Chapter 3

Chapter 3

Scientific Measurement

Measurement

A quantity that has both a number and a unit.Units used in sciences are those of the International System of Measurements (SI).

Sometimes in chemistry numbers can be very large or very small

1 gram of hydrogen = 602,000,000,000,000,000,000,000 atoms

Mass of an atom of gold =0.000 000 000 000 000 000 000 327 gram

Scientific Notation

A given number is written as the product of two numbers: a coefficient and 10 raised to a power. M x 10n

Example: 602,000,000,000,000,000,000,000 will be written as 6.02 x 1023.

Accuracy, Precision, and ErrorAccuracy is a measure of how close a measurement comes to the actual or true valuePrecision is a measure of how close a series of measurements are to one another

Determining ErrorTable T % error = x 100%

A student estimated the volume of a liquid in a beaker as 200mL. When she poured the liquid into a graduated cylinder she measured the volume as 208mL. Calculate the % error.

Significant Figures in Measurement

Include all of the digits that are known, plus the last digit that is estimated.

The Rules of Significant Figures

1. Every nonzero digit is significant, numbers 1-9.o Example: 24.7 meters (3 sig. figs.)

2. Zeros between nonzero digits are significant.o Example: 40.79 meters (4 sig. figs.)

3. Zeros appearing to the left of nonzero digits are not significant. They are only place holders.o Example: 0.0071 (2 sig. figs)

7.1 x 10-3 (2 sig. figs.)

4. Zeros at the end of a number and to the right of a decimal point are significant.o Example: 43.00 meters (4 sig. figs.)

1.010 meters (4 sig. figs)5. Zeros at the right end of a measurement that

lie to the left of an understood decimal point are not significant.o Example: 300 meters (1 sig. figs.)

27,210 meters (4 sig. figs.)

Practice Problems

• How many significant figures are in each measurement?

• 123 meters = • 9.8000 x 104 m =• 0.07080 m =• 40,506 mm = • 98, 000 m =

35

2

45

Practice Problems

Count the significant figures in each length0.05730 meters 8765 meters 0.00073 meters 40.007 meters

4

4

5

2

Practice Problems

How many significant figures are in each measurement?143 grams0.074 meters8.750 x 10-2 grams1.072 meters

3

2

4

4

Significant Figures in Calculations

A calculated answer cannot be more precise than the least precise measurement from which it was calculated.

Sample Problems

Round off each measurement to the number of significant figures shown in parentheses. 314.721 meters (four) 0.001775 meter (two)8792 meters (two)

0.0018314.7

8800

Practice Problems

•Round each measurement to three significant figures.

•87.073 meters•4.3621 x 108 meters•0.01552 meter•9009 meters•1.7777 x 10-3

meter•629.55 meters

87.1

0.0155

9010

1.78 x 10-3

4.36 x 108

630.

Addition and Subtraction

The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places

Sample Problem

Calculate the sum of the three measurements. Give the answer to the correct number of significant figures.

12.52 meters 349.0 meters + 8.24 meters

369.76

Practice Problems

Perform each operation. Express your answers to the correct number of significant figures.61.2 meters + 9.35 meters + 8.6 meters9.44 meters – 2.11 meters1.36 meters + 10.17 meters34.61 meters – 17.3 meters

79.27.3311.5317.3

Multiplication and Division

You need to round the answer to the same number of significant figures as the measurement with the least number of significant figures.

Sample Problem

Perform the following operations. Give the answers to the correct number of significant figures.7.55 meters x 0.34 meter2.10 meters x 0.70 meter2.4526 meters / 8.4 meters

2.6 m2

1.5 m2

0.29 m

Practice Problems

Solve each problem. Give your answers to the correct number of significant figures.8.3 meters x 2.22 meters8432 meters / 12.5 meters Calculate the volume of a warehouse that has inside dimensions of 22.4 meters by 11.3 meters by 5.2 meters (volume = l x w x h)

18 m2

675 m

1300 m3

Section Assessment

•A technician experimentally determined the boiling point of octane to be 124.1C. The actual boiling point of octane is 125.7C. Calculate the percent error.

1.27 %

Section Assessment

•Determine the number of significant figures in each of the following.

a. 0.070020 meterb. 10,800 metersc. 5.00 cubic meters

33

5

The International System of Units (SI)Table D

LengthMeters (m)

MassKilograms (Kg)

VolumeLiter (L)cm3

Temperature

A measure of how hot or cold an object is.Heat moves from the object at the higher temperature to the object at the lower temperature

Celsius (C)• Freezing point of water (0C)• Boiling point of water (100C)Kelvin (K)• Freezing point of water (273 K)• Boiling point of water (373 K)• Absolute Zero (0K), the coldest possible

temperature ( ? Celsius)K = C + 273C = K -273

Sample ProblemsNormal human body temperature is 37 C. What is that temperature in Kelvins?

Liquid nitrogen boils at 77.2 K. What is this temperature in degrees Celsius?

310 K -195.8 K

The element silver melts at 960.8 C and boils at 2212 C. Express these temperatures in Kelvins.

Melting Point: 1,233.8 K

Boiling Point: 2485 K

Section Assessment

What is the volume of a paperback book, 21cm tall, 12cm wide, and 3.5cm thick?

Surgical instruments may be sterilized by heating at 170 C for 1.5 hr. Convert 170 C to Kelvins.

882 cm3

443 K

Conversion Problems• A conversion factor is a ratio of equivalent

measurements.• When a measurement is multiplied by a conversion

factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.

Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements

Sample Problems

How many seconds are in a workday that lasts exactly 8 hours?

How many minutes are there in exactly one week?

How many seconds are in exactly a 40 hour work week?

10,080 minutes

28800 seconds

144,000 seconds

Converting Between Units

Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis

Sample Exercise•Convert the following

a. 0.044 km to metersb. 4.6 mg to gramsc. 0.107 g to centigramsd. 7.38 g to kilogramse. 6.7 s to millisecondsf. 94.5 g to micrograms

44 m

10.7 cg

0.00738 kg6700 ms

94500000 μg

0.0046 g

Section Assessment

Convert the following. •Light travels at a speed of 3.00 x 1010 cm/sec. What is the speed of light in kilometers/hour?

Density (Table T)

Density is an intensive property that depends only on the composition of a substance, not on the size of the sample.The density of a substance generally decreases as its temperature increases (inverse relationship)

Practice Problems

A copper (Cu) penny has a mass of 3.1g and a volume of 0.35 mL. What is the density of copper?

8.9 g/mL

A student finds a shiny piece of metal that she thinks is aluminum (Al). In the lab, she determines that the metal has a volume of 245 cm3 and a mass of 612 g. Calculate the density. Is the metal aluminum?

2.45 g/cm3

Practice Problems

A bar of silver (Ag) has a mass of 68.0 g and a volume 6.48 cm3. What is the density of silver?

What is the density of silver (Ag) if a 27.50 g sample has a volume of 2.62 mL?

10.5 g/cm3

10.5 g/cm3

A sample of ethylene glycol has a volume of 45.8 mL. What is the mass of this sample if the density of ethylene glycol is 1.11g/mL?

50.8 g

Sample Problem

• What is the volume of a pure silver coin that has a mass of 14 g.

1.33 cm3

Section Assessment

What is the volume in cubic centimeters, of a sample of cough syrup that has a mass of 50.0 g? The density of cough syrup is 0.950 g/ cm3.

52.6 cm3