Chapter 1

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 \(1 \mathrm{ft}\). An acre is \(4840 \mathrm{yd}^{2}\). An acrefoot is enough water to supply two typical households for \(1.00\) yr. (a) If desalinated water costs \(\$ 1950\) per acrefoot, 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 using the freezing point \(\left(-11.5^{\circ} \mathrm{C}\right)\) and boiling point \(\left(197.6^{\circ} \mathrm{C}\right)\) of ethylene glycol. If you set the freezing point as \(0^{\circ} \mathrm{G}\) and the boiling point as \(100^{\circ} \mathrm{G}\), what is the freezing point of water on this new scale?

Small spheres of equal mass are made of lead (density \(=11.3 \mathrm{~g} / \mathrm{cm}^{3}\), silver \(\left(10.5 \mathrm{~g} / \mathrm{cm}^{3}\right)\), and aluminum \(\left(2.70 \mathrm{~g} / \mathrm{cm}^{3}\right)\). Without doing a calculation, list the spheres in order from the smallest to the largest.

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 \(50.00\) 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) You are given a bottle that contains \(4.59 \mathrm{~cm}^{3}\) of a metallic solid. The total mass of the bottle and solid is \(35.66 \mathrm{~g}\). The empty bottle weighs \(14.23 \mathrm{~g}\). What is the density of the solid? (b) Mercury is traded by the "flask," a unit that has a mass of \(34.5 \mathrm{~kg}\). What is the volume of a flask of mercury if the density of mercury is \(13.5 \mathrm{~g} / \mathrm{mL} ?\) (c) 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? [The volume of a sphere is \(\boldsymbol{V}=(4 / 3) \pi r^{3}\).] Is he likely to be able to walk off with it unassisted?

Automobile batteries contain sulfuric acid, which is commonly referred to as "battery acid." Calculate the number of grams of sulfuric acid in \(0.500 \mathrm{~L}\) 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 coin dealer offers to sell you an ancient gold coin that is \(2.2 \mathrm{~cm}\) in diameter and \(3.0 \mathrm{~mm}\) in thickness. (a) The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3} .\) How much should the coin weigh if it is pure gold? (b) If gold sells for \(\$ 640\) per troy ounce, how much is the gold content worth? \((1\) troy ounce \(=31.1 \mathrm{~g})\)

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?

A \(15.0-\mathrm{cm}\) 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 \(11.86 \mathrm{~g}\). 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 \(9.85 \mathrm{~g}\) and has a volume of \(0.675 \mathrm{~cm}^{3}\). The jewelry contains only gold and silver, which have densities of \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\) 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 karats. Pure gold is 24 -karat, 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-karat. State the purity of the gold jewelry in karats.

Suppose you are given a sample of a homogeneous liquid. What would you do to determine whether it is a solution or a pure substance?

The concepts of accuracy and precision are not always easy to grasp. Here are two sets of studies: (a) The mass of a secondary weight standard is determined by weighing it on a very precise balance under carefully controlled laboratory conditions. The average of 18 different weight measurements is taken as the weight of the standard. (b) A group of 10,000 males between the ages of 50 and 55 is surveyed to ascertain a relationship between calorie intake and blood cholesterol level. The survey questionnaire is quite detailed, asking the respondents about what they eat, smoking and drinking habits, and so on. The results are reported as showing that for men of comparable lifestyles, there is a \(40 \%\) chance of the blood cholesterol level being above 230 for those who consume more than 40 calories per gram of body weight per day, as compared with those who consume fewer than 30 calories per gram of body weight per day. Discuss and compare these two studies in terms of the precision and accuracy of the result in each case. How do the two studies differ in nature in ways that affect the accuracy and precision of the results? What makes for high precision and accuracy in any given study? In each of these studies, what factors might not be controlled that could affect the accuracy and precision? What steps can be taken generally to attain higher precision and accuracy?