Chapter 3 Measurement and Chemical Calculations PDF

Mark S. Cracolice Edward I. Peters www.cengage.com/chemistry/cracolice Chapter 3 Measurement and Chemical Calculations Mark S. Cracolice The University of Montana Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives (3.1) Write in...

Mark S. Cracolice Edward I. Peters www.cengage.com/chemistry/cracolice Chapter 3 Measurement and Chemical Calculations Mark S. Cracolice The University of Montana Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives (3.1) Write in scientific notation a number given in ordinary decimal form; write in ordinary decimal form a number given in scientific notation Use a calculator to add, subtract, multiply, and divide numbers expressed in scientific notation (3.2) Convert an equivalency into two conversion factors (3.3) Learn and apply the algorithm for using conversion factors to solve quantitative problems Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives (3.4) Explain why the metric system of measurement is used in the sciences (3.5) State and write with appropriate metric prefixes the relationship between any metric unit and its corresponding kilounit, centiunit, and milliunit Using Table 3.1, state and write with appropriate metric prefixes the relationship between any metric unit and other larger and smaller metric units Distinguish between mass and weight Identify the metric units of mass, length, and volume Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives Given a mass, length, or volume expressed in basic metric units, kilounits, centiunits, or milliunits, express that quantity in the other three units Given a mass, length, or volume expressed in any metric units and Table 3.1 or the equivalent, express that quantity in any other metric unit (3.6) Given a description of a measuring instrument and an associated measurement, express the measured quantity with the uncertain digit in the correct location in the value State the number of significant figures in a given quantity Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives (3.7) Round off given values to a specified number of significant figures Add or subtract given measured quantities and express the result in the proper number of significant figures Multiply or divide given measured quantities and express the result in the proper number of significant figures (3.8) Given a metric–USCS conversion factor and a quantity expressed in any unit in Table 3.2, express that quantity in corresponding units in the other system Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives (3.9) Given a temperature in either Celsius or Fahrenheit degrees, convert it to the other scale Given a temperature in Celsius degrees or kelvins, convert it to the other scale (3.10) Write a mathematical expression indicating that one quantity is directly proportional to another quantity Use a proportionality constant to convert a proportionality to an equation Copyright ©2016 Cengage Learning. All Rights Reserved. Textbook Learning Objectives Given the values of two quantities that are directly proportional to each other, calculate the proportionality constant, including its units Write the defining equation for a proportionality constant and identify units in which it might be expressed Given two of the following for a sample of a pure substance, calculate the third: mass, volume, and density Copyright ©2016 Cengage Learning. All Rights Reserved. Course Learning Objectives (CLO) CLO 3.1 Define the common SI units and metric prefixes. CLO 3.2 Use dimensional analysis to convert between units of measure. CLO 3.3 Use of scientific notation and significant digits. Copyright ©2016 Cengage Learning. All Rights Reserved. Scientific Notation Method of writing numbers in the form: a.bcd × 10e Coefficient: a.bcd Number equal to or greater than 1 and less than 10 Exponential: 10e Exponent: Number e in 10e Whole number, may be positive or negative Copyright ©2016 Cengage Learning. All Rights Reserved. Conversion of Decimal Number to Scientific Notation Rewrite the number, place the decimal after first nonzero digit and write ×10 Count the number of places the decimal in the original number moved to its new place Write the number as the exponent of 10 Compare original number with new coefficient If the coefficient is smaller than original number, exponent has positive value If the coefficient is larger than original number, exponent has negative value Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Example: Convert 0.00818 dg to scientific notation Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Example: Convert 51,000,000 kg to scientific notation Copyright ©2016 Cengage Learning. All Rights Reserved. Conversion of Scientific Notation to Decimal Multiply the coefficient with the exponent Exponent gives the number of places the decimal point has to be moved Based off priority! Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Example: Convert 3.49 × 10 -11 to decimal form Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Example: Convert 5.16 × 104 to decimal form Copyright ©2016 Cengage Learning. All Rights Reserved. Key takeaways: Scientific Notation Know your Coefficients! For numbers less than 1: Simply count the zeros, and that will be your number (in negative) for the exponent For numbers at 1 or greater, include all numbers excluding highest priority number! Copyright ©2016 Cengage Learning. All Rights Reserved. Quantity In chemistry, quantities must be expressed as a product of a value and a unit Value × Unit = Quantity How many seconds are in 50 minutes? We know that there are 60 seconds in 1 minute. Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise You're currently driving at 60 mph, how many miles would you drive per minute? Copyright ©2016 Cengage Learning. All Rights Reserved. Equivalency And Conversion Factors Equivalency: Expression stating that two quantities with different units represent the same property Conversion factor: Relationship between different units of measurement that express the same quantity, written as fraction Two conversion factors result from each equivalency Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Write equivalency and conversion factors for the following One day is 24 hours, how many minutes are there in One day? Copyright ©2016 Cengage Learning. All Rights Reserved. Algorithm to Solve a Quantitative Chemistry Problem Step 1 Analyze the problem statement Determine the given quantity: Value x unit Describe the property of the given quantity Describe the property of the wanted quantity State the unit of the wanted quantity Step 2 Identify equivalences or an algebraic relationship that may be needed to solve the problem Change the equivalencies to conversion factors or solve algebraic equation for wanted variable Copyright ©2016 Cengage Learning. All Rights Reserved. Algorithm to Solve a Quantitative Chemistry Problem Step 3 Construct the solution setup Confirm that the units cancel correctly and calculate the value of the answer Step 4 Check the solution at two levels Making sense - Is the value reasonable? What was learned Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Calculate the number of weeks in a year Copyright ©2016 Cengage Learning. All Rights Reserved. Table 3.1 - Metric Prefixes Copyright ©2016 Cengage Learning. All Rights Reserved. Metric Takeaways 1 Gram = 100cg, 0.001kg, 1000mg 1 Meter = 100cm, 0.001km, 1000mm SI Unit of Length: Meter SI Unit of Mass: Kg SI Unit of Volume: Cubic Meter Know your conversions between Meters and Grams! Keep a chart handy on exam day! Copyright ©2016 Cengage Learning. All Rights Reserved. M/C Convert these quantities from scientific notation to decimal (standard) form. 8.4 x 105 mL Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise What distance, expressed in miles, will an automobile travel in 3 hours at an average speed of 80 miles per hour? Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise A little girl broke her piggy bank. Inside she found 2608 pennies. How many dollars does she have? Copyright ©2016 Cengage Learning. All Rights Reserved. Metric System Method of measurement used by most of the world based on a small number of basic units and standard set of prefixes Preferred by scientists as it is: Internationally standardized Agreed worldwide on definitions of metric units Decimal based SI units: Subset of units in the metric system, associated with the International System of Units Describe base units that serve as fundamental definitions Copyright ©2016 Cengage Learning. All Rights Reserved. Metric Units Identified by metric prefixes Units that are larger than the basic unit are larger by multiples of 10 For example, the kilo- unit is 1000 times larger than the basic unit Units that are smaller than the basic unit are smaller by fractions that are also multiples of 10 For example, the milli- unit is 1/1000 times smaller than the basic unit Copyright ©2016 Cengage Learning. All Rights Reserved. Table 3.1 - Metric Prefixes Copyright ©2016 Cengage Learning. All Rights Reserved. Mass And Weight Mass: Measure of quantity of matter Weight: Measure of the force of gravitational attraction on a body Proportional to mass, ratio between them depends on where in the universe one happens to be Copyright ©2016 Cengage Learning. All Rights Reserved. Video: Are Mass and Weight the same thing? https://youtu.be/rFdbY_V7vIo Copyright ©2016 Cengage Learning. All Rights Reserved. T/F You place an object on a balance. It reads 50lbs. Therefore, its Mass is 50lb’s. Copyright ©2016 Cengage Learning. All Rights Reserved. SI Units of Mass, Length, and Volume Kilogram (kg): Unit of mass equal to the mass of the International Prototype Kilogram Basic unit for mass is gram (g) Meter (m): Length of the path travelled by light in a vacuum ~300,000 m/s, Equivalent to 186,000 miles per second. Longer length unit is kilometer (km). 1km = 1000m Centimeter (cm) and millimeter (mm) is used for small distances Copyright ©2016 Cengage Learning. All Rights Reserved. Active exercise If you were to point a Laser pointer at the Moon. How long will it take for the ray of the laser to reach the Moon? Speed of light: 186,000 miles per second Distance of Earth to the Moon: 238,900 miles Hint: see how many times the speed goes into the total distance, and carry over those end units (seconds) Copyright ©2016 Cengage Learning. All Rights Reserved. SI Units of Mass, Length, and Volume SI unit of volume - Cubic meter (m3) Cubic centimeter (cm3): Unit of volume equal to the volume of a cube with a 1 cm length, width, and height Liter (L), milliliter (mL) Basic units for expressing volume of liquids and gases Copyright ©2016 Cengage Learning. All Rights Reserved. Figure 3.7 - International Prototype Kilogram The SI unit of mass is the kilogram It is defined as the mass of a platinum-iridium cylinder stored in a vault in France A kilogram weighs 2.2 pounds https://www.youtube.com/watch?v=D0v8PvxKHFA&ab_channel=Behindthe News Copyright ©2016 Cengage Learning. All Rights Reserved. Figure 3.8 - Length Measurements: Inches, Centimeters, and Millimeters One inch is defined as 2.54 centimeters Copyright ©2016 Cengage Learning. All Rights Reserved. Figure 3.11 - Relationship Between a Liter, a Milliliter, and a Cubic Milliliter One liter (L) is defined as exactly 1000 cubic centimeters 1 mL = 0.001 L = 1 cm3 Copyright ©2016 Cengage Learning. All Rights Reserved. Metric Units Metric Relationship 1000 units per kilounit 1000 u 1 ku ku 1000 u 100 centiunits per unit 100 cu 1u u 100 cu 1000 milliunits per unit 1000 mu 1u u 1000 mu Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise How many grams are in 0.711 kilograms? Hint: 1kg = 1000g Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise A fruit drink is sold in bottles that contain 1892 milliliters; how much is this in Cubic centimeters? Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures Digits in a measurement are known to be accurate plus one uncertain digit Recorded measurement should indicate size of uncertainty Attach ± value to recorded number Uncertain digit: Digit in a measured quantity that cannot be accurately measured Last digit written when expressing a measured quantity If the digit is a zero to the right of a decimal point, it must be written Copyright ©2016 Cengage Learning. All Rights Reserved. Uncertainty in Measurement Observing a Ruler, you will see these tick marks which indicate values of uncertainty (non-significant figures). On the other hand, the large numbers: 60- 1,2,3 Etc. Indicate the significant figures Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures Does not apply to exact numbers. Exact numbers are always significant Exact numbers: Values that have no associated uncertainty because they are counted or established by definition For example: 20 weeks (the 20 is a significant number, therefore there is only 1 significant figure) The measurement process determines the number of significant figures in a quantity Scientific notation must be used for very large numbers to show if final zeros are significant Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise How many significant figures are present in the quantities below? 0.109 in. 0.00025 kg Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures in Calculations Round off: Express a number with fewer digits If the first digit to be dropped is less than 5, leave the digit before it unchanged If the first digit to be dropped is 5 or greater, increase the digit before it by 1 Example: 1.42752 cm3 can be rounded off to 1.43 cm3 Rule for addition and subtraction Round off the answer to the first column that has an uncertain digit Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures in Calculations Example: A student weighs a beaker and four different chemicals using different balances. The individual masses are Beaker - 319.5 g, chemical A - 20.460 g, chemical B - 0.0639 g, chemical C - 45.642 g, chemical D - 4.173 g What is the total sum of Mass in grams? Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures in Calculations Rule for multiplication and division Round off the answer to the same number of significant figures as the smallest number of significant figures in any measured quantity Example: If the mass of 1.000 L of gas is 1.436 g, what is the mass of 0.0573 L of gas? Solution: 1.000 L = 1.436 g Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures in Calculations Rule for multiplication and division Round off the answer to the same number of significant figures as the smallest number of significant figures in any measured quantity Example: If the mass of 1.000 L of gas is 1.436 g, what is the mass of 0.0573 L of gas? Solution: 1.000 L = 1.436 g 0.0573 L × 1.436 g = 0.0822828 g (unrounded) 1.000 L Rounded to 0.0823 g Copyright ©2016 Cengage Learning. All Rights Reserved. Significant Figures in Calculations Rule for calculations which contains both addition/subtraction and multiplication/division Each individual rule must be applied to the significant rules separately Copyright ©2016 Cengage Learning. All Rights Reserved. Metric-USCS Conversions All countries in the world use metric system The U.S. uses the United States Customary System (USCS) Length 1 in. 2.54 cm (definition of an inch) Mass 1 lb 453.59237 g (definition of a pound) Volume 1 gal 3.785411784 L (exactly) Copyright ©2016 Cengage Learning. All Rights Reserved. Metric-USCS Conversions USCS–USCS conversions Length 1 ft 12 in. 1 yd 3 ft 1 mi 5280 ft Mass (Weight) 1 lb 16 oz Volume 1 qt 32 fl oz 1 gal 4 qt Copyright ©2016 Cengage Learning. All Rights Reserved. Metric–USCS Conversions Example: The TV you just purchased is 75 inches. What is this size in cm? Hint: 1 inch = 2.54 cm Copyright ©2016 Cengage Learning. All Rights Reserved. Temperature Fahrenheit scale: Temperature measurement assigning 32°F to freezing point of water and 212°F to boiling point of water, with 180 equally divided degrees in between Celsius scale: Temperature measurement assigning 0°F to freezing point of water and 100°F to boiling point of water, with 100 equally divided degrees in between Changing a temperature from degree Celsius to degree Fahrenheit T°C = T° F - 32 1.8 Copyright ©2016 Cengage Learning. All Rights Reserved. Temperature Kelvin temperature scale: Absolute temperature scale with 0 K at absolute zero, or -273.15°C TK = T°C + 273 Magnitude of the kelvin unit is 1/273.16 of the difference between absolute zero and the triple point of water, 273.16 K Copyright ©2016 Cengage Learning. All Rights Reserved. Figure 3.23 - Comparison Between Fahrenheit, Celsius, and Kelvin Temperature Scales Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Convert 288 K to its Fahrenheit scale equivalent Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise Convert 45 F to its Celsius scale equivalent Fahrenheit to Celsius equation: T°C = T° F - 32 1.8 Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise From each temperature given in the following table, calculate the equivalent temperatures in the other scales °F °C K -25 105 364 Copyright ©2016 Cengage Learning. All Rights Reserved. Proportionality and Density It is possible to describe direct proportionalities between measured quantities with equivalencies Direct proportionalities between measured quantities yield two conversion factors between the quantities Given either quantity in a direct proportionality and the conversion factor between the quantities, one can calculate the other quantity with dimensional analysis Copyright ©2016 Cengage Learning. All Rights Reserved. Proportionality and Density Direct proportionality between two variables (mass and volume, for instance) is indicated by m V Proportionality can be changed into an equation by inserting a proportionality constant Proportionality constant: Nonzero constant in the equation that expresses the relationship between two variables m V m=D×V Solving for the proportionality constant yields the defining equation for a physical property of a pure substance called its density D m V Copyright ©2016 Cengage Learning. All Rights Reserved. Proportionality and Density In words, density is the mass per unit volume of a substance Density mass volume Density is expressed in g/mL or g/cm3 Density is temperature dependent, volume varies with temperature Copyright ©2016 Cengage Learning. All Rights Reserved. Figure 3.26 - Particulate View of Solid and Liquid Water Copyright ©2016 Cengage Learning. All Rights Reserved. Figure 3.27 - Densities of Solids and Liquids Water is an unusual substance. Its solid phase is less dense than its liquid phase Solid ethanol sinks to the bottom of the liquid. The solid form of almost all substances is more dense than the liquid phase Copyright ©2016 Cengage Learning. All Rights Reserved. Table 3.4 - Densities of Some Common Substances (g/cm3 at 20°C and 1 atm) Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise The mass of a 50.00-milliliter sample of methanol is 39.59 grams Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise The density of a certain machine oil is 0.910 g/mL Find the volume occupied by 196 grams of that oil Copyright ©2016 Cengage Learning. All Rights Reserved. Active Exercise The density of a certain machine oil is 0.910 g/mL Find the volume occupied by 196 grams of that oil Solution: Given: g, metric mass Wanted: Volume, assume mL 0.910 g = 1 mL 1 mL 0.910 g 196 g × 1 mL = 215 mL 0.910 g Check: The value of the answer makes sense, OK Copyright ©2016 Cengage Learning. All Rights Reserved. Thoughtful and Reflective Practice The only way to learn how to solve problems is to solve them yourself A general guidelines for solving chemistry problems has been provided throughout the chapter End-of-chapter problems provide more opportunities to solve problems and gives immediate feedback The goal for solving problems is not to get the same answers as the textbook authors, but to learn how to solve the problem Copyright ©2016 Cengage Learning. All Rights Reserved. Active exercise Provide the metric equivalent for each quantity. 1mL = __ L Copyright ©2016 Cengage Learning. All Rights Reserved. Active exercise Provide the metric equivalent for each quantity. 1 kg = __ g Hint: Kilo means 1,000 Copyright ©2016 Cengage Learning. All Rights Reserved.