Chapter 1

The U.S. quarter has a mass of 5.67 \(\mathrm{g}\) and is approximately 1.55 \(\mathrm{mm}\) thick. (a) How many quarters would have to be stacked to reach 575 \(\mathrm{ft}\) , the height of the Washington Monument? (b) How much would this stack weigh? (c) How much money would this stack contain? (d) The U.S. National Debt Clock showed the outstanding public debt to be \(\$ 16,213,166,914,811\) on October \(28,2012 .\) How many stacks like the one described would be necessary to pay off this debt?

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd. An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \(\$ 1950\) per acre-foot, how much does desalinated water cost per liter? (b) How much would it cost one household per day if it were the only source of water?

Suppose you decide to define your own temperature scale with units of \(\mathrm{O},\) using the freezing point \(\left(13^{\circ} \mathrm{C}\right)\) and boiling point \(\left(360^{\circ} \mathrm{C}\right)\) of oleic acid, the main component of olive oil. If you set the freezing point of oleic acid as \(0^{\circ} \mathrm{O}\) and the boiling point as \(100^{\circ} \mathrm{O},\) what is the freezing point of water on this new scale?

Water has a density of 0.997 \(\mathrm{g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C} ;\) ice has a density of 0.917 \(\mathrm{g} / \mathrm{cm}^{3}\) at \(-10^{\circ} \mathrm{C}\) (a) If a soft-drink bottle whose volume is 1.50 \(\mathrm{L}\) is completely filled with water and then frozen to \(-10^{\circ} \mathrm{C},\) what volume does the ice occupy? (b) Can the ice be contained within the bottle?

A 32.65 -g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 \(\mathrm{mL} .\) The solid and toluene together weigh 58.58 \(\mathrm{g}\) . The density of toluene at the temperature of the experiment is 0.864 \(\mathrm{g} / \mathrm{mL}\) . What is the density of the solid?

A thief plans to steal a gold sphere with a radius of 28.9 \(\mathrm{cm}\) from a museum. If the gold has a density of \(19.3 \mathrm{g} / \mathrm{cm}^{3},\) what is the mass of the sphere in pounds? [The volume of a sphere is \(V=(4 / 3) \pi r^{3} . ]\) Is the thief likely to be able to walk off with the gold sphere unassisted?

Automobile batteries contain sulfuric acid, which is commonly referred to as "battery acid." Calculate the number of grams of sulfuric acid in 1.00 gal of battery acid if the solution has a density of 1.28 \(\mathrm{g} / \mathrm{mL}\) and is 38.1\(\%\) sulfuric acid by mass.

A 40 -lb container of peat moss measures \(14 \times 20 \times 30\) in. A 40 -lb container of topsoil has a volume of 1.9 gal. (a) Calculate the average densities of peat moss and topsoil in units of\(\mathrm{g} / \mathrm{cm}^{3} .\) Would it be correct to say that peat moss is "lighter" than topsoil? (b) How many bags of peat moss are needed to cover an area measuring 15.0 \(\mathrm{ft} \times 20.0 \mathrm{ft}\) to a depth of 3.0 in.?

A package of aluminum foil contains 50 \(\mathrm{ft}^{2}\) of foil, which weighs approximately 8.0 oz. Aluminum has a density of 2.70 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the approximate thickness of the foil in millimeters?

The total rate at which power is used by humans world wide is approximately 15 TW (terawatts). The solar flux averaged over the sunlit half of Earth is 680 \(\mathrm{W} / \mathrm{m}^{2}\) (assuming no clouds). The area of Earth's disc as seen from the Sun is \(1.28 \times 10^{14} \mathrm{m}^{2} .\) The surface area of Earth is approximately \(197,000,000\) square miles. How much of Earth's surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can convert only 10\(\%\) of the available sun light into useful power.

A 25.0 -cm-long cylindrical glass tube, sealed at one end, is filled with ethanol. The mass of ethanol needed to fill the tube is found to be 45.23 g. The density of ethanol is 0.789 \(\mathrm{g} / \mathrm{mL}\) . Calculate the inner diameter of the tube in centimeters.

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry. (a) Consider a piece of gold jewelry that weighs 9.85 \(\mathrm{g}\) gond has a volume of 0.675 \(\mathrm{cm}^{3} .\) The jewelry contains only gold and silver, which have densities of 19.3 and 10.5 \(\mathrm{g} / \mathrm{cm}^{3}\) , respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry. (b) The relative amount of gold in an alloy is commonly expressed in units of carats. Pure gold is 24 carat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is 50\(\%\) gold is 12 carat. State the purity of the gold jewelry in carats.

Judge the following statements as true or false. If you believe a statement to be false, provide a corrected version.(a) Air and water are both elements. (b) All mixtures contain at least one element and one compound.(c) Compounds can be decomposed into two or more other substances; elements cannot. (d) Elements can exist in any of the three states of matter. (e) When yellow stains in a kitchen sink are treated with bleach water, the disappearance of the stains is due to a physical change. (f) A hypothesis is more weakly supported by experimental evidence than a theory. (g) The number 0.0033 has more significant figures than 0.033 . (h) Conversion factors used in converting units always have a numerical value of one. (i) Compounds always contain at least two different elements.

In \(2009,\) a team from Northwestern University and Western Washington University reported the preparation of a new "spongy" material composed of nickel, molybdenum, and sulfur that excels at removing mercury from water. The density of this new material is 0.20 \(\mathrm{g} / \mathrm{cm}^{3}\) , and its surface area is 1242 \(\mathrm{m}^{2}\) per gram of material. (a) Calculate the volume of a 10.0 -mg sample of this material. (b) Calculate the surface area for a 10.0 -mg sample of this material. (c) A 10.0 -mL sample of contaminated water had 7.748 mg of mercury in it. After treatment with 10.0 \(\mathrm{mg}\) of the new spongy material, 0.001 \(\mathrm{mg}\) of mercury remained in the contaminated water. What percentage of the mercury was removed from the water? (d) What is the final mass of the spongy material after the exposure to mercury?