CHM 111 CHAPTER 1-A Measurements

© 2012 by W. W. Norton & Company

Accuracy, Precision, and Significant Figures in Measurement

Measure a centi-deskunit using ribbon and scissors.

1 cdu = ??

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Accuracy, Precision, and Significant Figures in Measurement •

Accuracy

is how close to the true value a given measurement is.

•

Precision

is how well a number of independent measurements agree with one another.

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Accuracy, Precision, and Significant Figures in Measurement •

Significant Figures

are the total number of digits in the measurement. • The results of calculations are only as reliable as the least precise measurement.

• Rules exist to govern the use of significant figures after the measurements have been made.

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Mass of a Tennis Ball

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Reading a Thermometer 6

Taking a Measurement 7

Taking a Measurement 8

Accuracy, Precision, and Significant Figures in Measurement •

Rules for Significant Figures:

Zeros in the middle of a number are significant Zeros at the beginning of a number are not significant Zeros at the end of a number and following a period are significant Zeros at the end of a number and before a period may or may not be significant.

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Accuracy, Precision, and Significant Figures in Measurement •

Rules for Rounding Numbers:

If the first digit removed is less than 5 - round down If the first digit removed is greater than 5 - round up If the first digit removed is 5 and following numbers are nonzero - round up If the first digit removed is 5 and following numbers are zero - round down 10

Accuracy, Precision, and Significant Figures in Measurement • How many significant figures does each of the following measurements have?

(a) 0.036653 m (b) 7.2100 x 10 –3 g (c) 72,100 km (d) $25.03

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Accuracy, Precision, and Significant Figures in Measurement • Round off each of the following measurements.

(a) 3.774499 L to four significant figures (b) 255.0974 K to three significant figures (c) 55.265 kg to four significant figures 12

Accuracy, Precision, and Significant Figures in Measurement •

Rules for Calculating Numbers:

During multiplication or division, the answer can’t have more sig figs than any of the original numbers.

During addition or subtraction, the answer can’t have more digits to the right of the decimal point than any of the original numbers.

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Significant Figures in Calculations 14

Significant Figures in Calculations 15

Significant Figure Calculations Ok, now…

Try These!

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Measurement and Units •

Seven Fundamental SI Units of Measurement.

Physical Quantity

Mass Length Temperature Amount of substance Time Electric current Luminous intensity

Name of Unit

kilogram meter kelvin mole second ampere candela

Abbreviation

kg m K mol s A cd 17

Measurement and Units 18

Measurement and Units •

Some Prefixes for Multiples of SI Units.

Factor

1,000,000,000 = 10 9 1,000,000 = 10 6 1,000 = 10 3 100 = 10 2 10 = 10 1 0.1 = 10 -1 0.01 = 10 -2 0.001 = 10 -3 0.000,001 = 10 -6 0.000,000,001 = 10 -9 0.000,000,000,001 = 10 -12

Prefix

giga mega kilo hecto deka deci centi milli micro nano pico

Symbol

G M k h da d c m µ n p 19

Measurement and Units 20

Measurement and Units •

Some Derived Quantities.

Quantity

Area Volume Density Speed Acceleration Force Pressure Energy

Definition

Length times length Area times length Mass per unit volume Distance per unit time Change in speed per unit time Mass times acceleration Force per unit area Force times distance

Derived Unit (Name)

m 2 m 3 kg/m 3 m/s m/s 2 (kg·m)/s 2 (newton, N) kg/(m·s 2 ) (pascal, Pa) (kg·m 2 )/s 2 (joule, J) 21

Measurement and Units •

Density

relates the mass of an object to its volume.

• Density decreases as a substance is heated because the substance’s volume increases.

• Knowing the density of a substance allows measurements in volume to be recorded in mass.

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Measurement and Units 23

Measurement and Units •

Densities of Some Common Materials.

Substance

Ice (0.0°C) Water (4.0°C) Gold Helium (25.0°C) Air (25.0°C)

Density (g/cm 3 )

0.917

1.0000

19.31

0.000164

0.001185

Substance

Human Fat Cork Table Sugar Balsa Wood Earth

Density (g/cm 3 )

0.94

0.22–0.26

1.59

0.12

5.54

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Measurement and Units • What is the density of glass (in grams per cubic centimeter) if a sample weighing 26.43 g has a volume of 12.40 cm 3 ?

• Chloroform, a substance once used as an anesthetic, has a density of 1.483 g/mL at 20 °C. How many mL would you use if you needed 9.37 g?

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Measurement and Units 26

Measurement and Units •

Temperature Conversions:

• The Kelvin and Celsius degree are essentially the same because both are one hundredth of the interval between freezing and boiling points of water.

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Measurement and Units •

Temperature Conversions:

• Celsius (°C) — Kelvin temperature conversion: Kelvin (K) = °C + 273.15

• Fahrenheit (°F) — Celsius temperature conversions: 

C

 5 ( 

F

9  32 ) 

F

 9 5

C

 32 28

Measurement and Units • Carry out the indicated temperature conversions: (a) –78°C = ? K (b) 158 °C = ? °F (c) 375 K = ?

°C (d) 98.6

°F = ? °C (e) 98.6

°F = ? K 29

English System of Units Volume: Gallon (gal) = 4 quarts (qt) = 8 pints (pt) = 128 fluid ounces (fl oz) Length: Mile (mi) = 1760 yards (yd) = 5280 feet (ft) = 63360 inches (in) Mass: 1 ton = 2000 pounds (lb) = 32000 ounces (oz) 30

Measurement and Units •

Dimensional-Analysis method

uses a conversion factor to express the relationship between units.

Original Quantity × ConversionFactor = Equivalent Quantity

Example: Express 2.50 kg in lb.

ConversionFactor: 1.00 kg = 2.205 lb arranged as 2.205 lb 1.00 kg \ 2.50 kg = 6.00 lb (correct to 3 significant figures) 31

Common Conversion Factors

2.54 cm = 1 in 454 g = 1 lb 0.946 L = 1 qt 1 mL = 1 cm

3

= 1 g water

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Ball Park Conversion Factors

1 m ~ 1 yd 1 L ~ 1 qt 1 kg ~ 2 lb

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Conversion Factors 34

Conversion Factors 35

Conversion Factors • The volcanic explosion that destroyed Krakatau on August 17, 1883, released an estimated 4.3 cubic miles (mi 3 ) of debris into the atmosphere. In SI units, how many cubic meters (m 3 ) were released?

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Conversion Factors • How many meters are there in a marathon race (26 miles and 385 yd)?

• How large, in cubic centimeters, is the volume of a red blood cell if the cell has a circular shape with a diameter of 6.0 x 10 –6 m and a height of 2.0 x 10 –6 m?

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Interesting Conversion Problem

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Interesting Conversion Problem

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Interesting Conversion Problem

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Interesting Conversion Problem • A test rat weighs 512 g • The rat begins to eat Bayer Aspirin tablets 1 at a time.

• How many tablets (on average) will have been consumed when the rat dies?

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