Chapter 1

Describe the separation method(s) involved in brewing a cup of coffee. [Section 1.3]

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (c) \(77 \mathrm{~K},(\mathbf{d}) 100,000 \mathrm{~km}^{2},\) (b) \(374.2 \mathrm{mg}\) (e) \(1.06 \mu \mathrm{m},(\mathrm{f}) 16 \mathrm{nm}^{2}\) \((g)-78^{\circ} \mathrm{C}\) (h) \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\), (i) \(28 \mathrm{~cm}^{3}\). [Section 1.4].

(a) Three spheres of equal size are composed of aluminum \(\left(\right.\) density \(\left.=2.70 \mathrm{~g} / \mathrm{cm}^{3}\right),\) silver \(\left(\right.\) density \(\left.=10.49 \mathrm{~g} / \mathrm{cm}^{3}\right),\) and nickel (density \(\left.=8.90 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the spheres from lightest to (b) Three cubes of equal mass are composed of gold \(\left(\right.\) density \(\left.=19.32 \mathrm{~g} / \mathrm{cm}^{3}\right)\), platinum (density \(\left.=21.45 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and lead (density \(\left.=11.35 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the cubes from smallest to largest. [Section 1.4]

When you convert units, how do you decide which part of the conversion factor is in the numerator and which is in the denominator? [Section 1.6]

Show the steps to convert the speed of sound, 344 meters per second, into miles per hour. [Section 1.6]

Classify each of the following as a pure substance or a mixture. If a mixture, indicate whether it is homogeneous or heterogeneous: (a) rice pudding, (b) seawater, (c) magnesium, (d) crushed ice.

Classify each of the following as a pure substance or a mixture. If a mixture, indicate whether it is homogeneous or heterogeneous: (a) air, (b) tomato juice, (c) iodine crystals, (d) sand.

Give the chemical symbol or name for the following elements, as appropriate: (a) sulfur, (b) gold, (c) potassium, (d) chlorine, (e) copper, (f) \(\mathrm{U},(\mathrm{g}) \mathrm{Ni}\) (h) \(\mathrm{Na},\) (i) \(\mathrm{Al},(\mathrm{j}) \mathrm{Si}\).

Give the chemical symbol or name for each of the following elements, as appropriate: (a) carbon, (b) nitrogen, (c) titanium, \((\mathbf{d})\) zinc, \((\mathbf{e})\) iron, \((\mathbf{f}) \mathrm{P},(\mathrm{g}) \mathrm{Ca},(\mathbf{h}) \mathrm{He},(\mathbf{i}) \mathrm{Pb},(\mathbf{j}) \mathrm{Ag} .\)

In the process of attempting to characterize a substance, a chemist makes the following observations: The substance is a silvery white, lustrous metal. It melts at \(649^{\circ} \mathrm{C}\) and boils at \(1105^{\circ} \mathrm{C}\). Its density at \(20{ }^{\circ} \mathrm{C}\) is \(1.738 \mathrm{~g} / \mathrm{cm}^{3}\). The substance burns in air, producing an intense white light. It reacts with chlorine to give a brittle white solid. The substance can be pounded into thin sheets or drawn into wires. It is a good conductor of electricity. Which of these characteristics are physical properties, and which are chemical properties?

Read the following description of the element zinc and indicate which are physical properties and which are chemical properties. Zinc is a silver-gray- colored metal that melts at \(420^{\circ} \mathrm{C}\). When zinc granules are added to dilute sulfuric acid, hydrogen is given off and the metal dissolves. Zinc has a hardness on the Mohs scale of 2.5 and a density of \(7.13 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\). It reacts slowly with oxygen gas at elevated temperatures to form zinc oxide, \(\mathrm{ZnO}\).

Label each of the following as either a physical process or a chemical process: (a) rusting of a metal can, (b) boiling a cup of water, (c) pulverizing an aspirin, (d) digesting a candy bar, (e) exploding of nitroglycerin.

A match is lit and held under a cold piece of metal. The following observations are made: (a) The match burns. (b) The metal gets warmer. (c) Water condenses on the metal. (d) Soot (carbon) is deposited on the metal. Which of these occurrences are due to physical changes, and which are due to chemical changes?

Suggest a method of separating each of the following mixtures into two components: (a) sugar and sand, (b) oil and vinegar.

Three beakers contain clear, colorless liquids. One beaker contains pure water, another contains salt water, and another contains sugar water. How can you tell which beaker is which? (No tasting allowed!)

What exponential notation do the following abbreviations (e) \(\mathrm{M},(\mathrm{f}) \mathrm{k},(\mathrm{g}) \mathrm{n},(\mathrm{h}) \mathrm{m}\) represent: (a) \(\mathrm{d},(\mathbf{b}) \mathrm{c},(\mathrm{c}) \mathrm{f},(\mathrm{d}) \mu\) (i) p?

Use appropriate metric prefixes to write the following measurements without use of exponents: (a) \(2.3 \times 10^{-10} \mathrm{~L}\) (b) \(4.7 \times 10^{-6} \mathrm{~g}\), (c) \(1.85 \times 10^{-12} \mathrm{~m}\) (d) \(16.7 \times 10^{6} \mathrm{~s}\); (e) \(15.7 \times 10^{3} \mathrm{~g}\) (f) \(1.34 \times 10^{-3} \mathrm{~m},(\mathrm{~g}) 1.84 \times 10^{2} \mathrm{~cm}\)

Make the following conversions: (a) \(72^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\), (b) \(216.7{ }^{\circ} \mathrm{C}\) to \({ }^{\circ} \mathrm{F},(\mathrm{c}) 233^{\circ} \mathrm{C}\) to \(\mathrm{K},\) (d) \(315 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F},(\mathrm{e}) 2500^{\circ} \mathrm{F}\) to \(\mathrm{K},(\mathrm{f}) 0 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\)

a) The temperature on a warm summer day is \(87^{\circ} \mathrm{F}\). What is the temperature in \({ }^{\circ} \mathrm{C} ?\) (b) Many scientific data are reported at \(25^{\circ} \mathrm{C}\). What is this temperature in kelvins and in degrees Fahrenheit? (c) Suppose that a recipe calls for an oven temperature of \(400{ }^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius and to kelvins. (d) Liquid nitrogen boils at \(77 \mathrm{~K}\). Convert this temperature to degrees Fahrenheit and to degrees Celsius.

(a) A sample of tetrachloroethylene, a liquid used in dry cleaning that is being phased out because of its potential to cause cancer, has a mass of \(40.55 \mathrm{~g}\) and a volume of \(25.0 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\). What is its density at this temperature? Will tetrachloroethylene float on water? (Materials that are less dense than water will float.) (b) Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is a gas at room temperature and pressure. However, carbon dioxide can be put under pressure to become a "supercritical fluid" that is a much safer drycleaning agent than tetrachloroethylene. At a certain pressure, the density of supercritical \(\mathrm{CO}_{2}\) is \(0.469 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the mass of a \(25.0-\mathrm{mL}\) sample of supercritical \(\mathrm{CO}_{2}\) at this pressure?

(a) A cube of osmium metal \(1.500 \mathrm{~cm}\) on a side has a mass of \(76.31 \mathrm{~g}\) at \(25^{\circ} \mathrm{C}\). What is its density in \(\mathrm{g} / \mathrm{cm}^{3}\) at this temperature? (b) The density of titanium metal is \(4.51 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\). What mass of titanium displaces \(125.0 \mathrm{~mL}\) of water at \(25^{\circ} \mathrm{C} ?\) (c) The density of benzene at \(15^{\circ} \mathrm{C}\) is \(0.8787 \mathrm{~g} / \mathrm{mL} .\) Calculate the mass of \(0.1500 \mathrm{~L}\) of benzene at this temperature.

(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\) sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL})\) or toluene (density \(0.866 / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires \(45.0 \mathrm{~g}\) of ethylene glycol, a liquid whose density is \(1.114 \mathrm{~g} / \mathrm{mL}\). Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) A cubic piece of metal measures \(5.00 \mathrm{~cm}\) on each edge. If the metal is nickel, whose density is \(8.90 \mathrm{~g} / \mathrm{cm}^{3},\) what is the mass of the cube?

(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A 25.0 -mL portion of the liquid had a mass of \(21.95 \mathrm{~g}\). A chemistry handbook lists the density of benzene at \(15^{\circ} \mathrm{C}\) as \(0.8787 \mathrm{~g} / \mathrm{mL}\). Is the calculated density in agreement with the tabulated value? (b) An experiment requires \(15.0 \mathrm{~g}\) of cyclohexane, whose density at \(25^{\circ} \mathrm{C}\) is \(0.7781 \mathrm{~g} / \mathrm{mL}\). What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of \(5.0 \mathrm{~cm}\). What is the mass of the sphere if lead has a density of \(11.34 \mathrm{~g} / \mathrm{cm}^{3}\) ? (The volume of a sphere is \((4 / 3) \pi r^{3}\) where \(r\) is the radius.)

In the year 2007 , an estimated amount of 31 billion tons of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) was emitted worldwide due to fossil fuel combustion and cement production. Express this mass of \(\mathrm{CO}_{2}\) in grams without exponential notation, using an appropriate metric prefix.

Silicon for computer chips is grown in large cylinders called "boules" that are \(300 \mathrm{~mm}\) in diameter and \(2 \mathrm{~m}\) in height. The density of silicon is \(2.33 \mathrm{~g} / \mathrm{cm}^{3}\). Silicon wafers for making integrated circuits are sliced from a \(2.0 \mathrm{~m}\) boule and are typically \(0.75 \mathrm{~mm}\) thick and \(300 \mathrm{~mm}\) in diameter. (a) How many wafers can be cut from a single boule? (b) What is the mass of a silicon wafer? (The volume of a cylinder is given by \(\pi r^{2} h\), where \(r\) is the radius and \(h\) is its height.)

Indicate which of the following are exact numbers: (a) the mass of a piece of paper, \((\mathbf{b})\) the volume of a cup of coffee, \((\mathbf{c})\) the number of inches in a mile, \((\mathbf{d})\) the number of ounces in a pound, (e) the number of microseconds in a week, (f) the number of pages in this book.

Indicate which of the following are exact numbers: (a) the mass of a 32 -oz can of coffee, (b) the number of students in your chemistry class, \((\mathbf{c})\) the temperature of the surface of the sun, (d) the mass of a postage stamp, (e) the number of milliliters in a cubic meter of water, (f) the average height of students in your school.

What is the number of significant figures in each of the following measured quantities? (a) \(601 \mathrm{~kg}\), (b) \(0.054 \mathrm{~s}\), (c) \(6.3050 \mathrm{~cm}\), (d) \(0.0105 \mathrm{~L}\) (e) \(7.0500 \times 10^{-3} \mathrm{~m}^{3}\) (f) \(400 \mathrm{~g}\).

Indicate the number of significant figures in each of the following measured quantities: (a) \(3.774 \mathrm{~km}\) (b) \(205 \mathrm{~m}^{2}\), (c) \(1.700 \mathrm{~cm}\), (d) \(350.00 \mathrm{~K}\), (e) \(307.080 \mathrm{~g}\), (f) \(1.3 \times 10^{3} \mathrm{~m} / \mathrm{s}\)

Round each of the following numbers to four significant figures, and express the result in standard exponential notation: (c) \(0.008543210,\) (d) 0.000257870 , (a) \(102.53070,(\mathbf{b}) 656,980,\) (e) -0.0357202 .

(a) The diameter of Earth at the equator is \(7926.381 \mathrm{mi}\). Round this number to three significant figures, and express it in standard exponential notation. (b) The circumference of Earth through the poles is \(40,008 \mathrm{~km}\). Round this number to four significant figures, and express it in standard exponential notation.

Carry out the following operations, and express the answers with the appropriate number of significant figures. (a) \(14.3505+2.65\) (b) \(952.7-140.7389\) (c) \(\left(3.29 \times 10^{4}\right)(0.2501)\) (d) \(0.0588 / 0.677\)

Carry out the following operations, and express the answer with the appropriate number of significant figures. (a) \(320.5-(6104.5 / 2.3)\) (b) \(\left[\left(285.3 \times 10^{5}\right)-\left(1.200 \times 10^{3}\right)\right] \times 2.8954\) (c) \((0.0045 \times 20,000.0)+(2813 \times 12)\) (d) \(863 \times[1255-(3.45 \times 108)]\)

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mathrm{mm}\) to \(\mathrm{nm},\) (b) \(\mathrm{mg}\) to \(\mathrm{kg}\), (c) \(\mathrm{km}\) to \(\mathrm{ft},\) (d) \(\mathrm{in} .{ }^{3}\) to \(\mathrm{cm}^{3}\).

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mu \mathrm{m}\) to \(\mathrm{mm},\) (b) \(\mathrm{ms}\) to \(\mathrm{ns}\), (c) \(\mathrm{mi}\) to \(\mathrm{km},\) (d) \(\mathrm{ft}^{3}\) to \(\mathrm{L}\)

(a) A bumblebee flies with a ground speed of \(15.2 \mathrm{~m} / \mathrm{s}\). Calculate its speed in \(\mathrm{km} / \mathrm{h}\). (b) The lung capacity of the blue whale is \(5.0 \times 10^{3} \mathrm{~L}\). Convert this volume into gallons. (c) The Statue of Liberty is 151 ft tall. Calculate its height in meters. (d) Bamboo can grow up to \(60.0 \mathrm{~cm} /\) day. Convert this growth rate into inches per hour.

Perform the following conversions: (a) 5.00 days to s, (b) 0.0550 mi to \(\mathrm{m}\), (c) $$\$ 1.89 /$$ gal to dollars per liter, (d) 0.510 in. \(/ \mathrm{ms}\) to (f) \(0.02500 \mathrm{ft}^{3}\) to \(\mathrm{cm}^{3}\) \(\mathrm{km} / \mathrm{hr},\) (e) \(22.50 \mathrm{gal} / \mathrm{min}\) to \(\mathrm{L} / \mathrm{s}\)

Carry out the following conversions: (a) 0.105 in. to \(\mathrm{mm},\) (b) 0.650 qt to \(\mathrm{mL},\) (c) \(8.75 \mu \mathrm{m} / \mathrm{s}\) to \(\mathrm{km} / \mathrm{hr}\), (d) \(1.955 \mathrm{~m}^{3}\) to \(\mathrm{yd}^{3}\), (e) $$\$ 3.99 / \mathrm{lb}$$ to dollars per \(\mathrm{kg}\), (f) \(8.75 \mathrm{lb} / \mathrm{ft}^{3}\) to \(\mathrm{g} / \mathrm{mL}\)

(a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal? (b) The recommended adult dose of Elixophyllin \(^{\circledast}\), a drug used to treat asthma, is \(6 \mathrm{mg} / \mathrm{kg}\) of body mass. Calculate the dose in milligrams for a 185 -lb person. (c) If an automobile is able to travel \(400 \mathrm{~km}\) on \(47.3 \mathrm{~L}\) of gasoline, what is the gas mileage in miles per gallon? (d) A pound of coffee beans yields 50 cups of coffee \((4\) cups \(=1 \mathrm{qt}) .\) How many milliliters of coffee can be obtained from \(1 \mathrm{~g}\) of coffee beans?

The density of air at ordinary atmospheric pressure and \(25^{\circ} \mathrm{C}\) is \(1.19 \mathrm{~g} / \mathrm{L}\). What is the mass, in kilograms, of the air in a room that measures \(14.5 \mathrm{ft} \times 16.5 \mathrm{ft} \times 8.0 \mathrm{ft} ?\)

By using estimation techniques, arrange these items in order from shortest to longest: a 57 -cm length of string, a 14 -in.-long shoe, and a \(1.1-\mathrm{m}\) length of pipe.

By using estimation techniques, determine which of the following is the heaviest and which is the lightest: a 5-lb bag of potatoes, a \(5-\mathrm{kg}\) bag of sugar, or 1 gal of water \((\) density \(=1.0 \mathrm{~g} / \mathrm{mL})\)

Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a \(100 \mathrm{ft} \times 82 \mathrm{ft}\) ceiling with gold leaf that is five-millionths of an inch thick. The density of gold is \(19.32 \mathrm{~g} / \mathrm{cm}^{3},\) and gold costs \(\$ 953\) per troy ounce \((1\) troy ounce \(=31.1034768 \mathrm{~g}) .\) How much will it cost the architect to buy the necessary gold?

A copper refinery produces a copper ingot weighing \(150 \mathrm{lb}\). If the copper is drawn into wire whose diameter is \(7.50 \mathrm{~mm}\), how many feet of copper can be obtained from the ingot? The density of copper is \(8.94 \mathrm{~g} / \mathrm{cm}^{3}\). (Assume that the wire is a cylinder whose volume \(V=\pi r^{2} h,\) where \(r\) is its radius and \(h\) is its height or length.)

(a) Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: a gold coin, a cup of coffee, a wood plank. (b) What ambiguities are there in answering part (a) from the descriptions given?

(a) What is the difference between a hypothesis and a theory? (b) Explain the difference between a theory and a scientific law. Which addresses how matter behaves, and which addresses why it behaves that way?

A sample of ascorbic acid (vitamin C) is synthesized in the laboratory. It contains \(1.50 \mathrm{~g}\) of carbon and \(2.00 \mathrm{~g}\) of oxygen. Another sample of ascorbic acid isolated from citrus fruits contains \(6.35 \mathrm{~g}\) of carbon. How many grams of oxygen does it contain? Which law are you assuming in answering this question?

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is \(22.52 \% .\) The students' results for three determinations are as follows: 1\. 22.52,22.48,22.54 2\. 22.64,22.58,22.62 (a) Calculate the average percentage for each set of data, and state which set is the more accurate based on the average. \((\mathbf{b})\) Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

Is the use of significant figures in each of the following statements appropriate? Why or why not? (a) Apple sold 22,727,000 iPods during the last three months of 2008 . (b) New York City receives 49.7 inches of rain, on average, per year. (c) In the United States, \(0.621 \%\) of the population has the surname Brown. (d) You calculate your grade point average to be \(3.87562 .\)

What type of quantity (for example, length, volume, density) do the following units indicate: (a) \(\mathrm{mL},(\mathbf{b}) \mathrm{cm}^{2},(\mathrm{c}) \mathrm{mm}^{3}\) (d) \(\mathrm{mg} / \mathrm{L},(\mathrm{e}) \mathrm{ps},(\mathrm{f}) \mathrm{nm},(\mathrm{g}) \mathrm{K} ?\)