Chapter 1

A bullet leaving the muzzle of a pistol was traveling at a speed of 2230 feet per second. What is this speed in miles per hour?

On average, water flows over Niagara Falls at a rate of \(2.05 \times 10^{5}\) cubic feet per second. One cubic foot of water weighs \(62.4 \mathrm{lb} .\) Calculate the rate of water flow in tons of water per day. \((1\) ton \(=2000 \mathrm{lb})\)

The brightest star in the night sky in the northern hemisphere is Sirius. Its distance from earth is estimated to be 8.7 light years. A light year is the distance light travels in one year. Light travels at a speed of \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Calculate the distance from earth to Sirius in miles. (1 \(\mathrm{mi}=\) \(5280 \mathrm{ft})\)

Calculate the density of kerosene, in \(\mathrm{g} / \mathrm{mL},\) if its mass is \(36.4 \mathrm{~g}\) and its volume is \(45.6 \mathrm{~mL}\).

$$ \begin{aligned} &\text { Calculate the density of magnesium, in } \mathrm{g} / \mathrm{cm}^{3}, \text { if its mass is }\\\ &14.3 \mathrm{~g} \text { and its volume is } 8.46 \mathrm{~cm}^{3} . \end{aligned} $$

Acetone, the solvent in some nail polish removers, has a density of \(0.791 \mathrm{~g} / \mathrm{mL}\). What is the volume, in \(\mathrm{mL}\), of \(25.0 \mathrm{~g}\) of acetone?

A glass apparatus contains \(26.223 \mathrm{~g}\) of water when filled at \(25^{\circ} \mathrm{C}\). At this temperature, water has a density of \(0.99704 \mathrm{~g} / \mathrm{mL}\). What is the volume, in \(\mathrm{mL}\), of the apparatus?

Chloroform, a chemical once used as an anesthetic, has a density of \(1.492 \mathrm{~g} / \mathrm{mL}\). What is the mass in grams of \(185 \mathrm{~mL}\) of chloroform?

Gasoline's density is about \(0.65 \mathrm{~g} / \mathrm{mL}\). How much does \(34 \mathrm{~L}\) (approximately 18 gallons) weigh in kilograms? In pounds?

A graduated cylinder was filled with water to the \(15.0 \mathrm{~mL}\) mark and weighed on a balance. Its mass was \(27.35 \mathrm{~g}\). An object made of silver was placed in the cylinder and completely submerged in the water. The water level rose to \(18.3 \mathrm{~mL}\). When reweighed, the cylinder, water, and silver object had a total mass of \(62.00 \mathrm{~g}\). Calculate the density of silver in \(\mathrm{g} \mathrm{cm}^{-3}\).

Titanium is a metal used to make golf clubs. A rectangular bar of this metal measuring \(1.84 \mathrm{~cm} \times 2.24 \mathrm{~cm} \times 2.44 \mathrm{~cm}\) was found to have a mass of \(45.7 \mathrm{~g}\). What is the density of titanium in \(\mathrm{g} \mathrm{cm}^{-3}\) ?

The space shuttle uses liquid hydrogen as its fuel. The external fuel tank used during takeoff carries \(227,641 \mathrm{lb}\) of hydrogen with a volume of 385,265 gallons. Calculate the density of liquid hydrogen in units of \(\mathrm{lb} / \mathrm{gal}\) and \(\mathrm{g} / \mathrm{mL}\). (Express your answer to three significant figures.) What is the specific gravity of liquid hydrogen?

Some time ago, a U.S. citizen traveling in Canada observed that the price of regular gasoline was 1.299 Canadian dollars per liter. The exchange rate at the time was 1.001 Canadian dollars per one U.S. dollar. Calculate the price of the Canadian gasoline in units of U.S. dollars per gallon. (Just the week before, the traveler had paid \(\$ 3.759\) per gallon in the United States.)

An astronomy web site states that neutron stars have a density of \(1.00 \times 10^{8}\) tons per cubic centimeter. The site does not specify whether "tons" means metric tons (1 metric ton \(=1000 \mathrm{~kg}\) ) or English tons ( 1 English ton \(=2000\) pounds). How many grams would one teaspoon of a neutron star weigh if the density were in metric tons per \(\mathrm{cm}^{3}\) ? How many grams would the teaspoon weigh if the density were in English tons per \(\mathrm{cm}^{3}\) ? (One teaspoon is defined as \(5.00 \mathrm{~mL} .\) )

The star Arcturus is \(3.50 \times 10^{14} \mathrm{~km}\) from the earth. How many days does it take for light to travel from Arcturus to earth? What is the distance to Arcturus in light years? One light year is the distance light travels in one year \(\left(365\right.\) days); light travels at a speed of \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\).

A pycnometer is a glass apparatus used for accurately determining the density of a liquid. When dry and empty, a certain pycnometer had a mass of \(27.314 \mathrm{~g}\). When filled with distilled water at \(25.0^{\circ} \mathrm{C}\), it weighed \(36.842 \mathrm{~g}\). When filled with chloroform (a liquid once used as an anesthetic before its toxic properties were known), the apparatus weighed 41.428 g. At \(25.0{ }^{\circ} \mathrm{C},\) the density of water is \(0.99704 \mathrm{~g} / \mathrm{mL}\). (a) What is the volume of the pycnometer? (b) What is the density of chloroform?

Suppose you have a job in which you earn \(\$ 7.35\) for each 30 minutes that you work. (a) Express this information in the form of an equivalence between dollars earned and minutes worked. (b) Use the equivalence defined in (a) to calculate the number of dollars earned in \(1 \mathrm{hr} 45 \mathrm{~min}\) (c) Use the equivalence defined in (a) to calculate the number of minutes you would have to work to earn \(\$ 333.50\).

When an object floats in water, it displaces a volume of water that has a weight equal to the weight of the object. If a ship has a weight of 4255 tons, how many cubic feet of seawater will it displace? Seawater has a density of \(1.025 \mathrm{~g} \mathrm{~cm}^{-3} ; 1\) ton \(=2000 \mathrm{lb}\), exactly.

Aerogel or "solid smoke" is a novel material that is made of silicon dioxide, like glass, but is a thousand times less dense than glass because it is extremely porous. Material scientists at NASA's Jet Propulsion Laboratory created the lightest aerogel ever in 2002 , with a density of 0.00011 pounds per cubic inch. The material was used for thermal insulation in the 2003 Mars Exploration Rover. If the maximum space for insulation in the spacecraft's hull was \(2510 \mathrm{~cm}^{3}\), what mass (in grams) did the aerogel insulation add to the spacecraft?

There exists a single temperature at which the value reported in \({ }^{\circ} \mathrm{F}\) is numerically the same as the value reported in \(^{\circ} \mathrm{C}\). What is this temperature?

Density measurements can be used to analyze mixtures. For example, the density of solid sand (without air spaces) is about \(2.84 \mathrm{~g} / \mathrm{mL}\). The density of gold is \(19.3 \mathrm{~g} / \mathrm{mL}\). If a \(1.00 \mathrm{~kg}\) sample of sand containing some gold has a density of \(3.10 \mathrm{~g} / \mathrm{mL}\) (without air spaces), what is the percentage of gold in the sample?

An artist's statue has a surface area of \(14.6 \mathrm{ft}^{2}\). The artist plans to apply gold leaf to the statue and wants the coating to be \(2.50 \mu \mathrm{m}\) thick. If the price of gold were \(\$ 1,774.10\) per troy ounce, how much would it cost to give the statue its gold coating? \((1\) troy ounce \(=31.1035 \mathrm{~g}\); the density of gold is \(19.3 \mathrm{~g} / \mathrm{mL}\).)

A solution is defined as a uniform mixture consisting of a single phase. With our vastly improved abilities to "see" smaller and smaller particles, down to the atomic level, present an argument for the proposition that all mixtures are heterogeneous. Present the argument that the ability to observe objects as small as an atom has no effect on the definitions of heterogeneous and homogeneous.

A student used a \(250 \mathrm{~mL}\) graduated cylinder having volume markings every \(2 \mathrm{~mL}\) to carefully measure \(100 \mathrm{~mL}\) of water for an experiment. A fellow student said that by reporting the volume as "100 mL" in her lab notebook, she was only entitled to one significant figure. The first student disagreed. Why did her fellow student say the reported volume had only one significant figure?

Because of the serious consequences of lead poisoning, the Federal Centers for Disease Control in Atlanta has set a threshold of concern for lead levels in children's blood. This threshold was based on a study that suggested that lead levels in blood as low as 10 micrograms of lead per deciliter of blood can result in subtle effects of lead toxicity. Suppose a child had a lead level in her blood of \(2.5 \times 10^{-4}\) grams of lead per liter of blood. Is this person in danger of exhibiting the effects of lead poisoning?