perform the appropriate calculations: (Eq. 1.29) (Eq. 1.26) Example 1.9 What is the normality of a 0.5 M solution of H2SO4? Continuing with the previous approach, the final equation is of the density of a material when compared with the density of pure water at a given temperature and allows the laboratorian a means of expressing density in terms of volume. The units for density are