Laboratory Techniques PDF

Chapter 1 1 Laboratory This section will provide a quick overview of the basic laboratory techniques relevant to the OAT. We will also look at some of the most common equipment...

Chapter 1 1 Laboratory This section will provide a quick overview of the basic laboratory techniques relevant to the OAT. We will also look at some of the most common equipment used and discuss some basic safety protocols. Finally, measures of accuracy & precision and key methods of data & error analysis will be reviewed. 1 Laboratory & Techniques Common Equipment Beakers are one of the most common glassware that you will nd in any general chemistry lab. They are useful for heating, mixing, or stirring solutions. They are a wide- mouth vessel with a spout at the top rim that makes it easier to pour liquids. Beakers often come in a wide range of sizes, however, they are not very accurate and therefore, are NOT a good choice for measuring volumes. A graduated cylinder with liquid. Test tubes are glass tubes with one open end and a round, closed end. Test tubes hold small volumes of samples and can also be used for mixing. They are primarily used to compare different samples based on qualitative measures such as color. They can be heated and cooled or used to store a solution over a A beaker half-filled with liquid. period of time. The open end of the test tube can be capped. They should NOT be used to Graduated cylinders, unlike beakers, are one measure volumes. of the go-to types of equipment for measuring the volume of a liquid. However, there are better tools available for situations where you need a high degree of accuracy (pipettes, burets, volumetric asks). Graduated cylinders are narrower and taller than beakers, and have graduated markings that indicate volume levels. Some test tubes filled with varying amounts of liquid. OAT Booster | Booster Prep™ fl fi  Chapter 1 2 Droppers are small glass tubes with a rubber Volumetric asks are round asks with at bulb on one end. Droppers are used to deliver bottoms and long, narrow necks. Volumetric a liquid (usually an indicator), in a drop-wise asks are typically used to obtain a very speci c fashion. They are also known as Pasteur volume of a liquid, which is indicated by a small pipettes. marking on the neck of the ask. A cap is commonly used to seal the top of the ask to prevent evaporation and facilitate vigorous shaking. One of the most common uses of a volumetric ask is for preparing or diluting a chemical solution. A dropper with a rubber bulb at the top used to draw in and dispense liquid. Types of Flasks Erlenmeyer asks are a type of conical ask with a narrow neck and a wider base. Like the beaker, Erlenmeyer asks can be used for mixing, heating, and stirring solutions. They are A volumetric flask has a very typically preferred over beakers for mixing and long and thin neck. swirling solutions as their shape minimizes the risk of spilling and splashing. They are NOT Boiling asks have round bottoms and a long very accurate in measuring volumes. They are neck. They are primarily used to swirl and heat also used during titrations, which will be liquids, but due to the nature of the round discussed later. bottom, a clamp is often required to keep it in position. They cannot and should NOT be used to measure the volumes of liquids. An Erlenmeyer flask has a thinner neck. Boiling flasks are also known as round- bottom flasks. These flasks need corkscrew rings to stand upright. OAT Booster | Booster Prep™ fl fl fl fl fl fl fl fl fl fl fl fi Chapter 1 3 Other Equipment Digital balances are very common in general Bunsen burners are metallic apparatuses that chemistry labs as they are essential for produce an open ame for heating purposes. accurately measuring the mass of a solid They are connected to a natural gas source sample. The “tare” button on a digital balance by rubber tubing and have both a valve that resets the reading to “0”, ensuring that the controls gas ow and a collar that can be current weight of any object on the scale is not rotated to adjust air ow. The amount of gas included in the nal measurement. that is provided to the Bunsen burner is related to the size of the ame. A striker is used to light the Bunsen burner and ignite the ame. A digital balance is used to measure the mass of a sample. Burettes are highly accurate and are used to dispense very precise volumes of a liquid. Burettes are long, graduated glass tubes with a very narrow opening at the bottom. A stopcock is positioned right above this opening and is A Bunsen burner. When turned on, the flame comes from the used to control the amount of liquid that is open end at the top. released by the burette. Burettes are most commonly used in titrations to deliver a titrant A pH meter, as the name suggests, is used to to a solution. To determine the total volume of accurately measure the pH of a solution. The the titrant delivered, rst record the initial pH meter should always be calibrated prior to volume in the burette before the titration, and use to ensure accurate measurements. This can then subtract the nal volume in the burette be used in acid-base titrations or any other after the titration. experiment where it is critical to record the change in pH. The burette is positioned atop the Erlenmeyer flask in a titration experiment. A pH meter. The probe is dipped The yellow plastic piece at the bottom of into the solution to measure pH. the burette is the stopcock. OAT Booster | Booster Prep™ fl fi fl fl fi fl fi fl Chapter 1 4 Reading Volumes OAT Pro-Tip: A titrant is a solution of known One thing you’ll notice when using a graduated concentration that is added to another solution of cylinder or burette is the presence of a unknown concentration in a process called titration. meniscus. The meniscus is the appearance of This allows for the determination of the unknown solution’s concentration. More about acid/base the surface of the liquid as being higher on the titrations will be discussed in future chapters. edges and dipping down at the center (see diagram below). The correct way to read the volume is to read the marking at the lowest Pipettes can be graduated, volumetric, or point of the meniscus while making sure that electronic and are the most precise glassware your eyes are perfectly level with the glassware. for measuring the volume of a liquid. Pipettes come in a wide range of sizes but are ultimately used to transfer a speci c volume of liquid to a container. Example of a meniscus. An accurate measurement is read from the bottom of the meniscus. A volumetric pipette (left) and an electronic Additionally, some burettes utilize the reverse pipette (right) are used to dispense very numbering system whereby the numbers start specific volumes of liquid. from 0 at the top of the burette and go down to the total volume of the burette (for example, 50 in the image below). In order to determine Example 1.11: the volume of the liquid within the burette, Which of the following would most accurately measure 5.0 mL of a liquid? take the total volume of the burette and A) Erlenmeyer Flask subtract the reading (which is the volume that is B) Test tube absent). So, if the burette reads 11 mL, subtract C) Boiling flask this from 50 mL (total burette volume) to get 39 D) Dropper mL as the volume of the titrant. E) Burette Volume = V −V Solution: The burette is the only piece of glassware that accurately measures and dispenses liquid. Erlenmeyer flasks are used for mixing, heating, and swirling solutions while test tubes are used primarily for mixing, comparing, and storing liquids. Boiling flasks are used to heat solutions and droppers are used to dispense liquids in a drop-wise fashion. Therefore, the answer is Option E. Example of a burette with reverse numbering system. OAT Booster | Booster Prep™ 𝗍 𝗈 𝗍 𝖺 𝗅 𝖺 𝖻 𝗌 𝖾 𝗇 𝗍 fi  Chapter 1 5 Example 1.12: Basic Techniques What is the volume contained in this Measuring the mass of a sample is one of the burette? most essential skills you need to be familiar with in a general chemistry lab. You can Solution: To obtain the volume of the measure the mass of any solid sample to a high liquid in the burette, which uses the degree of precision using digital balances. It is reverse numbering system, we important to never place the sample onto the subtract the reading (which is the absent balance directly because it may affect the volume) from the total volume of the accuracy of the scale through damage, burette. Here, we can see that the contamination, or corrosion. When measuring meniscus is at 5.6 mL, while the total the mass of a sample, you should rst tare the volume of the burette is 50 mL. Thus, we weighing paper or glassware that you will be can calculate: placing the sample on before proceeding to add the sample. Balances have a “tare” button Volume = V −V to press after placing the sample holder on it. Volume = 50 mL − 5.6 mL This resets the reading to “0”, allowing you to Volume = 44.4 mL remove the mass of the sample holder. Therefore, the volume of the liquid within the burette is 44.4 mL. OAT Pro-Tip: The term “volumetric” refers to any glassware that has a single marking that indicates a A balance with weighing paper on it specific volume. These are generally more precise containing a solid sample. than graduated glassware. In contrast, “graduated” refers to any glassware that has several markings Centrifugation is a process by which a indicating different volume levels. The order of centrifuge is used to separate different parts of precision from most to least precise is: a mixture. In general chemistry, they are most commonly used to separate a solid pellet from Pipettes > Burettes/Volumetric Flasks > the liquid supernatant, which lies on top. The Graduated Cylinders > Beakers/Erlenmeyer asks centrifuge spins the mixture at very high speeds and the resulting centrifugal force acts *Any glassware not listed here should not be used upon the denser components of the mixture to measure volumes. (the solids) such that they move towards the bottom of the vessel and form the pellet. OAT Booster | Booster Prep™ 𝗍 𝗈 𝗍 𝖺 𝗅 𝖺 𝖻 𝗌 𝖾 𝗇 𝗍 fi fl  Chapter 1 6 After the centrifugation process has nished, we can simply separate the liquid supernatant from the solid pellet by using either a pipette or by decanting the liquid. In some cases, ltration can also be used. Simple decantation involves pouring the liquid out of the original vessel, leaving the solid behind. An example of a titration set-up. Calorimetry is a method used across general chemistry labs to measure the amount of heat An example of a centrifuge. Small plastic vials are inserted into the machine to be spun. energy that is released or absorbed during a chemical reaction. This change in heat can help us determine whether a reaction is exothermic Titration is a method that delivers drop-by- or endothermic. An exothermic reaction drop volumes of a titrant to another solution releases heat while an endothermic reaction through a burette. The purpose of this is to absorbs heat. Most introductory general measure the volume of the titrant needed to chemistry labs use a basic calorimetry setup react completely with the other reagent. The with a Styrofoam cup sealed by a lid, and a point at which the added titrant has completely thermometer to measure the temperature. reacted with the reagent is known as the equivalence point. The endpoint is the point at which an observable property (e.g. color change) occurs and this is associated with either being at or near the equivalence point. Any deviation of the endpoint from the equivalence point is known as titration error. Indicators that are known to change color near an equivalence point of a given reaction are often added to solution to help mark the end of the titration. The pH of a solution can also be observed throughout the titration to identify periods of stabilization known as buffer zones. A diagram of a Styrofoam cup calorimeter. The most basic calorimetry setup involves a Styrofoam cup. OAT Booster | Booster Prep™ fi fi  Chapter 1 7 Laboratory Equipment Purpose Beaker A wide-mouthed vessel used to hold, heat, stir, or mix solutions. Not an accurate measurement of volume. Graduated cylinder A thinner cylindrical tube used to measure a variety of volumes. More accurate than beakers, but not as accurate as volumetric asks or burettes. Erlenmeyer ask A conical ask with a narrowed neck. Used to swirl mixtures and for mixing, heating, and stirring solutions. It is also used in titrations and is not an accurate measurement of volume. Volumetric ask Has a circular base with a long, thin neck. Used commonly to create dilute solutions, and is a more accurate form of measurement. Boiling ask Has a round bottom with a longer neck. Used to swirl and heat solutions, but is not used for measuring volume. It cannot stand up by itself. Pipette The most precise way of measuring volume. These are used to transfer a speci c amount of volume and come in a wide range of sizes. Burette Burettes are long and graduated and are used in titrations. They are used to dispense highly accurate volumes of liquid. Test tube These are small, glass tubes with rounded bottoms. They hold small volumes and are used for mixing or comparing solutions. They are not used to measure volumes. Dropper These are small glass tubes with rubber bulbs at the end. They are used to dispense small amounts of liquid drop-wise. Bunsen burner The burner is connected to a gas source through rubber tubing to create a small ame. The gas ow and air ow can both be controlled. pH meter Accurately measures the pH of a solution. It needs to be calibrated before each use. Digital balance Accurately measures the mass of a solid sample. OAT Booster | Booster Prep™ fi fl fl fl fl fl fl fl fl Chapter 1 8 Safety Protocols 5. Personal Protective Equipment: lab Even though this is not a common topic on the coats, safety goggles, and gloves are OAT, you are expected to know this. Luckily, a worn to protect the body, eyes, and lot of this information is very intuitive and hands, respectively, when working with should not be very dif cult to understand. Let’s potentially harmful chemicals. You look at some basic safety terms and protocols. should also wear closed-toed shoes and avoid wearing contact lenses in the lab, 1. Safety shower: delivers a continuous even with safety goggles, as dangerous stream of water to anyone splashed with fumes can concentrate under the toxic or corrosive chemicals. This can goggles and cause complications. also be used on anyone whose clothing 6. Broken glass container: most labs have may have caught on re. a container for the disposal of any broken glass. Broken glass should be cleaned up as soon as possible, with caution, using a dustpan. 7. Disposal of solutions: acids, alkalis, or other water miscible solutions can be poured down the drain with water. Organic and other water immiscible chemicals should NOT be ushed down Example of a safety shower. The lever on the drain and instead disposed of in the the side activates the safety shower. appropriate waste bin. 8. Don’t eat or drink in the lab: avoid 2. Eye wash station: treats any splashes of eating food where hazardous chemicals chemicals (acid, base, etc.) in or near the are used/stored. eyes. Thoroughly rinse the eyes by 9. Don’t add water directly to keeping both eyes open. concentrated acid: adding water to 3. Fume hood: provides proper ventilation acid can cause the acid to splash out in an enclosed space such that one’s and cause harm to those nearby. exposure to harmful vapors or fumes 10. Don’t pipette by mouth. from any volatile substances is minimized. Any containers containing volatile substances should be covered Example 1.13: with a watch glass when not in use. Which of the following is an unsafe laboratory 4. Fire extinguishers: are used to practice? exterminate solvent or electrical res. A) Working with a partner You should aim the discharge from the B) Wearing protective eye goggles extinguisher at the base of the re that C) Wearing close-toed shoes is the closest to you. You should always D) Washing your hands position yourself in between the re and E) Adding water to concentrated acid the exit. Extinguishers should only be used for solvent or electrical res and Solution: Adding water to concentrated acid can not those resulting from paper or wood. cause the acid to violently boil and splash out of the container. Therefore, the answer is Option E. OAT Booster | Booster Prep™ fi fi fl fi fi fi fi  Chapter 1 9 2 Data & Error Analysis Signi cant digits Signi cant digits are used to describe the Accuracy and Precision uncertainty of a speci c measurement. Let’s When conducting an experiment or analyzing review how to calculate the number of experimental results, it is important to signi cant digits in a value and how to gure understand the concepts of accuracy and out the correct number of signi cant digits for precision. Accuracy refers to how close a a calculation. These are the rules you should measured experimental value, such as the remember: melting point of a compound, is to the actual 1. All non-zero numbers are signi cant (ex. literature value for that compound. Precision 30.20) refers to the consistency of the measured 2. Zeroes that are between two non-zero experimental values such that all values are numbers are also signi cant (ex. 30.20) relatively close to each other. An important 3. Trailing zeros after the decimal point are note is that a value can be precise, but not signi cant (ex. 30.20) necessarily accurate. Similarly, a value can also 4. All other zeroes are NOT signi cant (ex. be accurate but not precise. 500, 0.003) Example 1.22: How many significant digits are in the following value: 403.050? Solution: First, identify the 3 non-zero numbers: In (a), the points are close to the bull’s eye, which 403.050. Next, identify the 2 zeros that are represents high accuracy, but far apart from each other between two non-zero numbers: 403.050. Finally, indicating low precision. In (b), the points are far away from identify the 1 trailing zero in the decimal portion: the bull’s eye, indicating low accuracy, but close together, 403.050. This means that there are 3 + 2 + 1 = 6 indicating high precision. significant numbers in this value. Therefore, 403.050 has 6 significant digits. Example 1.21: A student conducting an experiment regarding the concentration of a solution obtains the Example 1.23: following concentrations: 26.5, 27.0, 26.8, and How many significant digits are in the following 26.7 M. The known concentration of the solution value: 3020? is 30.0 M. In terms of accuracy and precision, how would you describe his results? Solution: First, identify the 2 non-zero digits: 3020. Next, identify the 1 zero that is between Solution: The values obtained by the student are two non-zero numbers: 3020. Since there is no all consistent, yet do not reflect the actual decimal, the trailing zero is not significant. This concentration of the solution. Due to their means that there are 2 + 1 = 3 significant consistency, these values can be described as numbers in this value. Therefore, 3020 has 3 precise. However, since they are not close to the significant digits. actual value, they are inaccurate. Therefore, these results are precise but not accurate. OAT Booster | Booster Prep™ fi fi fi fi fi fi fi fi fi fi  Chapter 1 10 Now, let’s look at some rules regarding In contrast, random errors are errors that are calculations using signi cant digits. When skewed in either direction - both above and multiplying or dividing, we simply express the below the true value, and to a different extent nal answer to the lowest degree of signi cant each time. These are often the result of human numbers based on the numbers that are being error such as discrepancies in reading the multiplied or divided. So, for example, let’s say meniscus on a piece of glassware. If our eyes we wanted to divide 550 by 10.0. We count the are not level to the plane of the meniscus, we number of signi cant digits in each number. may read the volume of the liquid as being The number 550 has two signi cant digits while higher or lower than what it is. the number 10.0 has three. Since the lowest number of signi cant digits is 2, we would We can nd the percent error of an express our answer with two signi cant digits experimentally derived value and a known to get an answer of 55. literature value using the following equation: Addition and subtraction have slightly | experimental − actual | % error = x 100% different rules. We write out the answer to actual these calculations with signi cance based on the digit of least accuracy. Let’s say we wanted to add 34 + 240 + 456.4. The rst number is Example 1.24: accurate to the ones place, the second number Which of the following option choices would is accurate to the tens place, and the last cause a random error? number is accurate to the tenths place. We see A) Using the wrong chemical solution that 240 is only accurate to the tens place while B) Electron balance tarred incorrectly the other numbers have more accurate digits, C) Using a stopwatch to measure the rate of reaction so we would need to round our nal answer to D) Incorrectly calibrated pH meter the tens place. The nal answer would E) Dropping laboratory glassware therefore be 730 with two signi cant digits. Solution: Having an electron balance tarred incorrectly or a pH meter calibrated incorrectly are Systematic, Random, and Percent Error examples of systematic errors. On the other hand, The two main types of error you will encounter using the wrong chemical solution or dropping in a laboratory setting are systematic and laboratory glassware are just errors. Using a stop- random error. Systematic errors are errors that watch to measure the rate of reaction can cause are consistently skewed in one direction - either random error because your ability to start and above or below the true value, and to the same stop the watch may vary. Therefore, the correct extent each time. They are often the result of answer is Option C. faulty equipment or an error in the procedure. An example of this would be forgetting to tare the electronic balance before taking the measurements. The mass of the weighing paper would be consistently added to the mass of the sample across all measurements. OAT Booster | Booster Prep™ fi fi fi fi fi fi fi fi fi fi fi fi fi Chapter 2 1 Periodic Properties This chapter will cover the periodic properties that are relevant to the OAT. Although the elements in the periodic table are arranged in order of increasing atomic number, there are several important trends in atomic radius, ionization energy, effective nuclear charge, electron affinity, and electronegativity. 1 Introduction to the Periodic Table Groups 13-17 elements: includes metalloids, which have a combination of Two important terms to know when looking at a both metallic and non-metallic periodic table are groups and periods. A characteristics as highlighted in orange group consists of elements in the same column. on the periodic table These elements have the same number of Group 17 elements: halogens valence electrons, which are the electrons in Group 18 elements: noble gases the outermost subshell. A period consists of elements that occupy the same row and these The oxidation state of an element is related to elements have the same number of electron the number of electrons that an atom loses, shells. The atomic number of an element is gains, or appears to use when bonding with equal to the number of protons in the atom. another atom. Almost all transition metals have For example, nitrogen has an atomic number of multiple oxidation states. They have this 7 because it has 7 protons. property because they have several electrons with similar energies, meaning that one or all of them can be removed, depending on the circumstances. Manganese, for example, shows oxidation states from +2 to +7. Although most transition metals have color, row 4 transition metals are an exception as they are colorless. The two rows (which belong in periods 6 and 7) at the bottom of the periodic table are known as the inner transition metals. Period 6 inner transition metals are the lanthanides and The periodic table. Notice the highlighted groups. Period 7 inner transition metals are the actinides. Inner transition metals are far less On the OAT, it is important to know the names abundant on earth compared to transition of the different groups on the periodic table: metals and these elements are separated from Group 1 elements (excluding the transition metals as their properties differ. hydrogen): alkali metals Transition metal atoms have their valence Group 2 elements: alkaline earth metals electrons in the outermost d-orbital, whereas Groups 3-12 elements: transition inner transition metal atoms have their valence metals electrons in the f-orbital. OAT Booster | Booster Prep™ Chapter 2 2 The most prominent oxidation state for transition metals is +2, whereas the most prominent oxidation state for inner transition metals is +3. It is also good to know your diatomic atoms for the OAT. Diatomic atoms are atoms that are usually found paired due to their unstable nature. For example, carbon is a monatomic atom, which means its atoms are not usually paired. On the other hand, oxygen gas, when found in nature, is a molecule In nature, carbon is monatomic, which means it is found consisting of two oxygen atoms and therefore unpaired. Oxygen, on the other hand, is a diatomic is a diatomic atom. The diatomic atoms you atom that is paired. need to know are: Hydrogen, Nitrogen, Fluorine, Oxygen, Iodine, Chlorine, and It is also important to know that metallic Bromine. character on the periodic table increases going from right to left across a period and increases going down a group. OAT Pro-Tip: A mnemonic device to remember the diatomic atoms is: Have No Fear Of Ice Cold Beer Metals Non-Metals Malleable, lustrous Brittle, dull Good conductors of electricity/heat Poor conductors of electricity/heat Form basic oxides Form acidic oxides Lose electrons to form cations Gain electrons to form anions Usually solid at room temperature, with the Gas or solid at room temperature, with the exception of mercury (Hg), which is liquid exception of bromine (Br), which is liquid Generally, high melting and boiling points Generally, low melting and boiling points Important: Know the key differences in properties of metals and non-metals for the OAT listed in the table above! OAT Booster | Booster Prep™  Chapter 2 3 2 Periodic Trends Atomic Radius De nition: Half the distance between the nuclei of two identical atoms bonded together. Atomic radius is half the distance between the nuclei of two identical atoms bonded together. Trend: Atomic radius increases from right to left across a period and increases going down a group. Effective Nuclear Charge Increases right to left across a period: Moving De nition: The effective nuclear charge (Zeff) is from right to left across a period, the number the amount of positive charge experienced by of protons in an atom decreases. The an electron. The shielding effect of lower decreasing number of protons results in a orbital electrons prevents higher orbital weaker nuclear attraction between the protons electrons from experiencing a strong attraction and electrons, which results in electron shells to the nucleus. This effect explains why valence being further apart from the nucleus, therefore electrons are more easily removed. The increasing the radius. effective nuclear charge is calculated given the following equation: Increases going down a group: Moving down a group, the number of electron shells Zeff = Z − S increases. Each additional electron level gets where Z = number of protons further and further away from the nucleus, S = number of shielding which causes the atomic radius to increase. (non-valence) electrons Trend: Effective nuclear charges increases left to right across a period and increases going up a group. Increases left to right across a period: Moving from left to right across a period, the numbers of protons increase with no increase in electron shells, and thus no increase in shielding effect. This results in electrons being pulled closer to the nucleus due to a stronger attraction. Increases going up a group: Moving up a Atomic radius increases from right to left group, the number of electron shells decreases across a period and going down a group. which brings outer shell electrons closer to the positively charged nucleus. This increases effective nuclear charge. OAT Booster | Booster Prep™ fi fi  Chapter 2 4 Anions have a larger radius: When a neutral atom gains electrons and becomes an anion, the increased electron number results in increased electron-electron repulsions. This expands the size of the electron cloud, resulting in a larger radius. Cations have a smaller radius: When a neutral In the shielding effect, because of other electrons between atom loses electrons and becomes a cation, the the electron of interest and the nucleus, the electron of decreased electron number results in interest experiences less attraction to the nucleus. decreased electron-electron repulsions. This reduces the size of the electron cloud, resulting in a smaller radius. Example 2.21: What is the effective nuclear charge for a valence Note: Metals typically form cations, resulting in electron of Gallium? ionic radii smaller than their atomic radii. Solution: The first step in determining effective Meanwhile, non-metals typically form anions, nuclear charge is to find the number of shielding resulting in ionic radii greater than their atomic electrons (non-valence electrons). Looking at the radii. periodic table, we can determine that Gallium (group 13) has 3 valence electrons. Ga has 31 protons so its non-valence electrons would be Example 2.22: 31 – 3 = 28. Use the equation: Which of the following ions has the smallest Zeff = Z – S radius? Zeff = 31 – 28 = +3 A) Na+ Note: Notice that the effective nuclear is equal to B) F- the number of valence electrons. This is often the C) O2- case, but not always. D) N3- E) Al3+ Isoelectronic Series Solution: In this case, all the elements provided are isoelectronic, which means that they all have De nition: These are atoms that have an the same number of electrons. We can eliminate identical number of electrons, but different the anions as a potential answer because anions numbers of protons. Anions are ions that have have a larger radius than cations. Since Al3+ has gained electrons and have more electrons than the most protons, the electrons will experience a protons, making them negatively charged. greater pull resulting in a smaller radius. Cations are ions that have lost electrons and Therefore, Al3+ has the smallest radius. have more protons than electrons, making them positively charged. OAT Booster | Booster Prep™ fi  Chapter 2 5 Ionization Energy De nition: The energy needed to remove an electron from an atom. Trend: Ionization energy increases going from left to right across a period and increases up a group. Increases left to right across a period: Across Ionization energy increases from left to right a period, the atomic number, or the number of across a period and going up a group. protons, increases. As the valence shell continues to ll, the electrons become harder Example 2.23: to remove (require more energy) due to an Which of the following elements has the highest increase in effective nuclear charge. Argon, for ionization energy? example, has a high ionization energy because it is a noble gas and has a completely lled A) Sodium valence shell. Due to this high stability, it would B) Fluorine take a lot of energy to remove an electron. C) Chlorine D) Carbon Increases going up a group: Moving up a E) Argon group, there are fewer electron shells and subsequently less of a shielding effect from the Solution: Argon has the highest ionization energy because it is a noble gas. It is nearly impossible to inner electrons. This creates dif culty in extract an electron from argon’s valence shell removing the electrons from valence shells. because it is completely filled and therefore VERY Furthermore, the distance decreases between stable. Noble gases are chemically inert because the nucleus and the highest-energy electron, their high degree of stability makes it unlikely for strengthening the nuclear attraction to that them to lose or gain electrons. Therefore, the electron, and therefore requiring more energy. correct answer is Option E. Multiple ionization energies: The rst ionization energy is the energy required to remove the outermost electron. Following the removal of the rst electron, elements can have second, third, fourth, etc. ionization energies. The energy associated with removing each successive electron from an atom or ion increases. For example, the rst ionization energy of sodium is 496 kJ mol-1. However, following that, there is a huge jump to 4562 kJ mol-1 for the second ionization energy because we would be removing an electron Notice the exceptions in the ionization energy from a stable con guration (a full outer shell). trends across different elements. OAT Booster | Booster Prep™ fi fi fi fi fi fi fi fi  Chapter 2 6 There are two notable exceptions to the Electron Af nity above rules for ionization energy: De nition: The amount of energy released 1. The rst is that alkaline earth metals when an electron is added to an atom. have lled orbitals, which gives them greater stability, leading to their higher Trend: Electron af nity increases going from ionization energy compared to Group left to right across a period and increases going 13 elements in the same period. This is up a group. why Be has higher ionization energy compared to B. Increases left to right across a period: Across a period, as the atom’s valence shell gets lled, 2. The second exception is that group 15 there is increased attraction between the elements have half- lled orbitals, which nucleus and the electrons of the atom. This gives it greater stability, leading to its creates a stronger af nity for electrons. higher ionization energy compared to Group 16 elements in the same period. Increases going up a group: Moving up a This is why N has a higher ionization group, there are fewer electron shells, leading energy compared to O. to decreased electron shielding and an increased proximity between the nucleus and valence electrons, increasing the nuclear Example 2.24: attraction and thereby increasing electron Which of the following elements has the highest af nity. second ionization energy? A) Beryllium There are three notable exceptions to the B) Calcium rules for electron af nity: C) Strontium D) Lithium 1. The rst is that group 2 elements have E) Potassium lled s-orbitals, so their electron af nities are very low Solution: The second ionization energy is the energy required to remove a second electron 2. The second exception is that group 15 from the valence shell. Beryllium, calcium, and elements have half- lled orbitals p- strontium are all group 2, so removing their orbitals, so their electron af nities are second electron would result in a full electron lower than group 14 elements of the shell and would not require as much energy. same period Lithium and potassium are in group 1, so removing their second electron would disturb the full electron shell and result in a higher second 3. The third exception is that noble gases ionization energy. Recalling the fact that ionization have lled electron shells, so their energy increases moving up a group, lithium has electron af nities are negligible the highest second ionization energy. Therefore, the correct answer is Option D. OAT Booster | Booster Prep™ fi fi fi fi fi fi fi fi fi fi fi fi fi fi fi fi fi  Chapter 2 7 Electronegativity De nition: The measurement of an atom’s ability to attract electrons in a bond. The higher the electronegativity of an atom, the greater ability to attract an electron pair. Trend: Electronegativity increases going from left to right across a period and increases up a Electron affinity increases from left to right group. The most electronegative element is across a period and going up a group. uorine, and if you remember this, the trend becomes very easy to remember. Example 2.25: Increases left to right across a period: With Which of the following elements has the greatest increasing protons as you go from left to right electron affinity (EA)? across a period, the ability of an atom to attract A) Beryllium an electron pair is increased. This is similar to B) Lithium the electron af nity trend; however, this trend is C) Nitrogen speci c to electron pairs in a bond, not the D) Carbon addition of a single electron. E) Neon Increases going up a group: Moving up a Solution: Following the trend of EA, lithium and group, as the atomic radius decreases, and the beryllium (far left of the periodic table) will have valence electrons experience less shielding, the the lowest EA. Neon, a noble gas, has a ability of an atom to attract an electron pair is negligible EA due to its complete valence shell. It increased. may appear that nitrogen will have the largest EA, however carbon has an electron configuration 1 Note: The noble gases are an exception to this electron away from a half-filled subshell therefore trend as they have full valence shells and carbon has the highest electron affinity. Therefore, therefore no electronegativity value. the correct answer is Option D. Electronegativity increases from left to right across a period and going up a group. Electron affinities in kJ/mol for certain elements. OAT Booster | Booster Prep™ fl fi fi fi Chapter 2 8 Example 2.26: Rank the following elements in order of increasing electronegativity: Cl, P, Sr, Al, F Solution: Looking at the periodic table, Sr would have the least amount of electronegativity as it is in group 2. Since Al, P, and Cl are all in period 3, and electronegativity increases from left to right across a period, Al, P, and Cl, respectively, will have progressively greater electronegativity levels. Right away, we also know that fluorine is the most electronegative atom therefore the answer is Sr < Al < P < Cl < F. In a water molecule, oxygen is more electronegative, thus electron density is more concentrated towards oxygen. 3 Summary of Periodic Trends A summary of important periodic trends to know are shown. OAT Booster | Booster Prep™ Chapter 3 1 Atomic and Molecular Structure This section will discuss the topic of atoms and molecules. Different fundamental concepts described by the atomic and quantum theories will be highlighted and Lewis dot structures will be introduced. This section will also discuss how to write quantum numbers and electron configurations, and how to predict the three- dimensional molecular geometry of different molecules. Different types of bonds, along with orbital interactions, will also be reviewed. Protons carry a charge of “+1e” where 1 Introduction to Atoms and e = 1.6 x 10-19 C. Protons also have a mass of 1 Subatomic Particles atomic mass unit (amu). The atomic number of Dalton’s atomic theory describes the atom as an atom is the number of protons found in that the fundamental unit of matter. There are four atom. Elements on the periodic table are listed main points regarding atoms: sequentially based on their atomic number. 1. All matter is composed of atoms. Atoms Boron, for example, has an atomic number of 5. are typically indivisible The atomic number can be used to identity an 2. Atoms of a speci c element are identical element because this number remains constant in mass and properties across all types of an element. For example, all 3. Compounds are formed by whole atoms of boron will have an atomic number of number ratios of two or more different 5, indicating that they all have exactly 5 atoms protons. 4. A chemical reaction is a rearrangement of atoms Subatomic Particles The inner core of an atom is known as the The element “boron.” The number nucleus. It consists of protons and neutrons. “5” represents the atomic number of Protons are positively charged subatomic this element. particles while neutrons carry no charge. Neutrons ensure the atom’s stability because Neutrons are neutral in charge and also have a without them, the protons would repel each mass of 1 amu. The mass number of an atom is other and make the nucleus unstable. Electrons equal to sum of the number of protons and are negatively charged subatomic particles neutrons of an atom. found in various energy levels around the nucleus. Electrons carry a charge of “-1e.” Electrons have a mass that is signi cantly less than that of A model of an a proton (1/1836 amu) and can be considered atom depicting negligible. That is why, when considering the subatomic mass of an atom, only the masses of the particles. protons and neutrons are accounted for. OAT Booster | Booster Prep™ fi fi  Chapter 3 2 A neutral atom has the same number of Atomic Notation protons and electrons. Since the charge of The atomic notation represents an element by protons and electrons are equal in magnitude describing its mass and atomic numbers. It can but opposite in sign, any molecule with an be used to distinguish between different types equal number of protons and electrons is of atoms. The image below depicts the atomic neutral. notation of a general atom, where “X” represents the chemical symbol of the atom, Electrons can be also categorized as core or “A” represents the mass number, and “Z” valence electrons. Core electrons are closest to represents the atomic number. the positively charged nucleus. They tend to be A X the most stable and are lowest in energy. In contrast, valence electrons are the electrons that are furthest from the nucleus. These electrons are found in the highest energy level Z and have higher energy than core electrons. Since they are the furthest away from the For example, carbon-12 is represented in the nucleus, they do not feel the attractive forces of following manner. The “X” symbol will be C, the nucleus as strongly and are loosely held. which is the chemical symbol for carbon in the This is why valence electrons are more reactive periodic table. The “A” will be 12, which is the and are involved in bond formation. These mass number of carbon. The “Z” will be 6, bonds are formed so that atoms can achieve a which is the atomic number, or the number of full valence shell, which makes an atom protons in carbon. “satis ed” and more stable. 12 The maximum number of electrons in each energy level is 2n2, where “n” is the energy 6 C level. So, the rst energy level will have 2 electrons, the second can carry up to 8, etc… Changing Subatomic Particles Evidently, subatomic particles constitute an atom. So what happens when the number of each subatomic particle is changed? Changing the number of protons in an atom results in a different element. For example, all carbon atoms will have 6 protons, which is evident from their atomic number. If a carbon atom were to gain an additional proton, it would no longer be a carbon atom. Instead, it would be a nitrogen atom with an atomic number of 7. The electrons in the red rings are valence electrons. OAT Booster | Booster Prep™ fi fi Chapter 3 3 Changing the number of neutrons of an atom, Lastly, changing the number of electrons in an on the other hand, does not change the atom produces ions. When an atom loses an identity of the element. Instead, it produces a electron, it now has more protons than new type of atom of the same element known electrons, producing a positively charged as an isotope. Isotopes are atoms of the same cation. On the other hand, when an atom gains element that have the same number of protons an electron, it now has more electrons than but different number of neutrons. So, although protons, producing a negatively charged anion. all carbon atoms have 6 protons, they can have varying numbers of neutrons. A carbon atom that has 6 neutrons and 6 protons will have a Example 3.11: mass number of 12. Meanwhile, a carbon atom How many electrons and protons are in Mg2+, with 7 neutrons and 6 protons will have a mass respectively? number of 13. The former is known as carbon-12 and the latter is carbon-13. Writing Solution: To solve this, let’s first obtain the atomic the mass number after the element’s name number of magnesium from the periodic table, helps distinguish between the different which is 12. A neutral magnesium atom has to isotopes of the same element. lose two electrons to become a Mg2+ cation. Thus, we take 12 electrons - 2 electrons = 10 electrons. We can change the number of electrons but we Many isotopes exist in nature with varying cannot change the number of protons because if levels of stability. They are also found in we changed the number of protons, we would no different abundances in nature. In other words, longer have magnesium. Therefore, Mg2+ has 10 some isotopes are readily found while others electrons and 12 protons. are more rare. The atomic mass, also known as the atomic Example 3.12: weight, of an element is calculated by taking How many valence electrons does O2- have? the weighted average of the element’s naturally occurring isotopes, taking into account their Solution: First, we find the number of electrons in respective abundances. For example, carbon’s an oxygen atom. Oxygen has an atomic number atomic mass is 12.011 amu. This is because of 8, so a neutral oxygen atom has 8 electrons. carbon-12 is much more abundant in nature Meanwhile, O2- has an additional two electrons for than carbon-13 or carbon-14. This means that a total of 10 electrons. The first energy level can the mass of carbon-12 contributes more hold 2n2 = 2(1)2 = 2 electrons, while the remaining towards the atomic mass of carbon. The 8 electrons will go in the second energy level. The presence of different isotopes of the same second energy level is the furthest away from the element explains why the periodic table reports nucleus and is the valence shell. Therefore, there the atomic mass, NOT the mass number of an are 8 valence electrons in O2-. element. The element “carbon.” The number “12.0” represents the atomic mass of this element. OAT Booster | Booster Prep™  Chapter 3 4 2 Types of Reactions However, when a piece of paper is burnt, it becomes ash. In other words, it becomes Elements vs Compounds something else! These two scenarios exemplify An element is a pure substance composed of the difference between a physical and chemical one type of atom. Elements cannot be broken change. The crumbling of paper represents a down into other substances through physical or physical change while the burning of paper into chemical reactions. The periodic table lists the ash represents a chemical change. various elements based on their number of protons. For example, iron is an element and is depicted on the periodic table as “Fe”. In a physical reaction, the molecules undergo rearrangement to produce a physical change. Each element has unique properties. For Speci cally, a physical reaction changes the example, the elements hydrogen and oxygen physical properties of a matter or substance. A will both have unique melting and boiling physical property, for example, is the density of points. a substance. A physical reaction may cause a substance to become more or less dense. Compounds, on the other hand, are formed Similarly, the phases of matter are also a when two or more atoms from different physical property. A physical reaction may elements combine. cause a substance to change its phase from solid to liquid. It is important to note that in a The law of constant composition tells us that physical reaction, no new substances are elements within a compound always combine in created and no new chemical bonds are formed a xed proportion. For example, the compound or destroyed. “water” will always have 2 hydrogens bound to 1 oxygen to form H2O. If the proportion of hydrogen to oxygen changes from being 2 hydrogens : 1 oxygen to 2 hydrogens : 2 oxygens, the resulting compound is not water. Rather, it is hydrogen peroxide (H2O2) - an entirely new compound! Changing the phase or density of a substance does not When elements undergo a chemical change the individual molecules that make-up the combination, they give rise to new substances substance. with distinct characteristics from those of the constituent elements. For example, although Chemical reactions, on the other hand, involve hydrogen and oxygen are both gasses, they the substances undergoing a chemical change combine to create liquid water. whereby a new substance is created. Unlike a physical reaction, in a chemical reaction, Reactions intramolecular bonds between atoms are A substance can undergo physical and chemical created or destroyed. For example, oxygen and changes. A piece of paper for example, can hydrogen atoms create bonds with each other either be crumpled up or burnt. When the to form water. paper is just crumpled up, its appearance changes but it is still a piece of paper. OAT Booster | Booster Prep™ fi fi  Chapter 3 5 Types of Chemical Reactions 5. Combustion Reaction: when a There are ve chemical reaction types you substance reacts with O2 gas to produce should be aware of. These are the synthesis, light and heat. These types of reactions decomposition, single displacement, double must involve oxygen as a reactant. displacement, and combustion reactions. Try to There are two types of combustion keep in mind that breaking bonds require reactions you should be aware of: energy and forming bonds release energy. combustion of hydrogen and the combustion of hydrocarbons. In the case 1. Synthesis Reaction occur when two or of a complete combustion of more atoms or molecules combine to form hydrocarbon, water and carbon dioxide a single compound. This reaction usually are always the products, regardless of involves the release of energy. which type of hydrocarbon was the reactant. 2. Decomposition Reaction occur when a compound breaks down into two or more products. This reaction usually requires the input of energy. 3. Single Displacement Reaction occur when one element is replaced by another in a compound. Example 3.21: Which of the following is an example of a compound? 4. Double Displacement Reaction, also called A) H2 exchange reactions, involve the exchange B) Cl2 of bonds between two reacting chemical C) Br2 species. Some common types of double D) Tn displacement reactions are neutralization E) CO2 and precipitation reactions. Solution: Compounds are substances formed when two or more different types of atoms combine. Options choices A, B, and C are not compounds because they are diatomic molecules composed of the same element (covered in chapter 2). Tn is simply an element. CO2, however, is a compound because it has two different elements: carbon and oxygen. Therefore, the answer is Option E. OAT Booster | Booster Prep™ fi  Chapter 3 6 Example 3.22: 3 Quantum Theory Which of the following represents a chemical change? Bohr’s Model and the Modern Atomic Theory A) Melting ice It was originally believed that electrons follow a B) Combining sodium with chloride to get table xed circular path around the nucleus. The salt centripetal force from the attraction of a C) Adding food coloring into water negatively charged electron to the positively D) Ripping a piece of paper charged protons of the atom was thought to E) Evaporating water cause this effect. This, however, is the out- dated Bohr’s model of the atom. Solution: Ice melting and water evaporating are both phase changes, and so they represent a physical, not chemical, change. Adding food In Bohr’s model of coloring into water involves diluting the food the atom, coloring. The food coloring does not break and electrons follow a fixed circular path. form any new chemical bonds with the water molecules. Similarly, ripping a piece of paper does not involve the destruction or creation of The modern quantum theory has replaced the chemical bonds. In both these examples, the outdated Bohr’s model for describing the original substances’ appearances merely change, electronic structure of an atom. We now realize and so, they represent physical changes. that instead of orbiting around the nucleus in a However, combining sodium with chloride to get de ned circular pathway, electrons are actually table salt involves the formation of chemical localized in a “cloud of electrons”. These bonds between sodium and chloride. Additionally, the product is different than both the clouds, or speci c regions of space around the reactants, which indicates that it is a chemical nucleus, are known as an orbitals. The change. Therefore, the answer is Option B. Heisenberg uncertainty principle describes that it is impossible to perfectly nd both the momentum and the location of an electron in Example 3.23: an atom. We can only gure out one or the HCl reacts with NaOH to produce NaCl and H2O. other. As such, orbitals describe the most likely What type of chemical reaction does this location of an electron around an atom. exemplify? Solution: This reaction can be written as follows: HCl + NaOH → NaCl + H2O Writing out the formula illustrates how the elements are exchanged amongst the reactants as follows: HCl + NaOH → NaCl + H2O Since the hydrogen in HCl is now bonded to the hydroxide from NaOH, and the sodium from The modern atomic theory depicts NaOH is now bonded to the chlorine from HCl, “electron clouds” as the most probable the elements have exchanged their bonding location of an electron in an atom. partners. Therefore, this is a double displacement reaction. OAT Booster | Booster Prep™ fi fi fi fi fi Chapter 3 7 Quantum Numbers 2. Azimuthal Quantum Number (l) Since electrons can seemingly exist anywhere, Describes the shape of the subshells quantum numbers were created to describe the or the orbital shape within each probable location and energy of an atom’s principal energy level electrons. Quantum numbers are unique to The possible values of the azimuthal each electron of an atom. In other words, no quantum number are all integers two electrons in the same atom will have between zero and n–1. For example, exactly the same quantum numbers. a principal quantum number of 3 would have potential azimuthal Modern atomic theory uses four quantum quantum numbers of 0, 1, and 2. numbers that help describe the electrons of an The subshells of the azimuthal atom. These are the: quantum number carry a letter 1. Principal Quantum Number (n) designation such that subshell l = 0 Represents the main energy level is “s,” subshell l = 1 is “p,” subshell l occupied by electrons. = 2 is “d” and subshell l = 3 is “f.” Is a positive integer, greater than or These subshells can hold 2, 6, 10, equal to 1. and 14 electrons, respectively. At n = 1, an electron is closest to the The s-orbital is spherical, the p- nucleus, and with each successive orbitals are shaped like dumbbells, electron shell, electrons get farther and 4 out of the 5 d-orbitals are and farther away from the nucleus. clover shaped. The last shape of the The maximum number of electrons d-orbital and the shapes of the f- that an electron shell can hold is orbitals can be seen in the images given by the formula: 2n2. below. A shortcut to deduce the energy To tie this together, an electron with level of a ground state atom’s values: n = 3 and l = 0, would be in valence electrons is by referring to the 3s subshell. the row it belongs to on the periodic On the other hand, an electron with table. Each row corresponds to a values: n = 4 and l = 2, would be in new energy level. So, the rst row is the 4d subshell. n = 1, the second row is n = 2, etc… An element such as Rubidium (Rb) is in the 5th row of the periodic table. This means that its valence electrons are in the 5th energy level (n = 5). s-subshell OAT Booster | Booster Prep™ fi Chapter 3 8 The magnetic quantum number ranges between the negative and positive magnitude of the azimuthal quantum number. For example, since a p-subshell is l = 1, it would have ml values of -1, 0, and 1. p-subshell 4. Spin Quantum Number (ms) Describes the angular momentum of an electron. This is denoted as either +1/2 or -1/2, representing an upward or downward spin. The assignment of a positive or negative value to the spin is arbitrary. Electrons in the same orbital must have opposite spins. d-subshell Electrons can have an upwards or downwards spin. So, if the electron of an atom has the following f-subshell quantum numbers: 2,1,0,+1/2, it would denote the fact that it is found in the second energy level (n = 2), and in one of the p-orbitals (l = 1). 3. Magnetic Quantum Number (ml) The third quantum number (ml = 0) informs us Describes the orientation of that this electron is in the py-orbital. The +1/2 orbitals in space. represents the angular momentum of the The p-subshell for example, splits electron which could be either an upward or into three unique orbitals. One downward spin. along the z-plane (pz), one along the x-plane (px), and one along the y- plane (py).