Chapter 1

Express the results of the following calculations with the correct number of significant figures: (a) \(4.884 \times 2.05\) (b) \(94.61 \div 3.7\) (c) \(3.7 \div 94.61\) (d) \(5502.3+24+0.01\) (e) \(86.3+1.42-0.09\) (f) \(5.7 \times 2.31\)

Express the results of the following calculations with the correct number of significant figures: (a) \(\frac{3.41-0.23}{5.233} \times 0.205\) (b) \(\frac{5.556 \times 2.3}{4.223-0.08}\)

The world record for the women's outdoor 20,000 -meter run, set in 2000 by Tegla Loroupe, is \(1: 05: 26.6\) (seconds are given to the nearest tenth). What was her average speed, expressed in miles per hour with the correct number of significant figures? (Assume that the race distance is accurate to 5 significant figures.)

In the United States, the emissions limit for carbon monoxide in motorcycle engine exhaust is \(12.0 \mathrm{~g}\) of carbon monoxide per kilometer driven. What is this limit expressed in mg per mile with the correct number of significant figures?

Carry out the following conversions: (a) How many grams of meat are in a quarter-pound hamburger \((0.25 \mathrm{lb}) ?\) (b) How tall in meters is the Willis Tower, formerly called the Sears Tower, in Chicago ( \(1454 \mathrm{ft}\) )? (c) How large in square meters is the land area of Australia \(\left(2,941,526 \mathrm{mi}^{2}\right) ?\)

Convert the following quantities into SI units with the correct number of significant figures: (a) \(5.4\) in. (b) \(66.31 \mathrm{lb}\) (c) \(0.5521\) gal (d) \(65 \mathrm{mi} / \mathrm{h}\) (e) \(978.3 \mathrm{yd}^{3}\) (f) \(2.380 \mathrm{mi}^{2}\)

The volume of water used for crop irrigation is measured in acrefeet, where 1 acre-foot is the amount of water needed to cover 1 acre of land to a depth of \(1 \mathrm{ft}\). (a) If there are 640 acres per square mile, how many cubic feet of water are in 1 acre-foot? (b) How many acre-feet are in Lake Erie (total volume \(=116 \mathrm{mi}^{3}\) )?

The height of a horse is usually measured in hands instead of in feet, where 1 hand equals \(1 / 3 \mathrm{ft}\) (exactly). (a) How tall in centimeters is a horse of \(18.6\) hands? (b) What is the volume in cubic meters of a box measuring \(6 \times 2.5 \times 15\) hands?

Weights in England are commonly measured in stones, where 1 stone \(=14 \mathrm{lb}\). What is the weight in pounds of a person who weighs \(8.65\) stones?

Concentrations of substances dissolved in solution are often expressed as mass per unit volume. For example, normal human blood has a cholesterol concentration of about \(200 \mathrm{mg} / 100 \mathrm{~mL}\). Express this concentration in the following units: (a) \(\mathrm{mg} / \mathrm{L}\) (b) \(\mu \mathrm{g} / \mathrm{mL}\) (c) \(\mathrm{g} / \mathrm{L}\) (d) \(\mathrm{ng} / \mu \mathrm{L}\) (e) How much total blood cholesterol in grams does a person have if the normal blood volume in the body is \(5 \mathrm{~L}\) ?

Administration of digitalis, a drug used to control atrial fibrillation in heart patients, must be carefully controlled because even a modest overdose can be fatal. To take differences between patients into account, drug dosages are prescribed in terms of \(\mathrm{mg} / \mathrm{kg}\) body weight. Thus, a child and an adult differ greatly in weight, but both receive the same dosage per kilogram of body weight. At a dosage of \(20 \mu \mathrm{g} / \mathrm{kg}\) body weight, how many milligrams of digitalis should a \(160 \mathrm{lb}\) patient receive?

Among many alternative units that might be considered as a measure of time is the shake rather than the second. Based on the expression "faster than a shake of a lamb's tail" we'll define 1 shake as equal to \(2.5 \times 10^{-4} \mathrm{~s}\). If a car is traveling at \(55 \mathrm{mi} / \mathrm{h}\), what is its speed in \(\mathrm{cm} /\) shake?

The normal body temperature of a goat is \(39.9{ }^{\circ} \mathrm{C}\), and that of an Australian spiny anteater is \(22.2^{\circ} \mathrm{C}\). Express these temperatures in degrees Fahrenheit.

Of the 90 or so naturally occurring elements, only four are liquid near room temperature: mercury (melting point = \(\left.-38.87^{\circ} \mathrm{C}\right)\), bromine \(\left(\right.\) melting point \(\left.=-7.2{ }^{\circ} \mathrm{C}\right)\), cesium (melting point \(\left.=28.40^{\circ} \mathrm{C}\right)\), and gallium (melting point \(=\) \(\left.29.78{ }^{\circ} \mathrm{C}\right)\). Convert these melting points to degrees Fahrenheit.

Suppose that your oven is calibrated in degrees Fahrenheit but a recipe calls for you to bake at \(175^{\circ} \mathrm{C}\). What oven setting should you use?

Tungsten, the element used to make filaments in lightbulbs, has a melting point of \(6192{ }^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius and to kelvin.

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of \(-117.3^{\circ} \mathrm{C}\) and a boiling point of \(78.5^{\circ} \mathrm{C}\), but on your new scale calibrated in units of degrees ethanol, \({ }^{\circ} \mathrm{E}\), you define ethanol to melt at \(0{ }^{\circ} \mathrm{E}\) and boil at \(200^{\circ} \mathrm{E}\). (a) How does your ethanol degree compare in size with a Celsius degree? (b) How does an ethanol degree compare in size with a Fahrenheit degree? (c) What are the melting and boiling points of water on the ethanol scale? (d) What is normal human body temperature \(\left(98.6^{\circ} \mathrm{F}\right)\) on the ethanol scale? (e) If the outside thermometer reads \(130{ }^{\circ} \mathrm{E}\), how would you dress to go out?

What is the density of glass in \(\mathrm{g} / \mathrm{cm}^{3}\) if a sample weighing \(27.43 \mathrm{~g}\) has a volume of \(12.40 \mathrm{~cm}^{3} ?\)

What is the density of lead in \(\mathrm{g} / \mathrm{cm}^{3}\) if a sample weighing \(206.77 \mathrm{~g}\) has a volume of \(15.50 \mathrm{~cm}^{3} ?\)

A vessel contains \(4.67 \mathrm{~L}\) of bromine, whose density is \(3.10 \mathrm{~g} / \mathrm{cm}^{3}\). What is the mass of the bromine in the vessel (in kilograms)?

Aspirin has a density of \(1.40 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the volume in cubic centimeters of an aspirin tablet weighing \(250 \mathrm{mg}\) ? Of a tablet weighing \(500 \mathrm{lb}\) ?

Gaseous hydrogen has a density of \(0.0899 \mathrm{~g} / \mathrm{L}\) at \(0{ }^{\circ} \mathrm{C}\), and gaseous chlorine has a density of \(3.214 \mathrm{~g} / \mathrm{L}\) at the same temperature. How many liters of each would you need if you wanted \(1.0078 \mathrm{~g}\) of hydrogen and \(35.45 \mathrm{~g}\) of chlorine?

The density of silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\). What is the mass (in kilograms) of a cube of silver that measures \(0.62 \mathrm{~m}\) on each side?

What is the density of lead in \(\mathrm{g} / \mathrm{cm}^{3}\) if a rectangular bar measuring \(0.50 \mathrm{~cm}\) in height, \(1.55 \mathrm{~cm}\) in width, and \(25.00 \mathrm{~cm}\) in length has a mass of \(220.9 \mathrm{~g}\) ?

What is the density of lithium metal in \(\mathrm{g} / \mathrm{cm}^{3}\) if a cylindrical wire with a diameter of \(2.40 \mathrm{~mm}\) and a length of \(15.0 \mathrm{~cm}\) has a mass of \(0.3624\) g?

You would like to determine if a set of antique silverware is pure silver. The mass of a small fork was measured on a balance and found to be \(80.56 \mathrm{~g} .\) The volume was found by dropping the fork into a graduated cylinder initially containing \(10.0 \mathrm{~mL}\) of water. The volume after the fork was added was \(15.90 \mathrm{~mL}\). Calculate the density of the fork. If the density of pure silver at the same temperature is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), is the fork pure silver?

An experiment is performed to determine if pennies are made of pure copper. The mass of 10 pennies was measured on a balance and found to be \(24.656 \mathrm{~g}\). The volume was found by dropping the 10 pennies into a graduated cylinder initially containing \(10.0 \mathrm{~mL}\) of water. The volume after the pennies were added was \(12.90 \mathrm{~mL}\). Calculate the density of the pennies. If the density of pure copper at the same temperature is \(8.96 \mathrm{~g} / \mathrm{cm}^{3}\), are the pennies made of pure copper?

Which has more kinetic energy, a \(1400 \mathrm{~kg}\) car moving at \(115 \mathrm{~km} / \mathrm{h}\) or a \(12,000 \mathrm{~kg}\) truck moving at \(38 \mathrm{~km} / \mathrm{h}\) ?

Assume that the kinetic energy of a \(1400 \mathrm{~kg}\) car moving at \(115 \mathrm{~km} / \mathrm{h}\) (Problem \(1.90\) ) is converted entirely into heat. How many calories of heat are released, and what amount of water in liters could be heated from \(20.0{ }^{\circ} \mathrm{C}\) to \(50.0^{\circ} \mathrm{C}\) by the car's energy? (One calorie raises the temperature of \(1 \mathrm{~mL}\) of water by \(1{ }^{\circ} \mathrm{C}\).)

The combustion of \(45.0 \mathrm{~g}\) of methane (natural gas) releases \(2498 \mathrm{~kJ}\) of heat energy. How much energy in kilocalories (kcal) would combustion of \(0.450\) ounces of methane release?

Sodium (Na) metal undergoes a chemical reaction with chlorine (Cl) gas to yield sodium chloride, or common table salt. If \(1.00 \mathrm{~g}\) of sodium reacts with \(1.54 \mathrm{~g}\) of chlorine, \(2.54 \mathrm{~g}\) of sodium chloride is formed and \(17.9 \mathrm{~kJ}\) of heat is released. How much sodium and how much chlorine in grams would have to react to release 171 kcal of heat?

A Big Mac hamburger from McDonald's contains 540 Calories. (a) How many kilojoules does a Big Mac contain? (b) For how many hours could the amount of energy in a Big Mac light a 100 watt lightbulb? \((1\) watt \(=1 \mathrm{~J} / \mathrm{s})\)

A 20 fluid oz. soda contains 238 Calories. (a) How many kilojoules does the soda contain? (b) For how many hours could the amount of energy in the soda light a 75 watt lightbulb? \((1 \mathrm{watt}=1 \mathrm{~J} / \mathrm{s})\)

When an irregularly shaped chunk of silicon weighing \(8.763 \mathrm{~g}\) was placed in a graduated cylinder containing \(25.00 \mathrm{~mL}\) of water, the water level in the cylinder rose to \(28.76 \mathrm{~mL}\). What is the density of silicon in \(\mathrm{g} / \mathrm{cm}^{3} ?\)

Lignum vitae is a hard, durable, and extremely dense wood used to make ship bearings. A sphere of this wood with a diameter of \(7.60 \mathrm{~cm}\) has a mass of 313 g. (a) What is the density of the lignum vitae sphere? (b) Will the sphere float or sink in water? (c) Will the sphere float or sink in chloroform? (The density of chloroform is \(1.48 \mathrm{~g} / \mathrm{mL} .\) )

Sodium chloride has a melting point of \(1074 \mathrm{~K}\) and a boiling point of \(1686 \mathrm{~K}\). Convert these temperatures to degrees Celsius and to degrees Fahrenheit.

The density of chloroform, a widely used organic solvent, is \(1.4832 \mathrm{~g} / \mathrm{mL}\) at \(20{ }^{\circ} \mathrm{C}\). How many milliliters would you use if you wanted \(112.5 \mathrm{~g}\) of chloroform?

More sulfuric acid (density \(\left.=1.8302 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is produced than any other chemical-approximately \(3.6 \times 10^{11} \mathrm{lb} / \mathrm{yr}\) worldwide. What is the volume of this amount in liters?

Answer the following questions: (a) An old rule of thumb in cooking says: "A pint's a pound the world around." What is the density in \(\mathrm{g} / \mathrm{mL}\) of a substance for which \(1 \mathrm{pt}=1\) lb exactly? (b) There are exactly 640 acres in 1 square mile. How many square meters are in 1 acre? (c) A certain type of wood has a density of \(0.40 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the mass of \(1.0\) cord of this wood in kg, where 1 cord is 128 cubic feet of wood?

A \(1.0\) ounce piece of chocolate contains \(15 \mathrm{mg}\) of caffeine, and \(a\) \(6.0\) ounce cup of regular coffee contains \(105 \mathrm{mg}\) of caffeine. How much chocolate would you have to consume to get as much caffeine as you would from \(2.0\) cups of coffee?

A bag of Hershey's Kisses contains the following information: Serving size: 9 pieces \(=41 \mathrm{~g}\) Calories per serving: 230 Total fat per serving: \(13 \mathrm{~g}\) (a) The bag contains \(2.0\) lbs of Hershey's Kisses. How many Kisses are in the bag? (b) The density of a Hershey's Kiss is \(1.4 \mathrm{~g} / \mathrm{mL}\). What is the volume of a single Hershey's Kiss? (c) How many Calories are in one Hershey's Kiss? (d) Each gram of fat yields 9 Calories when metabolized. What percent of the calories in Hershey's Kisses are derived from fat?

Vinaigrette salad dressing consists mainly of oil and vinegar. The density of olive oil is \(0.918 \mathrm{~g} / \mathrm{cm}^{3}\), the density of vinegar is \(1.006 \mathrm{~g} / \mathrm{cm}^{3}\), and the two do not mix. If a certain mixture of olive oil and vinegar has a total mass of \(397.8 \mathrm{~g}\) and a total volume of \(422.8 \mathrm{~cm}^{3}\), what is the volume of oil and what is the volume of vinegar in the mixture?

At a certain point, the Celsius and Fahrenheit scales "cross" giving the same numerical value on both. At what temperature does this crossover occur?

Imagine that you place a cork measuring \(1.30 \mathrm{~cm} \times 5.50 \mathrm{~cm} \times\) \(3.00 \mathrm{~cm}\) in a pan of water and that on top of the cork you place a small cube of lead measuring \(1.15 \mathrm{~cm}\) on each edge. The density of cork is \(0.235 \mathrm{~g} / \mathrm{cm}^{3}\), and the density of lead is \(11.35 \mathrm{~g} / \mathrm{cm}^{3}\). Will the combination of cork plus lead float or sink?

The density of polystyrene, a plastic commonly used to make CD cases and transparent cups is \(0.037 \mathrm{lbs} / \mathrm{in}^{3} .\) Calculate the density in units of \(\mathrm{g} / \mathrm{cm}^{3}\).

The density of polypropylene, a plastic commonly used to make bottle caps, yogurt containers, and carpeting, is \(0.55 \mathrm{oz} / \mathrm{in}^{3} .\) Calculate the density in units of \(\mathrm{g} / \mathrm{cm}^{3}\).

A \(125 \mathrm{~mL}\) sample of water at \(293.2 \mathrm{~K}\) was heated for \(8 \mathrm{~min}, 25 \mathrm{~s}\) so as to give a constant temperature increase of \(3.0{ }^{\circ} \mathrm{F} / \mathrm{min}\). What is the final temperature of the water in degrees Celsius?

A calibrated flask was filled to the \(25.00 \mathrm{~mL}\) mark with ethyl alcohol. By weighing the flask before and after adding the alcohol, it was determined that the flask contained \(19.7325 \mathrm{~g}\) of alcohol. In a second experiment, \(25.0920 \mathrm{~g}\) of metal beads were added to the flask, and the flask was again filled to the \(25.00 \mathrm{~mL}\) mark with ethyl alcohol. The total mass of the metal plus alcohol in the flask was determined to be \(38.4704 \mathrm{~g}\). What is the density of the metal in \(\mathrm{g} / \mathrm{mL}\) ?

Brass is a copper-zinc alloy. What is the mass in grams of a brass cylinder having a length of \(1.62\) in. and a diameter of \(0.514\) in. if the composition of the brass is \(67.0 \%\) copper and \(33.0 \%\) zinc by mass? The density of copper is \(8.92 \mathrm{~g} / \mathrm{cm}^{3}\), and the density of zinc is \(7.14 \mathrm{~g} / \mathrm{cm}^{3}\). Assume that the density of the brass varies linearly with composition.

Ocean currents are measured in Sverdrups \((\mathrm{sv})\) where \(1 \mathrm{sv}=10^{9} \mathrm{~m}^{3} / \mathrm{s}\). The Gulf Stream off the tip of Florida, for instance, has a flow of \(35 \mathrm{sv}\) (a) What is the flow of the Gulf Stream in milliliters per minute? (b) What mass of water in the Gulf Stream flows past a given point in 24 hours? The density of seawater is \(1.025 \mathrm{~g} / \mathrm{mL}\). (c) How much time is required for 1 petaliter \(\left(\mathrm{PL} ; 1 \mathrm{PL}=10^{15} \mathrm{~L}\right)\) of seawater to flow past a given point?