Chapter 1

Give the derived SI units for each of the following quantities in base SI units: (a) acceleration = distance/time \(^{2},\) (b) force \(=\) mass \(\times\) acceleration, \((\mathrm{c})\) work \(=\) force \(\times\) distance, (d) \(\quad\) pressure \(=\) force/area, (e) \(\quad\) power \(=\) work/time, (f) velocity \(=\) distance/time, \((\mathrm{g})\) energy \(=\operatorname{mass} \times(\text { velocity })^{2}\).

The distance from Earth to the Moon is approximately \(240,000 \mathrm{mi}\). (a) What is this distance in meters? (b) The peregrine falcon has been measured as traveling up to \(350 \mathrm{~km} / \mathrm{hr}\) in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take? (c) The speed of light is \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). How long does it take for light to travel from Earth to the Moon and back again? (d) Earth travels around the Sun at an average speed of \(29.783 \mathrm{~km} / \mathrm{s}\). Convert this speed to miles per hour.

The US 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 US National Debt Clock showed the outstanding public debt to be $$\$ 11,687,233,914,811.11$$ on August \(19,2009 .\) 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 \(1 \mathrm{ft}\). An acre is \(4840 \mathrm{yd}^{2}\). 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 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 \(32.65-\mathrm{g}\) 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 \(\left.V=(4 / 3) \pi r^{3} .\right]\) 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 gallon 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 \(40-\mathrm{lb}\) container of peat moss measures \(14 \times 20 \times 30 \mathrm{in}\). A \(40-\mathrm{lb}\) 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? Explain. (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?

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 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.

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 \(\mathrm{mg}\) sample of this material. (c) A \(10.0-\mathrm{mL}\) sample of contaminated water had \(7.748 \mathrm{mg}\) 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?

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, smoke, drink, 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 \(230 \mathrm{mg} / \mathrm{dL}\) 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 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?