chapter two

ChapterChapter Two TwoMeasurementsMeasurements in in

ChemistryChemistry

04/20/23 Chapter Two 2

OutlineOutline► 2.1 2.1 Physical QuantitiesPhysical Quantities► 2.2 2.2 Measuring MassMeasuring Mass► 2.3 2.3 Measuring Length and VolumeMeasuring Length and Volume► 2.4 2.4 Measurement and Significant FiguresMeasurement and Significant Figures► 2.5 2.5 Scientific NotationScientific Notation► 2.6 2.6 Rounding Off NumbersRounding Off Numbers► 2.7 2.7 Converting a Quantity from One Unit to AnotherConverting a Quantity from One Unit to Another► 2.8 2.8 Problem Solving: Estimating AnswersProblem Solving: Estimating Answers► 2.9 2.9 Measuring TemperatureMeasuring Temperature► 2.10 2.10 Energy and HeatEnergy and Heat► 2.11 2.11 DensityDensity► 2.12 2.12 Specific GravitySpecific Gravity


GoalsGoals

►1.1. How are measurements made, and what How are measurements made, and what units are used? units are used? Be able to name and use the metric Be able to name and use the metric and SI units of measure for mass, length, volume, and and SI units of measure for mass, length, volume, and temperature.temperature.

►2.2. How good are the reported How good are the reported measurements? measurements? Be able to interpret the number of Be able to interpret the number of significant figures in a measurement and round off significant figures in a measurement and round off numbers in calculations involving measurements.numbers in calculations involving measurements.

►3.3. How are large and small numbers best How are large and small numbers best represented? represented? Be able to interpret prefixes for units of Be able to interpret prefixes for units of measure and express numbers in scientific notation.measure and express numbers in scientific notation.


Goals Contd.Goals Contd.

►4.4. How can a quantity be converted from one unit How can a quantity be converted from one unit of measure to another? of measure to another? Be able to convert quantities Be able to convert quantities from one unit to another using conversion factors.from one unit to another using conversion factors.

►5.5. What techniques are used to solve problems? What techniques are used to solve problems? Be Be able to analyze a problem, use the factor-label method to able to analyze a problem, use the factor-label method to solve the problem, and check the result to ensure that it solve the problem, and check the result to ensure that it makes sense chemically and physically.makes sense chemically and physically.

►6.6. What are temperature, specific heat, density, What are temperature, specific heat, density, and specific gravity? and specific gravity? Be able to define these quantities Be able to define these quantities and use them in calculations. and use them in calculations.


2.1 Physical Quantities2.1 Physical Quantities

Physical properties such as height, volume, and Physical properties such as height, volume, and temperature that can be measured are called temperature that can be measured are called physical physical quantitiesquantities. Both a number . Both a number andand a unit of defined size a unit of defined size is required to describe physical quantity. is required to describe physical quantity.


► A number without a unit is meaningless.A number without a unit is meaningless.

► To avoid confusion scientists have agreed on a standard set of To avoid confusion scientists have agreed on a standard set of units.units.

► Scientists use SI or the closely related metric units.Scientists use SI or the closely related metric units.


► Scientists work with both very large and very Scientists work with both very large and very small numbers.small numbers.

► Prefixes are applied to units to make saying and Prefixes are applied to units to make saying and writing measurements much easier.writing measurements much easier.

► The prefix pico (p) means a trillionth of The prefix pico (p) means a trillionth of ► The radius of a lithium atom is 0.000000000152 The radius of a lithium atom is 0.000000000152

meter (m). Try to say it.meter (m). Try to say it.► The radius of a lithium atom is 152 picometers The radius of a lithium atom is 152 picometers

(pm). Try to say it.(pm). Try to say it.


Frequently used prefixes are shown below.Frequently used prefixes are shown below.


2.2 Measuring Mass2.2 Measuring Mass

► MassMass is a measure of the amount of matter in an is a measure of the amount of matter in an object. Mass does not depend on location.object. Mass does not depend on location.

► Weight Weight is a measure of the gravitational force is a measure of the gravitational force acting on an object. Weight depends on location.acting on an object. Weight depends on location.

► A scale responds to weight.A scale responds to weight.► At the same location, two objects with identical At the same location, two objects with identical

masses have identical weights.masses have identical weights.► The mass of an object can be determined by The mass of an object can be determined by

comparing the weight of the object to the weight comparing the weight of the object to the weight of a reference standard of known mass.of a reference standard of known mass.


a) The single-pan balance with sliding a) The single-pan balance with sliding counterweights. (b) A modern electronic balance.counterweights. (b) A modern electronic balance.


Relationships between metric units of mass and the Relationships between metric units of mass and the mass units commonly used in the United States are mass units commonly used in the United States are shown below.shown below.


2.3 Measuring Length and Volume2.3 Measuring Length and Volume

► The meter (m) is the standard measure of length or The meter (m) is the standard measure of length or distance in both the SI and the metric system. distance in both the SI and the metric system.

► Volume is the amount of space occupied by an Volume is the amount of space occupied by an object. A volume can be described as a lengthobject. A volume can be described as a length33..

► The SI unit for volume is the cubic meter (mThe SI unit for volume is the cubic meter (m33).).


Relationships between metric units of length and Relationships between metric units of length and volume and the length and volume units commonly volume and the length and volume units commonly used in the United States are shown below and on the used in the United States are shown below and on the next slide.next slide.


A mA m33 is the volume of a cube 1 m or 10 dm on edge. is the volume of a cube 1 m or 10 dm on edge. Each mEach m33 contains (10 dm) contains (10 dm)3 3 = 1000 dm= 1000 dm33 or liters. Each or liters. Each liter or dmliter or dm33 = (10cm) = (10cm)33 =1000 cm =1000 cm33 or milliliters. Thus, or milliliters. Thus, there are 1000 mL in a liter and 1000 L in a mthere are 1000 mL in a liter and 1000 L in a m33 . .


The metric system is based on factors of 10 and is The metric system is based on factors of 10 and is much easier to use than common U.S. units. Does much easier to use than common U.S. units. Does anyone know how many teaspoons are in a gallon?anyone know how many teaspoons are in a gallon?


2.4 Measurement and Significant 2.4 Measurement and Significant FiguresFigures

► Every experimental Every experimental measurement has a measurement has a degree of uncertainty.degree of uncertainty.

► The volume, V, at right The volume, V, at right is certain in the 10’s is certain in the 10’s place, 10mL<V<20mLplace, 10mL<V<20mL

► The 1’s digit is also The 1’s digit is also certain, 17mL<V<18mLcertain, 17mL<V<18mL

► A best guess is needed A best guess is needed for the tenths place.for the tenths place.


► To indicate the precision of a measurement, the To indicate the precision of a measurement, the value recorded should use all the digits known value recorded should use all the digits known with certainty, plus one additional estimated digit with certainty, plus one additional estimated digit that usually considered uncertain by plus or that usually considered uncertain by plus or minus 1.minus 1.

► No further, insignificant, digits should be No further, insignificant, digits should be recorded. recorded.

► The total number of digits used to express such a The total number of digits used to express such a measurement is called the number of measurement is called the number of significant significant figuresfigures..

► All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimateestimate.


Below are two measurements of the mass of the Below are two measurements of the mass of the same object. The same quantity is being described same object. The same quantity is being described at two different levels of accuracy or certainty.at two different levels of accuracy or certainty.


► When reading a measured value, all nonzero digits When reading a measured value, all nonzero digits should be counted as significant. There is a set of should be counted as significant. There is a set of rules for determining if a zero in a measurement is rules for determining if a zero in a measurement is significant or not.significant or not.

► RULE 1. RULE 1. Zeros in the middle of a number are like Zeros in the middle of a number are like any other digit; they are always significant. Thus, any other digit; they are always significant. Thus, 94.072 g has five significant figures.94.072 g has five significant figures.

► RULE 2. RULE 2. Zeros at the beginning of a number are Zeros at the beginning of a number are not significant; they act only to locate the decimal not significant; they act only to locate the decimal point. Thus, 0.0834 cm has three significant point. Thus, 0.0834 cm has three significant figures, and 0.029 07 mL has four.figures, and 0.029 07 mL has four.


► RULE 3. RULE 3. Zeros at the end of a number and Zeros at the end of a number and after after the decimal point are significant. It is assumed the decimal point are significant. It is assumed that these zeros would not be shown unless they that these zeros would not be shown unless they were significant. 138.200 m has six significant were significant. 138.200 m has six significant figures. If the value were known to only four figures. If the value were known to only four significant figures, we would write 138.2 m.significant figures, we would write 138.2 m.

► RULE 4. RULE 4. Zeros at the end of a number and Zeros at the end of a number and before before an implied decimal point may or may not be an implied decimal point may or may not be significant. We cannot tell whether they are part significant. We cannot tell whether they are part of the measurement or whether they act only to of the measurement or whether they act only to locate the unwritten but implied decimal point.locate the unwritten but implied decimal point.


2.5 Scientific Notation2.5 Scientific Notation

► Scientific NotationScientific Notation is a convenient way to is a convenient way to write a very small or a very large number.write a very small or a very large number.

► Numbers are written as a product of a number Numbers are written as a product of a number between 1 and 10, times the number 10 raised between 1 and 10, times the number 10 raised to power.to power.

► 215 is written in scientific notation as:

215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 102


Two examples of converting standard notation to Two examples of converting standard notation to scientific notation are shown below.scientific notation are shown below.


Two examples of converting scientific notation back to Two examples of converting scientific notation back to standard notation are shown below. standard notation are shown below.


► Scientific notation is helpful for indicating how Scientific notation is helpful for indicating how many significant figures are present in a number that many significant figures are present in a number that has zeros at the end but to the left of a decimal point.has zeros at the end but to the left of a decimal point.

► The distance from the earth to the sun is 150,000,000 The distance from the earth to the sun is 150,000,000 km. Written in standard notation this number could km. Written in standard notation this number could have anywhere from 2 to 9 significant figures.have anywhere from 2 to 9 significant figures.

► Scientific notation can indicate how many digits are Scientific notation can indicate how many digits are significant. Writing 150,000,000 as 1.5 x 10significant. Writing 150,000,000 as 1.5 x 1088 indicates 2 and writing it as 1.500 x 10indicates 2 and writing it as 1.500 x 1088 indicates 4. indicates 4.

► Scientific notation can make doing arithmetic easier. Scientific notation can make doing arithmetic easier. Rules for doing arithmetic with numbers written in Rules for doing arithmetic with numbers written in scientific notation are reviewed in Appendix A.scientific notation are reviewed in Appendix A.


2.6 Rounding off Numbers2.6 Rounding off Numbers

► Often when doing arithmetic on a pocket Often when doing arithmetic on a pocket calculator, the answer is displayed with more calculator, the answer is displayed with more significant figures than are really justified.significant figures than are really justified.

► How do you decide how many digits to keep?How do you decide how many digits to keep?► Simple rules exist to tell you how.Simple rules exist to tell you how.


RULE 1. RULE 1. In carrying out a multiplication or division, In carrying out a multiplication or division, the answer cannot have more significant figures than the answer cannot have more significant figures than either of the original numbers.either of the original numbers.


►RULE 2. RULE 2. In carrying out an addition or In carrying out an addition or subtraction, the answer cannot have more digits subtraction, the answer cannot have more digits after the decimal point than either of the original after the decimal point than either of the original numbers.numbers.


► Once you decide how many digits to retain, the rules Once you decide how many digits to retain, the rules for rounding off numbers are straightforward:for rounding off numbers are straightforward:

► RULE 1. RULE 1. If the first digit you remove is 4 or less, If the first digit you remove is 4 or less, drop it and all following digits. 2.4271 becomes 2.4 drop it and all following digits. 2.4271 becomes 2.4 when rounded off to two significant figures because when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less.the first dropped digit (a 2) is 4 or less.

► RULE 2. RULE 2. If the first digit removed is 5 or greater, If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. 4.5832 is round up by adding 1 to the last digit kept. 4.5832 is 4.6 when rounded off to 2 significant figures since 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater.the first dropped digit (an 8) is 5 or greater.

► If a calculation has several steps, it is best to round If a calculation has several steps, it is best to round off at the end.off at the end.


2.7 Problem Solving: Converting a 2.7 Problem Solving: Converting a Quantity from One Unit to AnotherQuantity from One Unit to Another

► Factor-Label Method:Factor-Label Method: A quantity in one unit is A quantity in one unit is converted to an equivalent quantity in a different converted to an equivalent quantity in a different unit by using a conversion factor that expresses the unit by using a conversion factor that expresses the relationship between units.relationship between units.

(Starting quantity) x (Conversion factor) = Equivalent quantity(Starting quantity) x (Conversion factor) = Equivalent quantity


Writing 1 km = 0.6214 mi as a fraction restates it in Writing 1 km = 0.6214 mi as a fraction restates it in the form of a conversion factor. This and all other the form of a conversion factor. This and all other conversion factors are numerically equal to 1.conversion factors are numerically equal to 1.

The numerator is equal to the denominator. The numerator is equal to the denominator. Multiplying by a conversion factor is equivalent to Multiplying by a conversion factor is equivalent to multiplying by 1 and so causes no change in value.multiplying by 1 and so causes no change in value.


When solving a problem, the idea is to set up anWhen solving a problem, the idea is to set up an

equation so that all unwanted units cancel, leaving equation so that all unwanted units cancel, leaving only the desired units.only the desired units.


2.8 Problem Solving: Estimating 2.8 Problem Solving: Estimating AnswersAnswers

► STEP 1: STEP 1: Identify the information given.Identify the information given.► STEP 2: STEP 2: Identify the information needed to answer.Identify the information needed to answer.► STEP 3: STEP 3: Find the relationship(s) between the known Find the relationship(s) between the known

information and unknown answer, and plan a series information and unknown answer, and plan a series of steps, including conversion factors, for getting of steps, including conversion factors, for getting from one to the other.from one to the other.

► STEP 4: STEP 4: Solve the problem.Solve the problem.► BALLPARK CHECK: BALLPARK CHECK: Make a rough estimate to Make a rough estimate to

be sure the value and the units of your calculated be sure the value and the units of your calculated answer are reasonable.answer are reasonable.


2.9 Measuring Temperature2.9 Measuring Temperature

► Temperature is commonly reported either in Temperature is commonly reported either in degrees Fahrenheit (degrees Fahrenheit (ooF) or degrees Celsius (F) or degrees Celsius (ooC). C).

► The SI unit of temperature is the Kelvin (K).The SI unit of temperature is the Kelvin (K).► 1 Kelvin, no degree, is the same size as 1 1 Kelvin, no degree, is the same size as 1 ooC.C.► 0 K is the lowest possible temperature, 0 0 K is the lowest possible temperature, 0 ooC = C =

273.15 K is the normal freezing point of water. 273.15 K is the normal freezing point of water. To convert, adjust for the zero offset.To convert, adjust for the zero offset.

► Temperature in K = Temperature in Temperature in K = Temperature in ooC + 273.15C + 273.15► Temperature in Temperature in ooC = Temperature in K - 273.15C = Temperature in K - 273.15


Freezing point of HFreezing point of H22O O Boiling point of Boiling point of

HH22OO

3232ooFF 212212ooFF

00ooCC 100100ooCC

212212ooF – 32F – 32ooF = 180F = 180ooF covers the same range of F covers the same range of temperature as 100temperature as 100ooC-0C-0ooC=100C=100ooC covers. Therefore, C covers. Therefore, a Celsius degree is exactly 180/100 = 1.8 times as a Celsius degree is exactly 180/100 = 1.8 times as large as Fahrenheit degree. The zeros on the two large as Fahrenheit degree. The zeros on the two scales are separated by 32scales are separated by 32ooF.F.


Fahrenheit, Celsius, and Kelvin temperature scales.Fahrenheit, Celsius, and Kelvin temperature scales.


► Converting between Fahrenheit and Celsius scales Converting between Fahrenheit and Celsius scales is similar to converting between different units of is similar to converting between different units of length or volume, but is a little more complex. length or volume, but is a little more complex. The different size of the degree The different size of the degree andand the zero offset the zero offset must both be accounted for.must both be accounted for.

► ooF = (1.8 x F = (1.8 x ooC) + 32C) + 32► ooC = (C = (ooF – 32)/1.8F – 32)/1.8


2.10 Energy and Heat2.10 Energy and Heat

► Energy: Energy: The capacity to do work or supply heat.The capacity to do work or supply heat.► Energy is measured in SI units by the Energy is measured in SI units by the JouleJoule (J), the (J), the

calorie is another unit often used to measure energy.calorie is another unit often used to measure energy.► One One caloriecalorie (cal) is the amount of heat necessary to (cal) is the amount of heat necessary to

raise the temperature of 1 g of water by 1°C.raise the temperature of 1 g of water by 1°C.► A kilocalorieA kilocalorie (kcal)= 1000 cal. A (kcal)= 1000 cal. A CalorieCalorie, with a , with a

capital C, usedcapital C, used by nutritionists equals 1000 cal.by nutritionists equals 1000 cal.► An important energy conversion factor is:An important energy conversion factor is:

1 cal = 4.184 J1 cal = 4.184 J


► Not all substances have their temperatures raised to Not all substances have their temperatures raised to the same extent when equal amounts of heat energy the same extent when equal amounts of heat energy are added.are added.

► One calorie raises the temperature of 1 g of water by One calorie raises the temperature of 1 g of water by 1°C but raises the temperature of 1 g of iron by 1°C but raises the temperature of 1 g of iron by 10°C.10°C.

► The amount of heat needed to raise the temperature The amount of heat needed to raise the temperature of 1 g of a substance by 1°C is called the of 1 g of a substance by 1°C is called the specific specific heat heat of the substance. of the substance.

► Specific heat is measured in units of cal/gSpecific heat is measured in units of cal/gCC


► Knowing the mass and specific heat of a Knowing the mass and specific heat of a substance makes it possible to calculate how substance makes it possible to calculate how much heat must be added or removed to much heat must be added or removed to accomplish a given temperature change.accomplish a given temperature change.

► (Heat Change)=(Mass) x (Specific Heat) x (Heat Change)=(Mass) x (Specific Heat) x (Temperature Change)(Temperature Change)

► Using the symbols Using the symbols for change, H for heat, m for change, H for heat, m for mass, C for specific heat and T for for mass, C for specific heat and T for temperature, a more compact form is:temperature, a more compact form is:

► H = mCH = mCTT


2.11 2.11 DensityDensity

Density relates the mass of an object to its volume. Density relates the mass of an object to its volume. Density is usually expressed in units of grams per cubic Density is usually expressed in units of grams per cubic centimeter (g/cmcentimeter (g/cm33) for solids, and grams per milliliter ) for solids, and grams per milliliter (g/mL) for liquids.(g/mL) for liquids.

Density =Density = Mass (g)Mass (g)

Volume (mL or cmVolume (mL or cm33))


►Which is heavier, a ton Which is heavier, a ton of feathers or a ton of of feathers or a ton of bricks?bricks?

►Which is larger?Which is larger?

►If two objects have the If two objects have the same mass, the one with same mass, the one with the higher density will the higher density will be smaller.be smaller.


2. 12 Specific Gravity2. 12 Specific Gravity

Specific GravitySpecific Gravity (sp gr):(sp gr): density of a substance density of a substance divided by the density of water at the same divided by the density of water at the same temperature. Specific Gravity is unitless. The temperature. Specific Gravity is unitless. The density of water is so close to 1 g/mL that the density of water is so close to 1 g/mL that the specific gravity of a substance at normal specific gravity of a substance at normal temperature is numerically equal to the density.temperature is numerically equal to the density.

Density of substance (g/ml)Density of substance (g/ml)

Density of water at the same temperature (g/ml)Density of water at the same temperature (g/ml)Specific gravity =Specific gravity =


The specific gravity of a The specific gravity of a liquid can be measured using liquid can be measured using an instrument called a an instrument called a hydrometer, which consists of hydrometer, which consists of a weighted bulb on the end of a weighted bulb on the end of a calibrated glass tube. The a calibrated glass tube. The depth to which the hydrometer depth to which the hydrometer sinks when placed in a fluid sinks when placed in a fluid indicates the fluid’s specific indicates the fluid’s specific gravity.gravity.


Chapter SummaryChapter Summary

► Physical quantitiesPhysical quantities require a number and a unit.require a number and a unit.► Preferred units are either SI units or metric units.Preferred units are either SI units or metric units.► Mass, the amount of matter an object contains, is Mass, the amount of matter an object contains, is

measured in kilogramsmeasured in kilograms (kg) or grams(kg) or grams (g). (g). ► Length is measured in metersLength is measured in meters (m). Volume is (m). Volume is

measured in cubic metersmeasured in cubic meters in the SI system and in in the SI system and in litersliters (L) or milliliters(L) or milliliters (mL) in the metric system. (mL) in the metric system.

► Temperature is measured in KelvinTemperature is measured in Kelvin (K) in the SI (K) in the SI system and in degrees Celsiussystem and in degrees Celsius (°C) in the metric (°C) in the metric system.system.


Chapter Summary Contd.Chapter Summary Contd.

► The exactness of a measurement is indicated by The exactness of a measurement is indicated by using the correct number of significant figures.using the correct number of significant figures.

► Significant figures in a number are all known with Significant figures in a number are all known with certainty except for the final estimated digit.certainty except for the final estimated digit.

► Small and large quantities are usually written in Small and large quantities are usually written in scientific notationscientific notation as the product of a number as the product of a number between 1 and 10, times a power of 10.between 1 and 10, times a power of 10.

► A measurement in one unit can be converted to A measurement in one unit can be converted to another unit by multiplying by a conversion factoranother unit by multiplying by a conversion factor that expresses the exact relationship between the that expresses the exact relationship between the units.units.


Chapter Summary Contd.Chapter Summary Contd.

► Problems are solved by the factor-label method.Problems are solved by the factor-label method.► Units can be multiplied and divided like numbers.Units can be multiplied and divided like numbers.► Temperature measures how hot or cold an object is.Temperature measures how hot or cold an object is.► Specific heat is the amount of heat necessary to Specific heat is the amount of heat necessary to

raise the temperature of 1 g of a substance by 1°C. raise the temperature of 1 g of a substance by 1°C. ► Density relates mass to volume in units of g/mL for a Density relates mass to volume in units of g/mL for a

liquid or g/cmliquid or g/cm33 for a solid. for a solid.► Specific gravity is density of a substance divided by Specific gravity is density of a substance divided by

the density of water at the same temperature. the density of water at the same temperature.


Key WordsKey Words

►Conversion factorConversion factor►DensityDensity►EnergyEnergy►Factor-label methodFactor-label method►MassMass►Physical quantityPhysical quantity►Rounding offRounding off►Scientific notationScientific notation

►SI unitsSI units►Significant figuresSignificant figures►Specific gravitySpecific gravity►Specific heatSpecific heat►TemperatureTemperature►UnitUnit►WeightWeight

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