Chapter Two Measurements in Chemistry Fundamentals of General, Organic and Biological Chemistry 6th Edition

Copyright © 2010 Pearson Education, Inc. Chapter Two 2 Outline ►2.1 Physical Quantities ►2.2 Measuring Mass ►2.3 Measuring Length and Volume ►2.9 Measuring Temperature ►2.4 Measurement and Significant Figures ►2.5 Scientific Notation ►2.6 Rounding Off Numbers ►2.7 Converting a Quantity from One Unit to Another ►2.11 Density

Copyright © 2010 Pearson Education, Inc. Chapter Two 3 Goals ►1.How are measurements made, and what units are used? Be able to name and use the metric and SI units of measure for mass, length, volume, and temperature. ►2.How good are the reported measurements? Be able to interpret the number of significant figures in a measurement and round off numbers in calculations involving measurements. ►3.How are large and small numbers best represented? Be able to interpret prefixes for units of measure and express numbers in scientific notation.

Copyright © 2010 Pearson Education, Inc. Chapter Two 4 Goals Contd. ►4.How can a quantity be converted from one unit of measure to another? Be able to convert quantities from one unit to another using conversion factors. ►5.What techniques are used to solve problems? Be able to analyze a problem, use the factor-label method to solve the problem, and check the result to ensure that it makes sense chemically and physically. ►6.What are temperature,density, and specific gravity? Be able to define these quantities and use them in calculations.

Copyright © 2010 Pearson Education, Inc. Chapter Two Physical Quantities Physical properties such as height, volume, and temperature that can be measured are called physical quantities. Both a number and a unit of defined size is required to describe physical quantity.

Copyright © 2010 Pearson Education, Inc. Chapter Two 6 ►A number without a unit is meaningless. ►To avoid confusion scientists have agreed on a standard set of units. ►Scientists use SI or the closely related metric units.

Copyright © 2010 Pearson Education, Inc. Chapter Two 7 ►Scientists work with both very large and very small numbers. ►Prefixes are applied to units to make saying and writing measurements much easier. ►The prefix pico (p) means a trillionth of ►The radius of a lithium atom is meter (m). Try to say it. ►The radius of a lithium atom is 152 picometers (pm). Try to say it.

Copyright © 2010 Pearson Education, Inc. Chapter Two 8 Frequently used prefixes are shown below.

 Use prefixes on SI base units when number is too large or too small for convenient usage Ex. 1 mL = 10 –3 L  1 km = 1000 m  1 ng = 10 –9 g  1,130,000,000 s = 1.13 × 10 9 s = 1.13 Gs 9

Copyright © 2010 Pearson Education, Inc. Chapter Two Measuring Mass ►Mass is a measure of the amount of matter in an object. Mass does not depend on location. ►Weight is a measure of the gravitational force acting on an object. Weight depends on location. ►A scale responds to weight. ►At the same location, two objects with identical masses have identical weights. ►The mass of an object can be determined by comparing the weight of the object to the weight of a reference standard of known mass.

Copyright © 2010 Pearson Education, Inc. Chapter Two 11 a) The single-pan balance with sliding counterweights. (b) A modern electronic balance.

Copyright © 2010 Pearson Education, Inc. Chapter Two 12 Relationships between metric units of mass and the mass units commonly used in the United States are shown below.

Copyright © 2010 Pearson Education, Inc. Chapter Two Measuring Length and Volume ►The meter (m) is the standard measure of length or distance in both the SI and the metric system. ►Volume is the amount of space occupied by an object. A volume can be described as a length 3. ►The SI unit for volume is the cubic meter (m 3 ). ►Scientists use the International System of Units (SI), which is based on the metric system.  The abbreviation SI comes from the French, phrase Système International d’Unités.

International System of Units (SI)  Standard system of units used in scientific & engineering measurements  Metric  7 Base Units 14

Learning Check  What is the SI unit for velocity?  What is the SI unit for volume of a cube? Volume (V) = length × width × height V = meter × meter × meter V = m 3 15

Your Turn! The SI unit of length is the A.millimeter B.meter C.yard D.centimeter E.foot 16

Some Useful Conversions 17

Copyright © 2010 Pearson Education, Inc. Chapter Two 18 Relationships between metric units of length and volume and the length and volume units commonly used in the United States are shown below and on the next slide.

Copyright © 2010 Pearson Education, Inc. Chapter Two 19 A m 3 is the volume of a cube 1 m or 10 dm on edge. Each m 3 contains (10 dm) 3 = 1000 dm 3 or liters. Each liter or dm 3 = (10cm) 3 =1000 cm 3 or milliliters. Thus, there are 1000 mL in a liter and 1000 L in a m 3.

Copyright © 2010 Pearson Education, Inc. Chapter Two Measuring Temperature ►Temperature is commonly reported either in degrees Fahrenheit ( o F) or degrees Celsius ( o C). ►The SI unit of temperature is the Kelvin (K). ►Temperature in K = Temperature in o C ►Temperature in o C = Temperature in K

Copyright © 2010 Pearson Education, Inc. Chapter Two 21 Freezing point of H 2 O Boiling point of H 2 O 32 o F212 o F 0 o C100 o C 212 o F – 32 o F = 180 o F covers the same range of temperature as 100 o C-0 o C=100 o C covers. Therefore, a Celsius degree is exactly 180/100 = 1.8 times as large as Fahrenheit degree. The zeros on the two scales are separated by 32 o F.

Copyright © 2010 Pearson Education, Inc. Chapter Two 22 Fahrenheit, Celsius, and Kelvin temperature scales. Fahrenheit, Celsius, and Kelvin temperature scales.

Copyright © 2010 Pearson Education, Inc. Chapter Two 23 ►Converting between Fahrenheit and Celsius scales is similar to converting between different units of length or volume, but is a little more complex. The different size of the degree and the zero offset must both be accounted for. ► o F = (1.8 x o C) + 32 ► o C = ( o F – 32)/1.8

Laboratory Measurements  4 common 1.Length 2.Volume 3.Mass 4.Temperature 24

Laboratory Measurements 1.Length  SI Unit is meter (m)  Meter too large for most laboratory measurements  Commonly use  Centimeter (cm)  1 cm = 10 – 2 m = 0.01 m  Millimeter (mm)  1 mm = 10 – 3 m = m 25

2. Volume (V)  Dimensions of (length) 3  SI unit for Volume = m 3  Most laboratory measurements use V in liters (L)  Chemistry glassware marked in L or mL  1 L = 1000 mL  What is a mL?  1 mL = 1 cm 3 26

3. Mass  SI unit is kilogram (kg)  Frequently use grams (g) in laboratory as more realistic size  1 kg = 1000 g 1 g = kg = g  Mass is measured by comparing weight of sample with weights of known standard masses  Instrument used = balance 27

4. Temperature  Measured with thermometer  3 common scales A.Fahrenheit scale  Common in US  Water freezes at 32 °F and boils at 212 °F  180 degree units between melting & boiling points of water 28

4. Temperature B.Celsius scale  Rest of world (aside from U.S.) uses  Most common for use in science  Water freezes at 0 °C  Water boils at 100 °C  100 degree units between melting & boiling points of water 29

4. Temperature C. Kelvin scale  SI unit of temperature is kelvin (K)  Note: No degree symbol in front of K  Water freezes at K & boils at K  100 degree units between melting & boiling points Absolute Zero  Zero point on Kelvin scale  Corresponds to nature’s lowest possible temperature 30

Copyright © 2010 Pearson Education, Inc. Chapter Two 31 ► o F = (1.8 x o C) + 32 ► o C = ( o F – 32)/1.8 ►Temperature in K = Temperature in o C ►Temperature in o C = Temperature in K Temperature Conversions

Learning Check: T Conversions 1. Convert 100. °F to the Celsius scale. 2. Convert 100. °F to the Kelvin scale.  We already have in °C so… 32 = 38 °C T K = 311 K

Learning Check: T Conversions 3. Convert 77 K to the Celsius scale. 4. Convert 77 K to the Fahrenheit scale.  We already have in °C so 33 = – 196 °C = – 321 °F

Your Turn! In a recent accident some drums of uranium hexafluoride were lost in the English Channel. The melting point of uranium hexafluouride is °C. What is the melting point of uranium hexafluoride on the Fahrenheit scale? A °F B °F C °F D °F E °F 34

Copyright © 2010 Pearson Education, Inc. Chapter Two Measurement and Significant Figures ►Every experimental measurement has a degree of uncertainty. ►The volume, V, at right is certain in the 10’s place, 10mL<V<20mL ►The 1’s digit is also certain, 17mL<V<18mL ►A best guess is needed for the tenths place.

Copyright © 2010 Pearson Education, Inc. Chapter Two 36 ►To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually considered uncertain by plus or minus 1. ►No further, insignificant, digits should be recorded. ►The total number of digits used to express such a measurement is called the number of significant figures. ► estimate ►All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.

Copyright © 2010 Pearson Education, Inc. Chapter Two 37 Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.

1.All non-zero numbers are significant. Ex has 4 sig. figs. 2.Zeros between non-zero numbers are significant. Ex. 20,089 or × 10 4 has 5 sig. figs 3.Trailing zeros always count as significant if number has decimal point Ex or 5.00 × 10 2 has 3 sig. figs 38 Rules for Significant Figures

4.Final zeros on number without decimal point are NOT significant Ex. 104,956,000 or × 10 8 has 6 sig. figs. 5.Final zeros to right of decimal point are significant Ex has 3 sig. figs. 6. Leading zeros, to left of 1 st nonzero digit, are never counted as significant Ex or1.2 × 10 –4 has 2 sig. figs. 39 Rules for Significant Figures

Learning Check How many significant figures does each of the following numbers have? scientific notation # of Sig. Figs , × × 10 – ×

Your Turn! How many significant figures are in ? A.2 B.3 C.4 D.5 E.6 41

Copyright © 2010 Pearson Education, Inc. Chapter Two Scientific Notation ►Scientific Notation is a convenient way to write a very small or a very large number. ►Numbers are written as a product of a number between 1 and 10, times the number 10 raised to power. ► ►215 is written in scientific notation as: 215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 10 2

Copyright © 2010 Pearson Education, Inc. Chapter Two 43 Two examples of converting standard notation to scientific notation are shown below.

Copyright © 2010 Pearson Education, Inc. Chapter Two 44 Two examples of converting scientific notation back to standard notation are shown below.

Learning Check Round each of the following to 3 significant figures. Use scientific notation where needed or 3.75 × × or 1.33 × × 10 –4

Copyright © 2010 Pearson Education, Inc. Chapter Two Rounding off Numbers ►Often when doing arithmetic on a pocket calculator, the answer is displayed with more significant figures than are really justified. ►How do you decide how many digits to keep? ►Simple rules exist to tell you how.

When rounding to the correct number of significant figures, round down if the last (or leftmost) digit dropped is four or less; round up if the last (or leftmost) digit dropped is five or more. Rules for Rounding

Round to two significant figures: 5.37 rounds to rounds to rounds to rounds to 5.3 Notice in the last example that only the last (or leftmost) digit being dropped determines in which direction to round—ignore all digits to the right of it.

Significant Figures in Calculations Multiplication and Division  Number of significant figures in answer = least number of significant figures Ex × 31.4 × sig. figs. × 3 sig. figs. × 5 sig. figs = 3 sig. figs. Ex ÷ sig. figs. ÷ 1 sig. fig. = 1 sig. fig. 49 = 5620 = 5.62×10 3 = 700 = 7×10 2

Your Turn! Give the value of the following calculation to the correct number of significant figures. A B C D. 1.2 E. 1 50

Significant Figures in Calculations Addition and Subtraction  Answer has same number of decimal places as quantity with fewest number of decimal places. Ex decimal places 1 decimal place 3 decimal places 1 decimal place 397 – decimal places 2 decimal places 0 decimal place

Your Turn! When the expression, – is evaluated, the result should be expressed as: A B C D E

Exact Numbers  Number that come from definitions  12 in. = 1 ft  60 s = 1 min  Numbers that come from direct count  Number of people in small room  Have no uncertainty  Assume they have infinite number of significant figures.  Do not affect number of significant figures in multiplication or division 53

Learning Check For each calculation, give the answer to the correct number of significant figures g g g = °C – °C = m × 4.52 m = g ÷ mL = g or 1.13 × 10 1 g °C or 4 × 10 –3 °C 1.48 × 10 3 m g/mL or g/mL

Learning Check For the following calculation, give the answer to the correct number of significant figures = 2 × 10 –4 m/s 2 = 0.87 cm 3 /s

Your Turn! For the following calculation, give the answer to the correct number of significant figures. A. 179 cm 2 B cm C cm D. 151 cm E cm 2 56

Copyright © 2010 Pearson Education, Inc. Chapter Two Problem Solving: Converting a Quantity from One Unit to Another ►Factor-Label Method: A quantity in one unit is converted to an equivalent quantity in a different unit by using a conversion factor that expresses the relationship between units. (Starting quantity) x (Conversion factor) = Equivalent quantity

Copyright © 2010 Pearson Education, Inc. Chapter Two 58 Writing 1 km = mi as a fraction restates it in the form of a conversion factor. This and all other conversion factors are numerically equal to 1. The numerator is equal to the denominator. Multiplying by a conversion factor is equivalent to multiplying by 1 and so causes no change in value.

Copyright © 2010 Pearson Education, Inc. Chapter Two 59 When solving a problem, the idea is to set up an equation so that all unwanted units cancel, leaving only the desired units.

Conversion Factors Ex. How to convert a person’s height from 68.0 in to cm?  Start with fact 2.54 cm = 1 in. 60

 multiply original number by conversion factor that cancels old units & leaves new  Factor-Label Method can tell us when we have done wrong arithmetic  Units not correct 61 Given Quantity Desired Quantity Conversion Factor ×= = 173 cm = 26.8 in 2 /cm

Ex. Convert m to mm.  Relationship is1 mm = 1 × 10 –3 m  Can make 2 conversion factors  Since going from m to mm use one on left. 62 = 173 cm

Non-metric to Metric Units Convert speed of light from 3.00×10 8 m/s to mi/hr  Use Factor-Label Method  1 min = 60 s60 min = 1 hr  1 km = 1000 m1 mi = km × m/hr 6.71 × 10 8 mi/hr

Copyright © 2010 Pearson Education, Inc. Chapter Two Density Density relates the mass of an object to its volume. Density is usually expressed in units of grams per cubic centimeter (g/cm 3 ) for solids, and grams per milliliter (g/mL) for liquids. Density = Mass (g) Volume (mL or cm 3 )

Learning Check  A student weighs a piece of gold that has a volume of cm 3 of gold. She finds the mass to be 212 g. What is the density of gold? g/cm 3

Density  Most substances expand slightly when heated  Same mass  Larger volume  Less dense  Density  slightly as T   Liquids & Solids  Change is very small  Can ignore except in very precise calculations  Density useful to transfer between mass & volume of substance 66

Learning Check 1. Glass has a density of 2.2 g/cm 3. What is the volume occupied by 22 g of glass? 2. What is the mass of 400 cm 3 of glass? g/cm g

Your Turn! Titanium is a metal used to make artificial joints. It has a density of 4.54 g/cm 3. What volume will a titanium hip joint occupy if its mass is 205 g? A × 10 2 cm 3 B × 10 1 cm 3 C × 10 –2 cm 3 D × 10 –3 cm 3 E × 10 –1 cm 3 68

Your Turn! A sample of zinc metal (density = 7.14 g cm -3 ) was submerged in a graduated cylinder containing water. The water level rose from cm 3 to cm 3 when the sample was submerged. How many grams did the sample weigh? A × 10 3 g B × 10 3 g C g D × 10 2 g E g 69

Specific Gravity  Ratio of density of substance to density of water  Unitless  Way to avoid having to tabulate densities in all sorts of different units 70

Learning Check Liquid hydrogen has a specific gravity of 7.08 × 10 –2. If the density of water is 1.05 g/cm 3 at the same temperature, what is the mass of hydrogen in a tank having a volume of 36.9 m 3 ? A × 10 –2 g B g C. 274 g D × 10 6 g E × 10 6 g 71 = 7.43 × 10 –2 g/cm 3

Copyright © 2010 Pearson Education, Inc. Chapter Two 72 Chapter Summary ►Physical quantities require a number and a unit. ►Preferred units are either SI units or metric units. ►Mass, the amount of matter an object contains, is measured in kilograms (kg) or grams (g). ►Length is measured in meters (m). Volume is measured in cubic meters in the SI system and in liters (L) or milliliters (mL) in the metric system. ►Temperature is measured in Kelvin (K) in the SI system and in degrees Celsius (°C) in the metric system.

Copyright © 2010 Pearson Education, Inc. Chapter Two 73 Chapter Summary Contd. ►The exactness of a measurement is indicated by using the correct number of significant figures. ►Significant figures in a number are all known with certainty except for the final estimated digit. ►Small and large quantities are usually written in scientific notation as the product of a number between 1 and 10, times a power of 10. ►A measurement in one unit can be converted to another unit by multiplying by a conversion factor that expresses the exact relationship between the units.