Chapter 1

A titanium bicycle frame displaces \(0.314 \mathrm{~L}\) of water and has a mass of 1.41 kg. What is the density of the titanium in \(g / \mathrm{cm}^{3} ?\)

Glycerol is a syrupy liquid often used in cosmetics and soaps. A \(3.25 \mathrm{~L}\) sample of pure glycerol has a mass of \(4.10 \times 10^{3} \mathrm{~g}\). What is the density of glycerol in \(\mathrm{g} / \mathrm{cm}^{3}\) ? MISSED THIS? Read Section 1.6; Watch KCV 1.6

A supposedly gold nugget displaces \(19.3 \mathrm{~mL}\) of water and has a mass of 371 g. Could the nugget be made of gold?

Ethylene glycol (antifreeze) has a density of \(1.11 \mathrm{~g} / \mathrm{cm}^{3}\) MISSED THIS? Read Section 1.6; Watch \(\mathrm{KCV} 1.6,\) IWE 1.10 a. What is the mass in g of \(417 \mathrm{~mL}\) of ethylene glycol? b. What is the volume in \(\mathrm{L}\) of \(4.1 \mathrm{~kg}\) of ethylene glycol?

Acetone (nail polish remover) has a density of \(0.7857 \mathrm{~g} / \mathrm{cm}^{3} .\) a. What is the mass in g of \(28.56 \mathrm{~mL}\) of acetone? b. What is the volume in \(\mathrm{mL}\) of \(6.54 \mathrm{~g}\) of acetone?

A small airplane takes on 245 L of fuel. If the density of the fuel is \(0.821 \mathrm{~g} / \mathrm{mL},\) what mass of fuel has the airplane taken on? MISSED THIS? Read Section 1.6; Watch KCV 1.6, IWE 1.10

For each number, underline the zeroes that are significant and draw an \(\mathbf{x}\) through the zeroes that are not. MISSED THIS? Read Section 1.7; Watch \(\mathrm{KCV} 1.6,\) IWE 1.5 a. \(1,050,501 \mathrm{~km}\) b. \(0.0020 \mathrm{~m}\) c. \(0.000000000000002 \mathrm{~s}\) d. \(0.001090 \mathrm{~cm}\)

For each number, underline the zeroes that are significant and draw an \(\mathbf{x}\) through the zeroes that are not. a. \(180,701 \mathrm{mi}\) b. \(0.001040 \mathrm{~m}\) c. \(0.005710 \mathrm{~km}\) d. \(90,201 \mathrm{~m}\)

How many significant figures are in each number? MISSED THIS? Read Section 1.7; Watch KCV \(1.6,\) IWE 1.5 a. \(0.000312 \mathrm{~m}\) b. \(312,000 \mathrm{~s}\) c. \(3.12 \times 10^{5} \mathrm{~km}\) d. 13,127 s e. 2000

How many significant figures are in each number? a. 0.1111 s b. \(0.007 \mathrm{~m}\) c. \(108,700 \mathrm{~km}\) d. \(1.563300 \times 10^{11} \mathrm{~m}\) e. 30,800

Which numbers are exact (and therefore have an unlimited number of significant figures)? MISSED THIS? Read Section 1.7; Watch KCV 1.6, IWE 1.5 a. \(\pi=3.14\) b. 12 in \(=1 \mathrm{ft}\) c. EPA gas mileage rating of 26 miles per gallon d. 1 gross \(=144\)

Indicate the number of significant figures in each number. If the number is an exact number, indicate an unlimited number of significant figures. a. 325,365,189 (July 4,2017 U.S. population) b. \(2.54 \mathrm{~cm}=1\) in c. \(11.4 \mathrm{~g} / \mathrm{cm}^{3}\) (density of lead) d. \(12=1\) dozen

Round each number to four significant figures. MISSED THIS? Read Section 1.7; Watch \(\mathrm{KCV} 1.7\) a. 156.852 b. 156.842 c. 156.849 d. 156.899

Round each number to three significant figures. a. 79,845.82 b. \(1.548937 \times 10^{7}\) c. 2.3499999995 d. 0.000045389

Calculate to the correct number of significant figures. MISSED THIS? Read Section 1.7; Watch KCVs 1.6, 1.7, IWEs 1.5, 1.6 a. \(9.15 \div 4.970\) b. \(1.54 \times 0.03060 \times 0.69\) c. \(27.5 \times 1.82 \div 100.04\) d. \(\left(2.290 \times 10^{6}\right) \div\left(6.7 \times 10^{4}\right)\)

Calculate to the correct number of significant figures. a. \(89.3 \times 77.0 \times 0.08\) b. \(\left(5.01 \times 10^{5}\right) \div\left(7.8 \times 10^{2}\right)\) c. \(4.005 \times 74 \times 0.007\) d. \(453 \div 2.031\)

Calculate to the correct number of significant figures. MISSED THIS? Read Section 1.7; Watch KCVs \(1.6,1.7,\) IWEs 1.5,1.6 a. \(43.7-2.341\) b. \(17.6+2.838+2.3+110.77\) c. \(19.6+58.33-4.974\) d. \(5.99-5.572\)

Calculate to the correct number of significant figures. a. \(0.004+0.09879\) b. \(1239.3+9.73+3.42\) c. \(2.4-1.777\) d. \(532+7.3-48.523\)

Calculate to the correct number of significant figures. a. \(\left[\left(1.7 \times 10^{6}\right) \div\left(2.63 \times 10^{5}\right)\right]+7.33\) b. \((568.99-232.1) \div 5.3\) c. \((9443+45-9.9) \times 8.1 \times 10^{6}\) d. \((3.14 \times 2.4367)-2.34\)

A flask containing \(11.7 \mathrm{~mL}\) of a liquid weighs \(132.8 \mathrm{~g}\) with the liquid in the flask and \(124.1 \mathrm{~g}\) when empty. Calculate the density of the liquid in \(\mathrm{g} / \mathrm{mL}\) to the correct number of significant digits. MISSED THIS? Read Section 1.6; Watch KCV 1.7, IWE 1.6

A flask containing \(9.55 \mathrm{~mL}\) of a liquid weighs \(157.2 \mathrm{~g}\) with the liquid in the flask and \(148.4 \mathrm{~g}\) when empty. Calculate the density of the liquid in \(\mathrm{g} / \mathrm{mL}\) to the correct number of significant digits.

Perform each unit conversion. MISSED THIS? Read Section 1.8; Watch \(K C V 1.8,\) IWE 1.8 a. \(27.8 \mathrm{~L}\) to \(\mathrm{cm}^{3}\) b. \(1898 \mathrm{mg}\) to \(\mathrm{kg}\) c. \(198 \mathrm{~km}\) to \(\mathrm{cm}\)

Perform each unit conversion. a. \(28.9 \mathrm{nm}\) to \(\mu \mathrm{m}\) b. \(1432 \mathrm{~cm}^{3}\) to \(\mathrm{L}\) c. 1211 Tm to Gm

Perform each unit conversion. MISSED THIS? Read Section 1.8; Watch \(\mathrm{KCV} 1.8, \mathrm{IWE} 1.8\) a. \(154 \mathrm{~cm}\) to in b. \(3.14 \mathrm{~kg}\) to \(\mathrm{g}\) c. \(3.5 \mathrm{~L}\) to \(\mathrm{qt}\) d. \(109 \mathrm{~mm}\) to in

A gas can holds 5.0 gal of gasoline. Express this quantity in \(\mathrm{cm}^{3}\).

A bedroom has a volume of \(115 \mathrm{~m}^{3} .\) What is its volume in each unit? a. \(\mathrm{km}^{3}\) b. \(\mathrm{dm}^{3}\) c. \(\mathrm{cm}^{3}\)

The average U.S. farm occupies 435 acres. How many square miles is this? \(\left(1\right.\) acre \(\left.=43,560 \mathrm{ft}^{2}, 1 \mathrm{mile}=5280 \mathrm{ft}\right)\) MISSED THIS? Read Section 1.8; Watch \(\mathrm{KCV} 1.8,\) IWE 1.9

Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre \(=43,560 \mathrm{ft}^{2}, 1 \mathrm{mi}=5280 \mathrm{ft}\) ). Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?

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

Determine the number of picoseconds in 2.0 hours.

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

At what temperatures are the readings on the Fahrenheit and Celsius thermometers the same?

On a new Jekyll temperature scale, water freezes at \(17^{\circ} \mathrm{J}\) and boils at \(97^{\circ} \mathrm{J} .\) On another new temperature scale, the Hyde scale, water freezes at \(0^{\circ} \mathrm{H}\) and boils at \(120^{\circ} \mathrm{H}\). If methyl alcohol boils at 84 \({ }^{\circ} \mathrm{H},\) what is its boiling point on the Jekyll scale?

A temperature measurement of \(25^{\circ} \mathrm{C}\) has three significant figures, while a temperature measurement of \(-196^{\circ} \mathrm{C}\) has only two significant figures. Explain.

Do each calculation without your calculator and give the answers to the correct number of significant figures. a. \(1.76 \times 10^{-3} / 8.0 \times 10^{2}\) b. \(1.87 \times 10^{-2}+2 \times 10^{-4}-3.0 \times 10^{-3}\) c. \(\left[\left(1.36 \times 10^{5}\right)(0.000322) / 0.082\right](129.2)\)

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 \(=22\) and radius \(=3.8 \mathrm{~cm}\) ). a. Calculate the mass of each cylinder (ignore the mass of 1 the can itself). (density of gold \(=19.3 \mathrm{~g} / \mathrm{cm}^{3},\) density of sand \(\left.=3.00 \mathrm{~g} / \mathrm{cm}^{3}\right)\) b. Does the thief set off the alarm? Explain.

The proton has a radius of approximately \(1.0 \times 10^{-13} \mathrm{~cm}\) and a mass of \(1.7 \times 10^{-24} \mathrm{~g} .\) Determine the density of a proton. For a sphere, \(V=(4 / 3) \pi r^{3}\).

A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of \(41 \mathrm{~g}\). What is the density of the steel in \(\mathrm{g} / \mathrm{cm}^{3} ?\)

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately \(1.0 \times 10^{-13} \mathrm{~cm} .\) The hydrogen atom itself has a radius of approximately \(52.9 \mathrm{pm} .\) What fraction of the space within the atom is occupied by the nucleus?

The diameter of a hydrogen atom is \(212 \mathrm{pm}\). Find the length in kilometers of a row of \(6.02 \times 10^{23}\) hydrogen atoms. The diameter of a ping pong ball is \(4.0 \mathrm{~cm} .\) Find the length in kilometers of a row of \(6.02 \times 10^{23}\) ping pong balls.

Table salt contains \(39.33 \mathrm{~g}\) of sodium per \(100 \mathrm{~g}\) of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than \(2.40 \mathrm{~g}\) of sodium per day. A particular snack mix contains \(1.25 \mathrm{~g}\) of salt per \(100 \mathrm{~g}\) 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.)

Kinetic energy can be defined as \(\frac{1}{2} m v^{2}\) or as \(\frac{3}{2} P V .\) Show that the derived SI units of each of these terms are those of energy. (Pressure is force/area and force is mass \(\times\) acceleration.)

In 1999 , scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of \(1 \times 10^{3}\) suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in \(\mathrm{g} / \mathrm{cm}^{3}\) ? The radius of our sun is \(7.0 \times 10^{5} \mathrm{~km}\), and it has an average density of \(1.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). The diameter of the moon is \(2.16 \times 10^{3} \mathrm{mi}\).

Nanotechnology, the field of building ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the body's oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person's bloodstream. If the person needed additional oxygen - due to a heart attack perhaps, or for the purpose of space travel- these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of \(25 \mathrm{nm}\). a. What is the volume of one nanocontainer? (Ignore the thickness of the nanocontainer's wall.) b. Suppose that each nanocontainer could contain pure oxygen pressurized to a density of \(85 \mathrm{~g} / \mathrm{L}\). How many grams of oxygen could each nanocontainer contain? c. Air typically contains about 0.28 g of oxygen per liter. An average human inhales about \(0.50 \mathrm{~L}\) of air per breath and takes about 20 breaths per minute. How many grams of oxygen does a human inhale per hour? (Assume two significant figures.) d. What is the minimum number of nanocontainers that a person would need in his or her bloodstream to provide 1 hour's worth of oxygen? e. What is the minimum volume occupied by the number of nanocontainers calculated in part d? Is such a volume feasible, given that total blood volume in an adult is about \(5 \mathrm{~L} ?\)

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?

A cube has an edge length of \(7 \mathrm{~cm} .\) If it is divided into \(1-\mathrm{cm}\) cubes, how many \(1-\mathrm{cm}\) cubes are there?

Substance A has a density of \(1.7 \mathrm{~g} / \mathrm{cm}^{3}\). Substance \(\mathrm{B}\) has a density of \(1.7 \mathrm{~kg} / \mathrm{m}^{3} .\) Without doing any calculations, determine which substance is more dense.

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.