Measurement (2024) PDF

MEASUREMENT INTENDED LEARNING OUTCOMES The students should be able to:  Use dimensional analysis in conversion of units  Solve problems related to temperature, mass, volume and density MEASUREMENT  Measurement is a collection of quantitative or numerical data that describes a prope...

MEASUREMENT INTENDED LEARNING OUTCOMES The students should be able to:  Use dimensional analysis in conversion of units  Solve problems related to temperature, mass, volume and density MEASUREMENT  Measurement is a collection of quantitative or numerical data that describes a property of an object or event.  It is made by comparing a quantity with a standard unit.  Measurements inherently include error, which is how much a measured value deviates from the true value. NUMBERS AND MEASUREMENTS IN CHEMISTRY  quantify data, expressing collected data with units and significant figures. Units - designate the type of quantity measured. Prefixes - provide scale to a base unit. Significant Figures - indicate the amount of information that is reliable when discussing a measurement. UNITS  Thebase unit designates the type of quantity being measured.  SIunits (from French Système International) are the base units of science.  Some units comprise combinations of these base units and are termed derived units  1 J = 1 kg m2 s-2 PREFIXES  Prefixes are used with base units to report and understand quantities of any size.  Prefixes are based on multiples of 10. SIGNIFICANT FIGURES  All digits reported are considered significant except for certain types of zeros.  When a zero establishes the decimal place, it is not significant.  51,300 m (3 significant figures)  0.043 g (2 significant figures) A zero is significant when it follows a decimal point or when it occurs between other significant figures.  4.30 mL (3 significant figures)  304.2 kg (4 significant figures)  All numbers are significant when written in correct scientific notation. SIGNIFICANT FIGURES  For calculated values, the number of significant figures should be consistent with the data used in the calculation.  For multiplication and division, the number of significant figures in a result must be the same as the number of significant figures in the factor with the fewest significant figures.  For addition and subtraction, the number of significant figures are determined from the position of the first uncertain digit. SIGNIFICANT FIGURES 0.24 kg 4621 m = 1100 kg m or 1.1 10 3 kg m 4.882 m + 0.3 m 5.2 m SIGNIFICANT FIGURES  When counting discrete objects, the result has no ambiguity. Such measurements use exact numbers. They have infinite significant figures.  two pennies would be 2.000000…  Exactly defined terms, such as metric prefixes, are also considered exact numbers. SCIENTIFIC NOTATION Scientific notation is used to easily write very small and very large numbers. Factor out powers of ten 4 54,000 = 5.4 10 5 0.000042 = 4.2 10 PROBLEM SOLVING IN CHEMISTRY AND ENGINEERING  There are several categories of problems: Calculations involving ratios Conceptual understanding of particulate level Visualization of phenomena on different levels DIMENSIONAL ANALYSIS also known as factor label method  uses a Conversion Factor- a fraction whose numerator and denominator are the same quantity expressed in different units Given quantity x conversion factor = desired quantity given unit x desired unit = desired unit given unit EXAMPLE PROBLEMS Convert the following: 1. 57.8 m to cm 57.8 m x 100 cm = 5,780 cm 1. 1m 2. 0.250 kg to g 0.250 kg x 1000 g = 250 g 1 kg 3. 500 mL to L 500 mL x 1L_____ = 0.5 L 1000 mL 4. 2.5 ft to cm 2.5 ft x 12 in x 2.54 cm = 76.2 cm 1 ft 1 in 5. 350.0 lb to g_ in3 cm3 350. lb x 453.59g x (1 in)3____ = in3 1 lb (2.54 cm)3 LENGTH  a measured dimension which can be expressed in meter or feet (English unit). One can call length as the first dimension or 1D.  Example 1: Convert 2 miles to kilometer. Solution: 2mi x 1.609km = 3.218km 1 mi  Example 2: How many cm are there 2.5 mi? Solution: 2.5mi (1.609km)(1000m)(100cm)=402,250 cm 1mi 1km 1m AREA  Area is a physical quantity that expresses the extent of two- dimensional figures.  The units of area are derived from units of length.  As a two-dimensional quantity it accounts the product of two lengths.  What is the area of a rectangular field with a length of 5 meters and width of 12 meters? Solution: Area of a rectangle= length⋅width Area of a rectangle = (5m)(12m)=60m2 PHYSICAL PROPERTIES COMMOLY MEASURED IN CHEMISTRY  MASS  VOLUME  TEMPERATURE  DENSITY VOLUME  Volume is length (m) cubed  Units for volume solid samples m3 1cm3 = 1 x 10-6 m3 1dm3 = 1 x 10-3 m3 REGULAR SOLID  WATER DISPLACEMENT METHOD  Normally used to get the volume of an irregular solid  Volume is a measure of the amount of space an object takes up. When a cylinder is submerged in the water it pushes water out of the way. If you measure the amount the water level increases, you can find the volume of the water pushed out of the way. CALCULATION OF VOLUME OF IRREGULAR SOLID VOLUME Liquid samples 1L = 1000 mL = 1000 cm3 = 1 dm3 1cc = 1cm3 = 1mL Gas samples L or mL MASS  Mass is the measure of quantity of matter contained in an object  Mass of an object can be measured readily with a balance, is the process called weighing  Mass is different from weight Weight is the force that gravity exerts on an object MASS  SIunits: g, kg  English units: lb, oz 1 kg = 1000 g 1 tonne = 1000 kg 1 lb = 453.59 g 1 lb = 16 oz A piece of iron metal has a mass of 2435.5 g. Express the mass in the following units: a. kg 2435.5 g x 1kg_____ = 1000 g b. lb 2435.5 g x 1lb______ = 453.59 g DENSITY  defined in a qualitative manner as the measure of the relative "heaviness" of objects with a constant volume.  a physical property of matter, as each element and compound has a unique density associated with it.  Temperature- and compound-specific DENSITY  ratio of an object’s mass to its volume ρ(rho) used to symbolize density ρ=m/v  Allows conversion between mass and volume.  Units: Solid: g/cm3 Liquid: g/mL Gas: g/L EXAMPLE PROBLEMS A piece of gold with a mass of 301g has a volume of 15.6 cm3. Calculate the density of gold. ρ = 301 g/ 15.6 cm3 ρ = 19.3 g/ cm3 A piece of platinum metal with a density of 21.5 g/ cm3 has a volume of 4.49 cm3. What is its mass? m = ρ x v = (21.5g/ cm3 ) (4.49 cm3) m = 96.5 g  Calculatethe volume of liquid which has a density of 0.94 g/mL and a mass of 26.4g. v = m/ ρ = 26.4 g / 0.94 g/mL v = 28 mL EXAMPLE PROBLEM  In the determination of the density of a rectangular metal bar, a student made the following measurements: length 8.53 cm; width 2.4 cm; height 1.0 cm, mass 52.7064g. Calculate the density of the metal bar. SOLUTION  v = length x width x height ρ = _____52.7064g_________ (8.53 cm)(2.4 cm)(1.0cm) ρ = 2.6 g/cm3  A silver object with a mass of 194.3g is placed in a graduated cylinder containing 242.0 mL water. The volume of water with the object now reads 260.5 mL. Determine the density of the silver object. water with object 260.5 mL water only - 242.0 mL volume of object 18.5 mL ρ = 194.3 g 18.5 mL ρ = 10.5 g/mL PROBLEMS RELATED TO DENSITY  The density of water at 25ºC is 0.997 g per mL. A child’s swimming pool holds 346 L of water at this temperature. What mass of water is in the pool? TEMPERATURE  hotness or coldness of an object  measure of average kinetic energy of the matter/system  Property of the body which determines the flow of heat  It is the measure of intensity or how energetic each particles of the sample is TEMPERATURE SCALES  Systems for measuring temperature, defined by choosing two reference points and setting a fixed number of degrees between them  Common temperature scales include: Fahrenheit Celsius Kelvin  Celsius This temperature scale was developed by Swedish astronomer Andres Celsius in 1742 0°C represents the freezing point of water 100°C represents the boiling point of water  Fahrenheit This temperature scale was proposed by physicist Daniel Gabriel Fahrenheit in 1724 32°F represents the freezing point of water 212°F represents the boiling point of water  Kelvin This temperature scale was developed by Belfast-born British inventor and scientist William Thomson — also known as Lord Kelvin in 1848 273.15 K represents the freezing point of water 373.15 K represents the boiling point of water KELVIN SCALE  The absolute temperature scale  Based on the idea of absolute zero, the theoretical temperature at which all molecular motion stops and no discernable energy can be tested  Absolute zero is defined as 0 K on Kelvin scale, which is a thermodynamic (absolute) temperature scale and the coldest temperature theoretically possible  No negative numbers on the Kelvin scale, thus it is convenient to use when measuring extremely low temperatures in scientific research TEMPERATURE  Temperature is measured using the Fahrenheit, Celsius, and Kelvin (absolute) temperature scales. TEMPERATURE SCALE CONVERSION  oF = [(9/5) oC] + 32  oC = 5/9 x (oF-32) TEMPERATURE SCALE CONVERSION o F = (1.8  o C) + 32 o C = ( o F -32)/1.8 o K = C + 273.15 o C = K - 273.15 PROBLEMS RELATED TO TEMPERATURE  Helium has the lowest boiling point of all the elements at -452 oF. Convert this temperature to o C and K o C= 5/9(-452 oF - 32) = -268.9 oC K = -268.9 oC + 273.15 K = 4.26K  Mercury, the only metal that exists as liquid at room temperature, melts at -38.9 oC. Convert the melting point to oF to K.  oF = 9/5(-38.9 oC) + 32 = -38.02 oF K = -38.9 oC + 273.15 = 234.25 K Solder is an alloy made of tin and lead that is used in electronic circuit. It has a melting point of 224 oC. What is the melting point in oF and K. ACCURACY AND PRECISION Accuracy - how close the observed value is to the “true” value. Precision - the spread in values obtained from measurements; the reproducibility of values. ACCURACY AND PRECISION ACCURACY PRECISION correctness reproducibility Check by using different Check by repeating method measurements Poor accuracy results Poor precision results from procedural or from poor techniques equipment flaws MEASUREMENTS  Measurements can have poor precision and poor accuracy.  Darts are scattered evenly across the board. MEASUREMENTS  Measurements can have good precision and poor accuracy.  Darts are clustered together.  But darts are clustered far from the bulls-eye. MEASUREMENTS  Measurements can have good precision and good accuracy.  Darts are clustered together, and  darts are clustered close to or on the bulls-eye. RESULTS OF MEASUREMENTS Trial Group Group Group A B C 1 99.99g 95.50g 97.50g 2 99.98g 95.60g 95.50g 3 99.99g 95.55g 96.50g Average 99.99g 95.55g 96.50g ERROR IN MEASUREMENTS  Measurements contain one of two types of errors: Random Error - may make a measurement randomly too high or too low. (e.g., variation associated with equipment limitations) Systematic Error - may make a measurement consistently too high or too low. (e.g., the presence of an impurity) REFERENCES  Brown,B.S, Holme,T.A,(2012) Chemistry for Engineering Students, 2ed: Cengage Learning Asia Pte Ltd  Chang, R. (2010). Chemistry. Boston: McGraw- Hill Higher Education.  Masterton,W.L, et al (2018) Principles and Reactions: Chemistry for Engineering Students, Cengage Learning Thank you for joining! Keep safe!