3.2 Units of Measurement > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems

3.2 Units of Measurement > 2OB OBJECTIVES: 1.Discuss commonly used scientific quantities and their units. 2.Explain the commonly used metric prefixes and use them. 3.Convert between the Celsius and the Kelvin temperature scales. 4.Explain and calculate density. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

3.2 Units of Measurement > 3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The standards of measurement used in science are those of the metric system. All metric units are based on multiples of 10. As a result, you can convert between units easily. Using SI Units

3.2 Units of Measurement > 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The metric system was originally established in France in The International System of Units (abbreviated SI) is a revised version of the metric system. Using SI Units

3.2 Units of Measurement > 5 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units There are seven SI base units. From these base units, all other SI units of measurement can be derived. SI Base Units QuantitySI base unit Symbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of substance molemol

3.2 Units of Measurement > 6 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. In SI, the basic unit of length, or linear measure, is the meter (m). Units of Length Using SI Units

3.2 Units of Measurement > 7 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units The table below lists the prefixes in common use. Units of Length Commonly Used Metric Prefixes PrefixSymbolMeaningFactor megaM1 million times larger than the unit it precedes10 6 kilok1000 times larger than the unit it precedes10 3 decid10 times smaller than the unit it precedes10 -1 centic100 times smaller than the unit it precedes10 -2 millim1000 times smaller than the unit it precedes10 -3 microμ1 million times smaller than the unit it precedes10 -6 nanon1 billion times smaller than the unit it precedes10 -9 picop1 trillion times smaller than the unit it precedes10 -12

3.2 Units of Measurement > 8 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. For example, the prefix milli- means 1/1000 (one-thousandth), so a millimeter (mm) is 1/1000 of a meter, or m. A hyphen (-) measures about 1 mm. For large distances, it is most appropriate to express measurements in kilometers (km). The prefix kilo- means 1000, so 1 km equals 1000 m. Units of Length Using SI Units

3.2 Units of Measurement > 9 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The space occupied by any sample of matter is called its volume. You calculate the volume of any cubic or rectangular solid by multiplying its length by its width by its height. The unit for volume is thus derived from the units of length. Units of Volume Using SI Units

3.2 Units of Measurement > 10 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge. This volume is a cubic meter (m 3 ). A more convenient unit of volume for everyday use is the liter, a non-SI unit. A liter (L) is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm x 10 cm x 10 cm = 1000 cm 3 = 1 L). Units of Volume Using SI Units

3.2 Units of Measurement > 11 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. A smaller, non-SI unit of volume is the milliliter (mL); 1 mL is 1/1000 of a liter. Thus, there are 1000 mL in 1 L. Because 1 L is defined as 1000 cm 3, 1 mL and 1 cm 3 are the same volume. The units milliliter and cubic centimeter are thus used interchangeably. Units of Volume Using SI Units

3.2 Units of Measurement > 12 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. These figures give you some idea of the relative sizes of a liter and a milliliter. Units of Volume Using SI Units 1 mL 1 L

3.2 Units of Measurement > 13 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The volume of substances will change with temperature, so accurate volume-measuring devices are calibrated at a given temperature—usually 20 degrees Celsius (20°C), which is about normal room temperature. Units of Volume Using SI Units

3.2 Units of Measurement > 14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass. Units of Mass Using SI Units

3.2 Units of Measurement > 15 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units The relationships among units of mass are shown in the table below. Units of Mass Metric Units of Mass UnitSymbolRelationshipExample Kilogram (base unit) kg1 kg = 10 3 gsmall textbook ≈ 1 kg Gramg1 g = kgdollar bill ≈ 1 g Milligrammg10 3 mg = 1 gten grains of salt ≈ 1 mg Microgramμgμg10 6 μg = 1 gparticle of baking powder ≈ 1 μg

3.2 Units of Measurement > 16 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. What is the SI unit of volume?

3.2 Units of Measurement > 17 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. What is the SI unit of volume? The SI unit of volume is the cubic meter (m 3 ). A liter (L) can be converted to the SI unit of volume, because a liter is defined as 1000 cm 3.

3.2 Units of Measurement > 18 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Temperature is a measure of how hot or cold an object is. When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature. Temperature Scales

3.2 Units of Measurement > 19 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. Temperature Scales

3.2 Units of Measurement > 20 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The Celsius scale sets the freezing point of water at 0°C and the boiling point of water at 100°C. Temperature Scales

3.2 Units of Measurement > 21 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Another temperature scale used in the physical sciences is the Kelvin, or absolute, scale. On the Kelvin scale, the freezing point of water is 273 K, and the boiling point is 373 K. Temperature Scales

3.2 Units of Measurement > 22 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 1 degree Celsius scale = 1 Kelvin You simply add or subtract 273, as shown in the following equations. Temperature Scales K = °C °C = K – 273

3.2 Units of Measurement > 23 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 Converting Between Temperature Scales Normal human body temperature is 37°C. What is this temperature in kelvins?

3.2 Units of Measurement > 24 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 Analyze List the known and the unknown. Use the known value and the equation K = °C to calculate the temperature in kelvins. KNOWN Temperature in °C = 37°C UNKNOWN Temperature in K = ? K 1

3.2 Units of Measurement > 25 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 Calculate Solve for the unknown. Substitute the known value for the Celsius temperature into the equation and solve. K = °C = = 310 K 2

3.2 Units of Measurement > 26 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 Evaluate Does the result make sense? You should expect a temperature in this range, since the freezing point of water is 273 K and the boiling point of water is 373 K; normal body temperature is between these two values. 3

3.2 Units of Measurement > 27 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Density What determines the density of a substance? Density

3.2 Units of Measurement > 28 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The relationship between an object’s mass and its volume tells you whether it will float or sink. Density is the ratio of the mass of an object to its volume. Density mass volume Density =

3.2 Units of Measurement > 29 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. When mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm 3 ). The SI unit of density is kilograms per cubic meter (kg/m 3 ). Density

3.2 Units of Measurement > 30 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. This figure compares the density of four substances: lithium, water, aluminum, and lead. Density Increasing density (mass per unit volume) 10.0 g 0.53 g/cm 3 19 cm g 10. cm g 3.7 cm g cm g/cm g/cm g/cm 3

3.2 Units of Measurement > 31 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Density is an intensive property that depends only on the composition of a substance, not the size of the sample. Density

3.2 Units of Measurement > 32 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. What happens to the density of a substance as its temperature increases? The volume of most substances increases as the temperature increases, while the mass remains the same. Since density is the ratio of an object’s mass to its volume, the density of a substance generally decreases as its temperature increases. Water is an important exception. Density

3.2 Units of Measurement > 33 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Calculating Density A copper penny has a mass of 3.1 g and a volume of 0.35 cm 3. What is the density of copper?

3.2 Units of Measurement > 34 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Analyze List the knowns and the unknown. Use the known values and the equation for density to solve the problem. KNOWNS mass = 3.1 g volume = 0.35 cm 3 UKNOWN density = ? g/cm 3 1

3.2 Units of Measurement > 35 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Density = mass volume Calculate Solve for the unknown. Start with the equation for density. 2

3.2 Units of Measurement > 36 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Calculate Solve for the unknown. Substitute the known values for mass and volume and then calculate. Sample Problem Density = 3.1 g 0.35 cm 3 = g/cm 3 = 8.9 g/cm 3 The calculated answer must be rounded to two significant figures.

3.2 Units of Measurement > 37 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Evaluate Does the result make sense? 3

3.2 Units of Measurement > 38 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Can you assume that something with a low weight will float in water?

3.2 Units of Measurement > 39 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. END OF 3.2