Chapter 1

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(5 \mathrm{~ns}\), (b) \(5.5 \mathrm{~kg} / \mathrm{m}^{3}\), (c) \(0.88 \mathrm{pm}\), (d) \(540 \mathrm{~km}^{2}\), (e) \(173 \mathrm{~K}\), (f) \(2 \mathrm{~mm}^{3}\), (g) \(23{ }^{\circ} \mathrm{C}\). [Section 1.4]

Three spheres of equal size are composed of aluminum (density \(=2.70 \mathrm{~g} / \mathrm{cm}^{3}\) ), silver (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 heaviest.

What is wrong with the following statement? Twenty years ago an ancient artifact was determined to be 1900 years old. It must now be 1920 years old. [Section 1.5]

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]

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) gasoline.

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) magnesium, (c) potassium, (d) chlorine, (e) copper, (f) \(\mathrm{F}\), (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, \((\mathrm{c})\) bromine, \((\mathrm{d})\) zinc, \((\mathrm{e})\) iron, \((\mathrm{f}) \mathrm{P},(\mathrm{g}) \mathrm{Ca},(\mathrm{h}) \mathrm{He}\), (i) \(\mathrm{Pb},(\mathrm{j}) \mathrm{Ag}\)

A solid white substance \(A\) is heated strongly in the absence of air. It decomposes to form a new white substance \(B\) and a gas \(C\). The gas has exactly the same properties as the product obtained when carbon is burned in an excess of oxygen. Based on these observations, can we determine whether solids \(\mathrm{A}\) and \(\mathrm{B}\) and the gas \(\mathrm{C}\) are elements or compounds? Explain your conclusions for each substance.

In 1807 the English chemist Humphry Davy passed an electric current through molten potassium hydroxide and isolated a bright, shiny reactive substance. He claimed the discovery of a new element, which he named potassium. In those days, before the advent of modern instruments, what was the basis on which one could claim that a substance was an element?

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) corrosion of aluminum metal, (b) melting of ice, (c) pulverizing an aspirin, (d) digesting a candy bar, (e) explosion 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) iron and sulfur.

A beaker contains a clear, colorless liquid. If it is water, how could you determine whether it contained dissolved table salt? Do not taste it!

Use appropriate metric prefixes to write the following measurements without use of exponents: (a) \(6.35 \times 10^{-2} \mathrm{~L}\), (b) \(6.5 \times 10^{-6} \mathrm{~s}\), (c) \(9.5 \times 10^{-4} \mathrm{~m}\), (d) \(4.23 \times 10^{-9} \mathrm{~m}^{3}\) (e) \(12.5 \times 10^{-8} \mathrm{~kg}\) (f) \(3.5 \times 10^{-10} \mathrm{~g}\) (g) \(6.54 \times 10^{9} \mathrm{fs}\)

Makethe following conversions: (a) \(62^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\), (b) \(216.7\) \({ }^{\circ} \mathrm{C}\) to \({ }^{\circ} \mathrm{F}\), (c) \(233^{\circ} \mathrm{C}\) to \(\mathrm{K}\), (d) \(315 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\), \((\mathrm{e}) 2500^{\circ} \mathrm{F}\) to \(\mathrm{K}\).

(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 \(175^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius and to kelvins.(d) The melting point of sodium bromide (a salt) is \(755^{\circ} \mathrm{C}\). Calculate this temperature in \({ }^{\circ} \mathrm{F}\) and in kelvins. (e) Neon, a gaseous element at room temperature, is used to make electronic signs. Neon has a melting point of \(-248.6^{\circ} \mathrm{C}\) and a boiling point of \(-246.1^{\circ} \mathrm{C}\). Convert these temperatures to kelvins.

(a) A sample of carbon tetrachloride, a liquid once used in dry cleaning, has a mass of \(39.73 \mathrm{~g}\) and a volume of \(25.0 \mathrm{mLat} 25^{\circ} \mathrm{C}\). What is its density at this temperature? Will carbon tetrachloride float on water? (Materials that are less dense than water will float.) (b) The density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). Calculate the mass of \(75.00 \mathrm{~cm}^{3}\) of platinum at this temperature. (c) The density of magnesium is \(1.738 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). What is the volume of \(87.50 \mathrm{~g}\) of this metal at this temperature?

(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a 45-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 \(25.0-\mathrm{mL}\) 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 \(\left(\frac{4}{3}\right) \pi r^{3}\) where \(r\) is the radius.)

Gold can be hammered into extremely thin sheets called gold leaf. If a 200-mg piece of gold (density \(=19.32 \mathrm{~g} / \mathrm{cm}^{3}\) ) is hammered into a sheet measuring \(2.4 \times 1.0 \mathrm{ft}\), what is the average thickness of the sheet in meters? How might the thickness be expressed without exponential notation, using an appropriate metric prefix?

A cylindrical rod formed from silicon is \(16.8 \mathrm{~cm}\) long and has a mass of \(2.17 \mathrm{~kg}\). The density of silicon is \(2.33 \mathrm{~g} / \mathrm{cm}^{3}\). What is the diameter of the cylinder? (The volume of a cylinder is given by \(\pi r^{2} h\), where \(r\) is the radius, and \(h\) is its length.)

Indicate which of the following are exact numbers: (a) the mass of a paper clip, (b) the surface area of a dime, (c) the number of inches in a mile, (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, (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) \(358 \mathrm{~kg}\), (b) \(0.054 \mathrm{~s}\), (c) \(6.3050 \mathrm{~cm}\), (d) \(0.0105 \mathrm{~L}\), (e) \(7.0500 \times 10^{-3} \mathrm{~m}^{3}\).

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) \(350.00 \mathrm{~K}_{1}\) (e) \(307.080 \mathrm{~g}\).

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

(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) \(12.0550+9.05\) (b) \(257.2-19.789\) (c) \(\left(6.21 \times 10^{3}\right)(0.1050)\) (d) \(0.0577 / 0.753\)

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 \(\mathrm{ft}\), \((\mathrm{d})\) 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 \(\mathrm{mm},(\mathrm{b}) \mathrm{ms}\) tons, \((\mathrm{c}) \mathrm{mi}\) to \(\mathrm{km},(\mathrm{d}) \mathrm{ft}^{3}\) to \(\mathrm{L}\).

Perform the following conversions: (a) \(0.076 \mathrm{~L}\) to \(\mathrm{mL}\), (b) \(5.0 \times 10^{-8} \mathrm{~m}\) to \(\mathrm{nm}\), (c) \(6.88 \times 10^{5} \mathrm{~ns}\) to \(\mathrm{s}\), (d) \(0.50 \mathrm{lb}\) to \(\mathrm{g}\), (e) \(1.55 \mathrm{~kg} / \mathrm{m}^{3}\) to \(\mathrm{g} / \mathrm{L}\), (f) \(5.850 \mathrm{gal} / \mathrm{hr}\) 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 \(\mathrm{g} / \mathrm{mL}\).

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 \(12.5 \times 15.5 \times 8.0 \mathrm{ft}\) ?

By using estimation techniques, arrange these items in order from shortest to longest: a \(57-\mathrm{cm}\) 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 \(=1.0 \mathrm{~g} / \mathrm{mL}\) ).

The Morgan silver dollar has a mass of \(26.73\) g. By law, it was required to contain \(90 \%\) silver, with the remainder being copper. (a) When the coin was minted in the late \(1800 \mathrm{~s}\), silver was worth \(\$ 1.18\) per troy ounce (31.1 g). At this price, what is the value of the silver in the silver dollar? (b) Today, silver sells for about \(\$ 13.25\) per troy ounce. How many Morgan silver dollars are required to obtain \(\$ 25.00\) worth of pure silver?

A copper refinery produces a copper ingot weighing \(150 \mathrm{lb}\). If the copper is drawn into wire whose diameter is \(8.25 \mathrm{~mm}\), 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 is \(\boldsymbol{V}=\pi r^{2} h\) where \(r\) is its radius and \(h\) is its height or length.)

What is meant by the terms composition and structure when referring to matter?

(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 \(\mathrm{C}\) ) 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?

Is the use of significant figures in each of the following statements appropriate? Why or why not? (a) The 2005 circulation of \(N\) ational Geographic was \(7,812,564\). (b) On July 1, 2005, the population of Cook County, Illinois, was \(5,303,683 .\) (c) In the United States, \(0.621 \%\) of the population has the surname Brown.

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

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; (c) work \(=\) force \(X\) distance; (d) pressure \(=\) force/area; (e) power = work/time.

The distance from Earth to the Moon is approximately 240,000 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?

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) At the beginning of 2007 , the national debt was \(\$ 8.7\) trillion. How many stacks like the one described would be necessary to pay off this debt?