chapter 1

Find the radius ( r ) in centimeters of a spherical water droplet with a volume ( V ) of 0.058 cm^3 . For a sphere, V = (4>3) pr 3 .

0.24 cm

Glycerol is a syrupy liquid often used in cosmetics and soaps. A 3.25 L sample of pure glycerol has a mass of 4.10 * 103 g . What is the density of glycerol in g/cm^3 ?

1.26 g /cm^3

How many cubic centimeters are there in 2.11 yd^3?

1.61 * 106 cm^3

Approximate the percent increase in waist size that occurs when a 155 lb person gains 40.0 lb of fat. Assume that the volume of the person can be modeled by a cylinder that is 4.0 feet tall. The average density of a human is about 1.0 g/cm^3 , and the density of fat is 0.918 g/cm^3 .

13% increase

Convert 1.76 yards to centimeters.

161 cm

Convert 9255 cm 3 to gallons.

2.446 gal

A backyard swimming pool holds 185 cubic yards (yd^3) of water. What is the mass of the water in pounds?

3.11 * 10^5 lb

A sick child has a temperature of 40.00 °C. What is the child's temperature in (a) K and (b) °F?

313.15 K 104.00 F

A cube has an edge length of 7 cm. If it is divided up into 1 cm cubes, how many 1 cm cubes are there?

343 1 cm cubes

A metal cube has an edge length of 11.4 mm and a mass of 6.67 g. Calculate the density of the metal

4.50 g/cm^3 The metal is titanium.

Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than 2.40 g of sodium per day. A particular snack mix contains 1.25 g of salt per 100 g of the mix. What mass of the snack mix can an adult consume and still be within the FDA limit? (Assume three significant figures for 100 g.)

488 grams

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0 * 10-13 cm . The hydrogen atom itself has a radius of approximately 52.9 pm. What fraction of the space within the atom is occupied by the nucleus?

6.8 * 10 ^-15

A chemist mixes sodium with water and witnesses a violent reaction between the metal and water. This is best classified as a) an observation. b) a law. c) a hypothesis. d) a theory.

a

A wooden block has a volume of 18.5 in^3 . Express the volume of the cube in cm^3 . a) 303 cm^3 b) 47.0 cm^3 c) 1.13 cm^3 d) 7.28 cm^3

a

Perform the calculation to the correct number of significant figures. (43.998 * 0.00552)/2.002 a) 0.121 b) 0.12 c) 0.12131 d) 0.1213

a

What is the mass of a 1.75 L sample of a liquid that has a density of 0.921 g/mL? a) 1.61 * 10 ^3 g b) 1.61 * 10 ^-3 g c) 1.90 * 10^3 g d) 1.90 * 10^ -3 g

a

Perform each calculation to the correct number of significant figures. (a) 3.10007 * 9.441 * 0.0301 / 2.31 (b) 0.881 +132.1 -12.02 (c) 2.5110 * 21.20 / (44.11 + 1.223) (d) (12.01 * 0.3) + 4.811

a) 0.381 b) 121.0 c) 1.174 d) 8

Calculate to the correct number of significant figures. a. 9.15 / 4.970 b. 1.54 * 0.03060 * 0.69 c. 27.5 * 1.82 / 100.04 d. (2.290 * 10^6) / (6.7 * 10^4)

a. 1.84 b. 0.033 c. 0.500 d. 34

A house has an area of 195 m^2 . What is its area in each unit? a. km^2 b. dm^2 c. cm^2

a. 1.95 * 10^-4 km^2 b. 1.95 * 10^4 dm^2 c. 1.95 * 10^6 cm^2

Do each calculation without using your calculator and give the answers to the correct number of significant figures. a. 1.76 * 10^-3/8.0 * 10^2 b. 1.87 * 10^-2 + 2 * 10^-4 - 3.0 * 10^-3 c. [(1.36 * 10^5)(0.000322)/0.0824](129.2)

a. 2.2 * 10^-6 b. 0.0159 c. 6.9 * 10^4

Calculate to the correct number of significant figures. a. (24.6681 * 2.38) + 332.58 b. (85.3 - 21.489) / 0.0059 c. (512 / 986.7) + 5.44 d. 3(28.7 * 10^5) / 48.5334 + 144.99

a. 391.3 b. 1.1 * 10^4 c. 5.96 d. 5.93 * 10^4

Use scientific notation to express each quantity with only the base units (no prefix multipliers). a. 4.5 ns b. 18 fs c. 128 pm d. 35 mm

a. 4.5 * 10^-9 s b. 1.8 * 10^-14 s c. 1.28 * 10^-10 m d. 3.5 * 10^-5 m

Calculate to the correct number of significant figures. a. 43.7 - 2.341 b. 17.6 + 2.838 + 2.3 + 110.77 c. 19.6 + 58.33 - 4.974 d. 5.99 - 5.572

a. 41.4 b. 133.5 c. 73.0 d. 0.42

Classify each change as physical or chemical. a. Natural gas burns in a stove. b. The liquid propane in a gas grill evaporates because the valve was left open. c. The liquid propane in a gas grill burns in a flame. d. A bicycle frame rusts on repeated exposure to air and water

a. chemical b. physical c. chemical d. chemical

Classify each property as physical or chemical. a. the tendency of ethyl alcohol to burn b. the shine on silver c. the odor of paint thinner d. the flammability of propane gas

a. chemical b. physical c. physical d. chemical

Which numbers are exact (and therefore have an unlimited number of significant figures)? a. p = 3.14 b. 12 inches = 1 foot c. EPA gas mileage rating of 26 miles per gallon d. 1 gross = 144

a. not exact b. exact c. not exact d. exact

Classify each statement as an observation, a law, or a theory. a. All matter is made of tiny, indestructible particles called atoms. b. When iron rusts in a closed container, the mass of the container and its contents does not change. c. In chemical reactions, matter is neither created nor destroyed. d. When a match burns, heat is released.

a. theory b. observation c. law d. observation

Express the quantity 33.2 * 10^ -4 m in mm. a) 33.2 mm b) 3.32 mm c) 0.332 mm d) 3.32 * 10^ -6 mm

b

Convert 85.0 °F to K. a) 181.1 K b) 358 K c) 29.4 K d) 302.6 K

d

A new penny has a mass of 2.49 g and a volume of 0.349 cm^3 . Is the penny made of pure copper? Explain.

no

Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 175 L tanks. The liquid vaporizes quickly to gaseous nitrogen (which has a density of 1.15 g/L at room temperature and atmospheric pressure) when the liquid is removed from the tank. Suppose that all 175 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 10.00 m * 10.00 m * 2.50 m . What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?

0.492

A length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω/km). What is the overall resistance of the wire?

0.661 Ω

A force of 2.31 * 10^4 N is applied to a diver's face mask that has an area of 125 cm^2 . Find the pressure in atm on the face mask.

18.2 atm

The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of 6.02 * 10^23 hydrogen atoms. The diameter of a ping pong ball is 4.0 cm. Find the length in kilometers of a row of 6.02 * 10^23 ping pong balls.

2.4 * 10^19 km

Find the density, in g/cm^3 , of a metal cube with a mass of 50.3 g and an edge length ( l ) of 2.65 cm. For a cube, V = l^3.

2.70 g/cm^3

A drop of gasoline has a mass of 22 mg and a density of 0.754 g/cm^3 . What is its volume in cubic centimeters?

2.9 * 10-2 cm^3

Calculate the displacement (the total volume of the cylinders through which the pistons move) of a 5.70 L automobile engine in cubic inches.

348 in^3

A European automobile has a gas mileage of 17 km/L. What is the gas mileage in miles per gallon?

4.0 * 10^1 mi/gal

Find the density (in g>cm^3) of a metal cylinder with a mass ( m ) of 8.3 g, a length ( l ) of 1.94 cm, and a radius ( r ) of 0.55 cm. For a cylinder, v = (pi)2l .

4.5 g/cm^3

A runner wants to run 10.0 km. She knows that her running pace is 7.5 miles per hour. How many minutes must she run?

5.0 * 10^1 min

Recall from Section 1.7 that in 1997 Los Angeles County air had carbon monoxide (CO) levels of 15.0 ppm. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many milligrams of carbon monoxide does the average person inhale in an 8-hour period at this level of carbon monoxide pollution? Assume that the carbon monoxide has a density of 1.2 g>L. (Hint: 15.0 ppm CO means 15.0 L CO per 10 6 L air.)

9.0 * 10^1 mg CO

We put a drop of water into a container and seal the container. The drop of water then vaporizes. Does the mass of the sealed container and its contents change upon vaporization?

No, the mass does not change. The water vaporizes and becomes a gas, but the water molecules are still present within the fl ask and have the same mass.

Perform each calculation to the correct number of significant figures. (a) 1.10 * 0.5120 * 4.0015 , 3.4555 (b) 0.355 +105.1 -100.5820 (c) 4.562 * 3.99870 / (452.6755 - 452.33) (d) (14.84 * 0.55) - 8.02

a) 0.652 b) 4.9 c) 53 d) 0.1

How many significant figures are in each number? (a) 554 km (b) 7 pennies (c) 1.01 * 105 m (d) 0.00099 s (e) 1.4500 km (f) 21,000 m

a) 3 b) unlimited c) 3 d) 2 e) 5 f) 2

How many significant figures are in each number? (a) 0.04450 m (b) 5.0003 km (c) 10 dm = 1 m (d) 1.000 * 105 s (e) 0.00002 mm (f) 10,000 m

a) 4 b) 5 c) unlimited d) 4 e) 1 f) ambiguous

Classify each of the listed properties of isopropyl alcohol (also known as rubbing alcohol) as physical or chemical. a. colorless b. flammable c. liquid at room temperature d. density = 0.79 g/mL e. mixes with water

a)physical, b)chemical, c) physical, d) physical, e)physical

A thief uses a can of sand to replace a solid gold cylinder that sits on a weight-sensitive, alarmed pedestal. The can of sand and the gold cylinder have exactly the same dimensions ( length = 22 cm and radius = 3.8 cm ). a. Calculate the mass of each cylinder (ignore the mass of the can itself). ( density of gold = 19.3 g/cm^3 , density of sand = 3.00 g/cm^3 ) b. Did the thief set off the alarm? Explain.

a. mass of can of gold = 1.9 * 10^4 g mass of can of sand = 3.0 * 10^3 g b. Yes, the thief sets off the trap because the can of sand is lighter than the gold cylinder.

Classify each substance as a pure substance or a mixture. If it is a pure substance, classify it as an element or a compound. If it is a mixture, classify it as homogeneous or heterogeneous. a. sweat b. carbon dioxide c. aluminum d. vegetable soup

a. mixture, homogeneous b. pure substance, compound c. pure substance, element d. mixture, heterogeneous

For each box, examine the blocks attached to the balances. Based on their positions and sizes, determine which block is more dense (the dark block or the lighter-colored block), or if the relative densities cannot be determined. (Think carefully about the information being shown.)

a. the dark block b. the light-colored block c. cannot tell

Perform the calculation to the correct number of significant figures. (8.01 - 7.50)/3.002 a) 0.1698867 b) 0.17 c) 0.170 d) 0.1700

b

Which property of rubbing alcohol is a chemical property? a) its density (0.786 g>cm 3 ) b) its fl ammability c) its boiling point (82.5 °C) d) its melting point (-89 °C)

b

Convert 1285 cm ^2 to m ^2 . a) 1.285 * 107 m ^2 b) 12.85 m ^2 c) 0.1285 m ^2 d) 1.285 * 105 m^ 2

c

German automobile gets a gas mileage of 22 km/L. Convert this quantity to miles per gallon. a) 9.4 mi/gal b) 1.3 * 10 ^2 mi/gal c) 52 mi/gallon d) 3.6 mi/gallon

c

Three samples, each of a different substance, are weighed and their volume is measured. The results are tabulated below. List the substances in order of decreasing density. Substance I 10.0 g 10.0 mL Substance II 10.0 kg 12.0 L Substance III 12.0 mg 10.0 μL a) III > II > I b) I > II > III c) III > I > II d) II > I > III

c

A solid metal sphere has a radius of 3.53 cm and a mass of 1.796 kg. What is the density of the metal in g/cm^3 ? (The volume of sphere is V = (4/3)(pi)r^3.) a) 34.4 g>cm ^3 b) 0.103 g>cm ^3 c) 121 g>cm ^3 d) 9.75 g>cm^ 3

d

Determine whether each change is physical or chemical. What kind of property (chemical or physical) is demonstrated in each case? (a) the evaporation of rubbing alcohol (b) the burning of lamp oil (c) the bleaching of hair with hydrogen peroxide (d) the forming of frost on a cold night

(a) When rubbing alcohol evaporates, it changes from liquid to gas, but it remains alcohol—this is a physical change. The volatility (the ability to evaporate easily) of alcohol is a therefore a physical property. (b) Lamp oil burns because it reacts with oxygen in air to form carbon dioxide and water—this is a chemical change. The flammability of lamp oil is therefore a chemical property. (c) Applying hydrogen peroxide to hair changes pigment molecules in hair that give it color—this is a chemical change. The susceptibility of hair to bleaching is therefore a chemical property. (d) Frost forms on a cold night because water vapor in air changes its state to form solid ice—this is a physical change. The temperature at which water freezes is therefore a physical property.

Which statement best explains the difference between a law and a theory? (a) A law is truth; a theory is mere speculation. (b) A law summarizes a series of related observations; a theory gives the underlying reasons for them. (c) A theory describes what nature does; a law describes why nature does it.

(b) A law only summarizes a series of related observations; a theory gives the underlying reasons for them.

The density of copper decreases as temperature increases (as does the density of most substances). Which statement accurately describes the changes in a sample of copper when it is warmed from room temperature to 95 °C? (a) The sample will become lighter. (b) The sample will become heavier. (c) The sample will expand. (d) The sample will contract.

(c) The copper sample expands. However, because its mass remains constant while its volume increases, its density decreases.

Suppose you design a new thermometer called the X thermometer. On the X scale the boiling point of water is 130 °X and the freezing point of water is 10 °X. At what temperature will the readings on the Fahrenheit and X thermometers be the same?

-34 F

The coldest temperature ever measured in the United States is -80 °F on January 23, 1971, in Prospect Creek, Alaska. Convert that temperature to °C and K. (Assume that -80 °F is precise to two significant figures.)

-62.2 C, 210.9 K

The average U.S. farm occupies 435 acres. How many square miles is this? ( 1 acre = 43,560 ft^2 , 1 mile = 5280 ft )

0.680 mi^2

Find the radius ( r ) of an aluminum cylinder that is 2.00 cm long and has a mass of 12.4 g. For a cylinder, V = (pi)r^2l.

0.855 cm

An acetaminophen suspension for infants contains 80 mg/0.80 mL suspension. The recommended dose is 15 mg/kg body weight. How many mL of this suspension should be given to an infant weighing 14 lb? (Assume two significant figures.)

0.95 mL

Kinetic energy can be defined as 1/2 mv^2 or as 3/2 PV. Show that the derived SI units of each of these terms are those of energy. (Pressure is force/area and force is mass * acceleration.)

1 J = 1 kg m^2/s^2 m = kg, v^b^2 = (m/s)^2 mv = kg m^2/s 2 P = N>m^2 = kg m/s^2/m^2 = kg/m s^2 V = m^3 PV = kg m^3/m s^2 = kg m^2/s^2

Backpackers often use canisters of white gas to fuel a cooking stove's burner. If one canister contains 1.45 L of white gas, and the density of the gas is 0.710 g/cm^3 , what is the mass of the fuel in kilograms?

1.03 kg

The mass of fuel in a jet must be calculated before each flight to ensure that the jet is not too heavy to fly. A 747 is fueled with 173,231 L of jet fuel. If the density of the fuel is 0.768 g/cm^3 , what is the mass of the fuel in kilograms?

1.33 * 105 kg

Convert 1.8 quarts to cubic centimeters.

1.7 * 103 cm^3

How many 1 cm squares would it take to construct a square that is 1 m on each side?

10,000 1 cm squares

A man receives a platinum ring from his fiancée. Before the wedding, he notices that the ring feels a little light for its size and decides to determine its density. He places the ring on a balance and finds that it has a mass of 3.15 grams. He then finds that the ring displaces 0.233 cm 3 of water. Is the ring made of platinum ? (Note: The volume of irregularly shaped objects is often measured by the displacement of water. To use this method, the object is placed in water and the change in volume of the water is measured. This increase in the total volume represents the volume of water displaced by the object and is equal to the volume of the object.)

13.5 g>cm^3

A small airplane takes on 245 L of fuel. If the density of the fuel is 0.821 g/mL, what mass of fuel has the airplane taken on?

201. * 10^3 g

The woman in this example is shocked that the ring is fake and returns it. She buys a new ring that has a mass of 4.53 g and a volume of 0.212 cm^3 . Is the new ring genuine?

21.4 g/cm^3 . This matches the density of platinum.

The density of titanium is 4.51 g/cm^3. What is the volume (in cubic inches) of 3.5 lb of titanium?

22 in^3

Convert 288 cm to yards.

3.15 yd

There are exactly 60 seconds in a minute, there are exactly 60 minutes in an hour, there are exactly 24 hours in a mean solar day, and there are 365.24 solar days in a solar year. How many seconds are in a solar year? Be sure to give your answer with the correct number of significant figures.

3.1557 * 10^7 s /solar year

A vineyard has 145 acres of Chardonnay grapes. A particular soil supplement requires 5.50 grams for every square meter of vineyard. How many kilograms of the soil supplement are required for the entire vineyard? (1 km^2 = 247 acres)

3.23 * 103 kg

The Toyota Prius, a hybrid electric vehicle, has an EPA gas mileage rating of 52 mi/gal in the city. How many kilometers can the Prius travel on 15 liters of gasoline?

3.3 * 10^2 km

A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm^3?

7.6 g /cm^3

Force is defined as mass times acceleration. Starting with SI base units, derive a unit for force. Using SI prefixes, suggest a convenient unit for the force resulting from a collision with a 10-ton trailer truck moving at 55 miles per hour and for the force resulting from the collision of a molecule of mass around 10-20 kg moving almost at the speed of light (3 * 108 m>s) with the wall of its container. (Assume a 1-second deceleration time for both collisions.)

F = kg(m/s^2) = N (for newton), kN, pN

A volatile liquid (one that easily evaporates) is put into a jar and the jar is then sealed. Does the mass of the sealed jar and its contents change upon the vaporization of the liquid?

No. Since the container is sealed the atoms and molecules can move around, but they cannot leave. If no atoms or molecules can leave, the mass must be constant.

What prefi x multiplier is appropriate for reporting a measurement of 5.57 * 10 -5 m?

The prefi x micro (10-6) is appropriate. The measurement would be reported as 55.7 μm.

Convert each temperature a. 32 °F to °C (temperature at which water freezes) b. 77 K to °F (temperature of liquid nitrogen) c. -109 °F to °C (temperature of dry ice) d. 98.6 °F to K (body temperature)

a. 0 C b. -321 F c. -78.3 F d. 310.2 K

Use the prefix multipliers to express each measurement without any exponents. a. 1.2 * 10^-9 m b. 22 * 10^-15 s c. 1.5 * 10^9 g d. 3.5 * 10^6 L

a. 1.2 nm b. 22 fs c. 1.5 Gg d. 3.5 ML

Round each number to four significant figures. a. 156.852 b. 156.842 c. 156.849 d. 156.899

a. 156.9 b. 156.8 c. 156.8 d. 156.9

Perform each unit conversion. a. 27.8 L to cm^3 b. 1898 mg to kg c. 198 km to cm

a. 2.79 * 10 4 cm^3 b. 1.898 * 10^-3 kg c. 1.98 * 10^7 cm

Express the quantity 254,998 m in each unit. a. km b. Mm c. mm d. cm

a. 254.998 km b. 2.54998 * 10^ -1 Mm c. 254998 * 10^3 mm d. 254998 * 10^2 cm

Gallium is a solid metal at room temperature but will melt to a liquid in your hand. The melting point of gallium is 85.6 °F. What is this temperature on (a) the Celsius scale and (b) the Kelvin scale?

a. 29.8 C b. 302.9 K

How many significant figures are in each number? a. 0.000312 m b. 312,000 s c. 3.12 * 10^5 km d. 13,127 s e. 2000

a. 3 b. ambiguous, without more information assume three significant figures c. 3 d. 5 e. ambiguous, without more information assume one significant figure

Ethylene glycol (antifreeze) has a density of 1.11 g/cm^3 . a. What is the mass in g of 417 mL of this liquid? b. What is the volume in L of 4.1 kg of this liquid?

a. 463 g b. 3.7 L

Perform each unit conversion. a. 154 cm to in b. 3.14 kg to g c. 3.5 L to qt d. 109 mm to in

a. 60.6 in b. 3.14 * 10^3 g c. 3.7 qt d. 4.29 in

Determine whether each change is physical or chemical. What kind of property (chemical or physical) is demonstrated in each case? (a) A copper wire is hammered flat. (b) A nickel dissolves in acid to form a blue-green solution. (c) Dry ice sublimes without melting. (d) A match ignites when struck on a flint.

a. The composition of the copper is not changing; thus, being hammered flat is a physical change that signifies a physical property. b. The dissolution and color change of the nickel indicate that it is undergoing a chemical change and exhibiting a chemical property. c. Sublimation is a physical change indicative of a physical property. d. When a match ignites, a chemical change begins as the match reacts with oxygen to form carbon dioxide and water. Flammability is a chemical property.

Classify each property as intensive or extensive. a. volume b. boiling point c. temperature d. electrical conductivity e. energy

a. extensive b. intensive c. intensive d. intensive e. extensive

Identify each statement as being most like an observation, a law, or a theory. a. All coastal areas experience two high tides and two low tides each day. b. The tides in Earth's oceans are caused mainly by the gravitational attraction of the moon. c. Yesterday, high tide in San Francisco Bay occurred at 2:43 a.m. and 3:07 p.m. d. Tides are higher at the full moon and new moon than at other times of the month.

a. law b. theory c. observation d. law

Which change is a physical change? a) wood burning b) iron rusting c) dynamite exploding d) gasoline evaporating

d