Chapter 1

Hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}, d=0.766 \mathrm{g} / \mathrm{cm}^{3}\right),\) perfluorohexane \(\left(\mathrm{C}_{6} \mathrm{F}_{14}, d=1.669 \mathrm{g} / \mathrm{cm}^{3}\right),\) and water are immiscible liq- uids; that is, they do not dissolve in one another. You place 10 mL of each liquid in a graduated cylinder, along with pieces of high-density polyethylene (HDPE, \(d=\) \(\left.\left.0.97 \mathrm{g} / \mathrm{cm}^{3}\right), \text { polyvinyl chloride (PVC, } d=1.36 \mathrm{g} / \mathrm{cm}^{3}\right)\) and Teflon (density \(=2.3 \mathrm{g} / \mathrm{cm}^{3}\) ). None of these common plastics dissolve in these liquids. Describe what you expect to see.

You are given a sample of a silvery metal. What information would you seek to prove that the metal is silver?

Suggest a way to determine whether the colorless liquid in a beaker is water. If it is water, does it contain dissolved salt? How could you discover whether salt is dissolved in the water?

Describe an experimental method that can be used to determine the density of an irregularly shaped piece of metal.

Three liquids of different densities are mixed. Because they are not miscible (do not form a homogeneous solution with one another), they form discrete layers, one on top of the other. Sketch the result of mixing carbon tetrachloride \(\left(\mathrm{CCl}_{4}, d=1.58 \mathrm{g} / \mathrm{cm}^{3}\right),\) mercury \((d=\) \(\left.13.546 \mathrm{g} / \mathrm{cm}^{3}\right),\) and water \(\left(d=1.00 \mathrm{g} / \mathrm{cm}^{3}\right)\)

Diabetes can alter the density of urine, so urine density can be used as a diagnostic tool. People with diabetes may excrete too much sugar or too much water. What do you predict will happen to the density of urine under each of these conditions? (Hint: Water containing dissolved sugar has a higher density than pure water.)

The following photo shows the element potassium reacting with water to form the element hydrogen, a gas, and a solution of the compound potassium hydroxide. (IMAGE CAN'T COPY) (a) What states of matter are involved in the reaction? (b) Is the observed change chemical or physical? (c) What are the reactants in this reaction and what are the products? (d) What qualitative observations can be made concerning this reaction?

A copper-colored metal is found to conduct an electric current. Can you say with certainty that it is copper? Why or why not? Suggest additional information that could provide unequivocal confirmation that the metal is copper.

What experiment can you use to: (a) Separate salt from water? (b) Separate iron filings from small pieces of lead? (c) Separate elemental sulfur from sugar?

Four balloons (each with a volume of \(10 \mathrm{L}\) and a mass of \(1.00 \mathrm{g})\) are filled with a different gas: Helium, \(d=0.164 \mathrm{g} / \mathrm{L}\) Neon, \(d=0.825 \mathrm{g} / \mathrm{L}\) Argon, \(d=1.633 \mathrm{g} / \mathrm{L}\) Krypton, \(d=4.425 \mathrm{g} / \mathrm{L}\) If the density of dry air is \(1.12 \mathrm{g} / \mathrm{L},\) which balloon or balloons float in air?

Many foods are fortified with vitamins and minerals. For example, some breakfast cereals have elemental iron added. Iron chips are used instead of iron compounds because the compounds can be converted by the oxygen in air to a form of iron that is not biochemically useful. Iron chips, in contrast, are converted to useful iron compounds in the gut, and the iron can then be absorbed. Outline a method by which you could remove the iron (as iron chips) from a box of cereal and determine the mass of iron in a given mass of cereal. (IMAGE CAN'T COPY)

Describe what occurs when a hot object comes in contact with a cooler object.

Express the following numbers in exponential or scientific notation. (a) 0.054 (b) 5462 (c) 0.000792

Express the following numbers in fixed notation (e.g., \(\left.123 \times 10^{2}=123\right)\) (a) \(1.62 \times 10^{3}\) (b) \(2.57 \times 10^{-4}\) (c) \(6.32 \times 10^{-2}\)

Carry out the following operations. Provide the answer with the correct number of significant figures. (a) (1.52)\(\left(6.21 \times 10^{-3}\right)\) (b) \(\left(6.21 \times 10^{3}\right)-\left(5.23 \times 10^{2}\right)\) (c) \(\left(6.21 \times 10^{3}\right) \div\left(5.23 \times 10^{2}\right)\)

Carry out the following operations. Provide the answer with the correct number of significant figures. (a) \(\left(6.25 \times 10^{2}\right)^{3}\) (b) \(\sqrt{2.35 \times 10^{-3}}\) (c) \(\left(2.35 \times 10^{-3}\right)^{1 / 3}\)

Give the number of significant figures in each of the following numbers: (a) \(0.0123 \mathrm{g}\) (b) \(3.40 \times 10^{3} \mathrm{mL}\) (c) \(1.6402 \mathrm{g}\) (d) \(1.020 \mathrm{L}\)

Give the number of significant figures in each of the following numbers: (a) \(0.00546 \mathrm{g}\) (b) \(1600 \mathrm{mL}\) (c) \(2.300 \times 10^{-4} \mathrm{g}\) (d) \(2.34 \times 10^{9}\) atoms

Carry out the following calculation, and report the answer with the correct number of significant figures. $$ (0.0546)(16.0000)\left[\frac{7.779}{55.85}\right] $$

Carry out the following calculation, and report the answer to the correct number of significant figures. $$ (1.68)\left[\frac{23.56-2.3}{1.248 \times 10^{3}}\right] $$

You are asked to calibrate a spectrophotometer in the laboratory and collect the following data. Plot the data with concentration on the \(x\) -axis and absorbance on the \(y\) -axis. Draw the best straight line using the points on the graph (or do a least-squares or linear regression analysis using a computer program) and then write the equation for the resulting straight line. What is the slope of the line? What is the concentration when the absorbance is \(0.635 ?\) $$\begin{array}{ll} \hline \text { Concentration }(\mathrm{M}) & \text { Absorbance } \\ \hline 0.00 & 0.00 \\ 1.029 \times 10^{-3} & 0.257 \\ 2.058 \times 10^{-3} & 0.518 \\ 3.087 \times 10^{-3} & 0.771 \\ 4.116 \times 10^{-3} & 1.021 \\ \hline \end{array}$$

To determine the average mass of a popcorn kernel you collect the following data: $$\begin{array}{ll} \hline \text { Number of kernels } & \text { Mass }(\mathrm{g}) \\ \hline 5 & 0.836 \\ 12 & 2.162 \\ 35 & 5.801 \\ \hline \end{array}$$ Plot the data with number of kernels on the \(x\) -axis and mass on the y-axis. Draw the best straight line using the points on the graph (or do a least- squares or linear regression analysis using a computer program) and then write the equation for the resulting straight line. What is the slope of the line? What does the slope of the line signify about the mass of a popcorn kernel? What is the mass of 50 popcorn kernels? How many kernels are there in a handful of popcorn \((20.88 \mathrm{g}) ?\)

Solve the following equation for the unknown value, \(C\). $$ (0.502)(123)=(750 .) C $$

Solve the following equation for the unknown value, \(n\) $$ (2.34)(15.6)=n(0.0821)(273) $$

Solve the following equation for the unknown value, \(T\) \((4.184)(244)(T-292.0)+(0.449)(88.5)(T-369.0)=0\)

Solve the following equation for the unknown value, \(n\) $$ -246.0=1312\left[\frac{1}{2^{2}}-\frac{1}{n^{2}}\right] $$

Diamond has a density of \(3.513 \mathrm{g} / \mathrm{cm}^{3} .\) The mass of diamonds is often measured in "carats," where 1 carat equals \(0.200 \mathrm{g} .\) What is the volume (in cubic centimeters) of a 1.50 -carat diamond?

A The smallest repeating unit of a crystal of common salt is a cube (called a unit cell) with an edge length of \(0.563 \mathrm{nm}\). (a) What is the volume of this cube in cubic nanometers? In cubic centimeters? (b) The density of \(\mathrm{NaCl}\) is \(2.17 \mathrm{g} / \mathrm{cm}^{3} .\) What is the mass of this smallest repeating unit ("unit cell")? (c) Each repeating unit is composed of four NaCl "molecules." What is the mass of one NaCl molecule? (IMAGE CAN'T COPY)

An ancient gold coin is \(2.2 \mathrm{cm}\) in diameter and \(3.0 \mathrm{mm}\) thick. It is a cylinder for which volume = (\pi) (radius) \(^{2}\) (thickness). If the density of gold is 19.3 \(\mathrm{g} / \mathrm{cm}^{3},\) what is the mass of the coin in grams?

Copper has a density of \(8.96 \mathrm{g} / \mathrm{cm}^{3} .\) An ingot of copper with a mass of \(57 \mathrm{kg}(126 \mathrm{lb})\) is drawn into wire with a diameter of \(9.50 \mathrm{mm} .\) What length of wire (in meters) can be produced? [Volume of wire \(\left.=(\pi) \text { (radius) }^{2} \text { (length) }\right]\).

A In July \(1983,\) an Air Canada Boeing 767 ran out of fuel over central Canada on a trip from Montreal to Edmonton. (The plane glided safely to a landing at an abandoned airstrip.) The pilots knew that 22,300 kg of fuel were required for the trip, and they knew that 7682 L of fuel were already in the tank. The ground crew added 4916 L of fuel, which was only about one fifth of what was required. The crew members used a factor of 1.77 for the fuel density-the problem is that 1.77 has units of pounds per liter and not kilograms per liter! What is the fuel density in units of kg/L? What mass of fuel should have been loaded? \((1 \mathrm{lb}=453.6 \mathrm{g} .)\)

When you heat popcorn, it pops because it loses water explosively. Assume a kernel of corn, with a mass of \(0.125 \mathrm{g},\) has a mass of only \(0.106 \mathrm{g}\) after popping. (a) What percentage of its mass did the kernel lose on popping? (b) Popcorn is sold by the pound in the United States. Using \(0.125 \mathrm{g}\) as the average mass of a popcorn kernel, how many kernels are there in a pound of popcorn? \((1 \mathrm{lb}=453.6 \mathrm{g} .)\)

The aluminum in a package containing \(75 \mathrm{ft}^{2}\) of kitchen foil weighs approximately 12 ounces. Aluminum has a density of \(2.70 \mathrm{g} / \mathrm{cm}^{3} .\) What is the approximate thickness of the aluminum foil in millimeters? \((1 \mathrm{oz}=28.4 \mathrm{g} .)\)

The fluoridation of city water supplies has been practiced in the United States for several decades. It is done by continuously adding sodium fluoride to water as it comes from a reservoir. Assume you live in a medium-sized city of 150,000 people and that \(660 \mathrm{L}(170 \mathrm{gal})\) of water is consumed per person per day. What mass of sodium fluoride (in kilograms) must be added to the water supply each year (365 days) to have the required fluoride concentration of 1 ppm (part per million)-that is, 1 kilogram of fluoride per 1 million kilograms of water? (Sodium fluoride is \(45.0 \%\) fluoride, and water has a density of \(1.00 \mathrm{g} / \mathrm{cm}^{3} .\) )

About two centuries ago, Benjamin Franklin showed that 1 teaspoon of oil would cover about 0.5 acre of still water. If you know that \(1.0 \times 10^{4} \mathrm{m}^{2}=2.47\) acres, and that there is approximately \(5 \mathrm{cm}^{3}\) in a teaspoon, what is the thickness of the layer of oil? How might this thickness be related to the sizes of molecules?

Automobile batteries are filled with an aqueous solution of sulfuric acid. What is the mass of the acid (in grams) in \(500 .\) mL of the battery acid solution if the density of the solution is \(1.285 \mathrm{g} / \mathrm{cm}^{3}\) and if the solution is \(38.08 \%\) sulfuric acid by mass?

A piece of copper has a mass of \(0.546 \mathrm{g} .\) Show how to set up an expression to find the volume of this piece of copper in units of liters. (Copper density \(=8.96 \mathrm{g} / \mathrm{cm}^{3} .\) )

Evaluate the value of \(x\) in the following expressions: (a) \(x=\left[\left(9.345 \times 10^{-4}\right)\left(6.23 \times 10^{6}\right)\right]^{3}\) (b) \(x=\sqrt{\left(1.23 \times 10^{-2}\right)\left(4.5 \times 10^{5}\right)}\) (c) \(x=\sqrt[3]{\left(1.23 \times 10^{-2}\right)\left(4.5 \times 10^{5}\right)}\) Show the answers to the correct number of significant figures.

A 26 -meter tall statue of Buddha in Tibet is covered with 279 kg of gold. If the gold was applied to a thickness of \(0.0015 \mathrm{mm},\) what surface area is covered (in square meters)? (Gold density \(=19.3 \mathrm{g} / \mathrm{cm}^{3} .\) )

At \(25^{\circ} \mathrm{C}\) the density of water is \(0.997 \mathrm{g} / \mathrm{cm}^{3},\) whereas the density of ice at \(-10^{\circ} \mathrm{C}\) is \(0.917 \mathrm{g} / \mathrm{cm}^{3} .\) (a) If a soft-drink can (volume \(=250 . \mathrm{mL}\) ) is filled completely with pure water at \(25^{\circ} \mathrm{C}\) and then frozen at \(-10^{\circ} \mathrm{C},\) what volume does the solid occupy? (b) Can the ice be contained within the can?

Suppose your bedroom is \(18 \mathrm{ft}\) long, \(15 \mathrm{ft}\) wide, and the distance from floor to ceiling is \(8 \mathrm{ft}, 6\) in. You need to know the volume of the room in metric units for some scientific calculations. (a) What is the room's volume in cubic meters? In liters? (b) What is the mass of air in the room in kilograms? In pounds? (Assume the density of air is \(1.2 \mathrm{g} / \mathrm{L}\) and that the room is empty of furniture.)

A spherical steel ball has a mass of \(3.475 \mathrm{g}\) and a diameter of \(9.40 \mathrm{mm} .\) What is the density of the steel? [The volume of a sphere \(\left.=(4 / 3) \pi r^{3} \text { where } r=\text { radius. }\right]\)

The substances listed below are clear liquids. You are asked to identify an unknown liquid that is known to be one of these liquids. You pipette a 3.50 -mL sample into a beaker. The empty beaker had a mass of \(12.20 \mathrm{g}\), and the beaker plus the liquid weighed \(16.08 \mathrm{g}\) $$\begin{array}{ll} \hline \text { Substance } & \text { Known Density at } 25^{\circ} \mathrm{C}\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\ \hline \text { Ethylene glycol } & 1.1088 \text { (the major component of antifreeze) } \\ \text { Water } & 0.9997 \\ \text { Ethanol } & 0.7893 \text { (the alcohol in alcoholic beverages) } \\ \text { Acetic acid } & 1.0492 \text { (the active component of vinegar) } \\ \text { Glycerol } & 1.2613 \text { (a solvent, used in home care } \\ \text { products) } \\ \hline \end{array}$$ (a) Calculate the density and identify the unknown. (b) If you were able to measure the volume to only two significant figures (that is, \(3.5 \mathrm{mL},\) not \(3.50 \mathrm{mL}\) ), will the results be sufficiently accurate to identify the unknown? Explain.

You have an irregularly shaped chunk of an unknown metal. To identify it, you determine its density and then compare this value with known values that you look up in the chemistry library. The mass of the metal is \(74.122 \mathrm{g}\) Because of the irregular shape, you measure the volume by submerging the metal in water in a graduated cylinder. When you do this, the water level in the cylinder rises from \(28.2 \mathrm{mL}\) to \(36.7 \mathrm{mL}\) (a) What is the density of the metal? (Use the correct number of significant figures in your answer.) (b) The unknown is one of the seven metals listed below. Is it possible to identify the metal based on the density you have calculated? Explain. $$\begin{array}{llll} \hline \text { Metal } & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) & \text { Metal } & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\ \hline \text { zinc } & 7.13 & \text { nickel } & 8.90 \\ \text { iron } & 7.87 & \text { copper } & 8.96 \\ \text { cadmium } & 8.65 & \text { silver } & 10.50 \\ \text { cobalt } & 8.90 & & \\ \hline \end{array}$$

A \(7.50 \times 10^{2}\) -mL sample of an unknown gas has a mass of \(0.9360 \mathrm{g}\) (a) What is the density of the gas? Express your answer in units of g/L. (b) Nine gases and their densities are listed below. Compare the experimentally determined density with these values. Can you determine the identity of the gas based on the experimentally determined density? (c) A more accurate measure of volume is made next, and the volume of this sample of gas is found to be \(7.496 \times 10^{2} \mathrm{mL} .\) Using a more accurate density calculated using this value, can you now determine the identity of the gas? $$\begin{array}{llll} \hline \text { Gas } & \text { Density }(\mathrm{g} / \mathrm{L}) & \text { Gas } & \text { Density }(\mathrm{g} / \mathrm{L}) \\ \hline \mathrm{B}_{2} \mathrm{H}_{6} & 1.2345 & \mathrm{C}_{2} \mathrm{H}_{4} & 1.2516 \\ \mathrm{CH}_{2} 0 & 1.3396 & \mathrm{C} 0 & 1.2497 \\ \mathrm{Dry} \text { air } & 1.2920 & \mathrm{C}_{2} \mathrm{H}_{6} & 1.3416 \\\ \mathrm{N}_{2} & 1.2498 & \mathrm{N} 0 & 1.2949 \\ 0_{2} & 1.4276 & & \\ \hline \end{array}$$

A The density of a single, small crystal can be determined by the flotation method. This method is based on the idea that if a crystal and a liquid have precisely the same density, the crystal will hang suspended in the liquid. A crystal that is more dense will sink; one that is less dense will float. If the crystal neither sinks nor floats, then the density of the crystal equals the density of the liquid. Generally, mixtures of liquids are used to get the proper density. Chlorocarbons and bromocarbons (see the list below) are often the liquids of choice. If the two liquids are similar, then volumes are usually additive and the density of the mixture relates directly to composition. (An example: \(1.0 \mathrm{mL}\) of \(\mathrm{CHCl}_{3}, d=1.4832 \mathrm{g} / \mathrm{mL},\) and 1.0 mL of \(\mathrm{CCl}_{4}, d=1.5940 \mathrm{g} / \mathrm{mL},\) when mixed, give \(2.0 \mathrm{mL}\) of a mixture with a density of \(1.5386 \mathrm{g} / \mathrm{mL} .\) The density of the mixture is the average of the values of the two individual components.) The problem: A small crystal of silicon, germanium, tin, or lead (Group 4A in the periodic table) will hang suspended in a mixture made of \(61.18 \%\) (by volume) \(\mathrm{CH}\) IBr \(_{3}\) and \(38.82 \%\) (by volume) \(\mathrm{CHCl}_{3} .\) Calculate the density and identify the element. (You will have to look up the values of the density of the elements in a manual such as the The Handbook of Chemistry and Physics in the library or in a World Wide Web site such as WebElements at, www.webelements.com.) $$\begin{array}{llll} \hline \text { Liquid } & \text { Density }(\mathrm{g} / \mathrm{mL}) & \text { Liquid } & \text { Density }(\mathrm{g} / \mathrm{mL}) \\ \hline \mathrm{CH}_{2} \mathrm{Cl}_{2} & 1.3266 & \mathrm{CH}_{2} \mathrm{Br}_{2} & 2.4970 \\ \mathrm{CH} \mathrm{Cl}_{3} & 1.4832 & \mathrm{CHBr}_{3} & 2.8899 \\ \mathrm{CCl}_{4} & 1.5940 & \mathrm{CBr}_{4} & 2.9609 \\ \hline \end{array}$$

Suppose you have a cylindrical glass tube with a thin capillary opening, and you wish to determine the diameter of the capillary. You can do this experimentally by weighing a piece of the tubing before and after filling a portion of the capillary with mercury. Using the following information, calculate the diameter of the capillary. Mass of tube before adding mercury \(=3.263 \mathrm{g}\) Mass of tube after adding mercury \(=3.416 \mathrm{g}\) Length of capillary filled with mercury \(=16.75 \mathrm{mm}\) Density of mercury \(=13.546 \mathrm{g} / \mathrm{cm}^{3}\) Volume of cylindrical capillary filled with mercury \(=(\pi)(\text { radius })^{2}(\text { length })\)