Chapter 2

Which one of the following expresses the measured value \(0.000003 \mathrm{~L}\) with the correct number of significant figures? (a) \(3 \mathrm{~mL}\) (b) \(3 \mu \mathrm{L}\) (c) \(3.00 \times 10^{-6} \mathrm{~L}\) (d) \(3.00 \times 10^{-3} \mathrm{~mL}\)

The SI unit of speed is meters per second. In the United States, speed is often expressed in miles per hour. If a car is traveling \(60.0\) miles \(/ \mathrm{h}\), what is its speed in meters per second? \([1\) mile \(=1.61 \mathrm{~km}]\)

In the United States, car fuel efficiency is expressed in miles per gallon of gasoline. However, fuel efficiency can also be expressed in kilometers per liter of gasoline. If the fuel efficiency of a car is \(11.0 \mathrm{~km} / \mathrm{L}\), what is its fuel efficiency in miles per gallon? \([1\) mile \(=1.61 \mathrm{~km}, 1\) gallon \(=3.79 \mathrm{~L}]\)

Convert: (a) \(72{ }^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\) and \(\mathrm{K}\) (b) \(-12{ }^{\circ} \mathrm{C}\) to \({ }^{\circ} \mathrm{F}\) and \(\mathrm{K}\) (c) \(178 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\) and \({ }^{\circ} \mathrm{C}\)

Use Greek prefixes to express the relationship between the calorie and the Calorie.

When a 16.74-g rubber stopper is placed in a graduated cylinder containing \(25.46 \mathrm{~mL}\) of water, the water level rises to \(37.42 \mathrm{~mL}\). What is the density of the stopper in grams per milliliter?

Solve each equation for the underlined quantity: (a) \({ }^{\circ} \mathrm{F}=9 / 5^{\circ} \mathrm{C}+32\) (b) \(P V=n R T\) (c) \(E=h c / \underline{\lambda}\)

Convert: (a) \(2.37 \times 10^{2} \mathrm{~L}\) to milliliter (b) \(800 \mathrm{~kg}\) to grams (c) \(0.592 \mathrm{~mm}\) to meters (d) \(8.31 \mathrm{~g}\) to kilograms (e) \(9.62 \times 10^{-6} \mathrm{~L}\) to microliters (f) \(8000 \mathrm{~m}\) to kilometers (g) \(19.3 \mathrm{mg}\) to grams (h) \(0.00345 \mathrm{~mL}\) to liters

For solids, the amount of material per unit volume is often expressed in grams per milliliter, whereas for gases the amount of material per unit volume is usually expressed in grams per liter. If the amount of matter in air is \(1.34 \mathrm{~g} / \mathrm{L}\), what is this value in: (a) \(\mathrm{g} / \mathrm{mL}\) (b) \(\mathrm{kg} / \mathrm{L}\) (c) \(\mathrm{kg} / \mathrm{mL}\) ?

The specific heat of methane gas is \(2.20 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If the temperature of a sample of methane gas rises by \(15^{\circ} \mathrm{C}\) when \(8.8 \mathrm{~kJ}\) of heat energy is added to the sample, what is the mass of the sample?

Explain how determining the number of significant figures allowed in an answer when measured values are multiplied or divided is different from determining the number of significant figures allowed in an answer when measured values are added or subtracted.

Convert: (a) \(23.0{ }^{\circ} \mathrm{C}\) to \(\mathrm{K}\) (b) \(98.6^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\) (c) \(296 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\) (d) \(32^{\circ} \mathrm{F}\) to \(\mathrm{K}\) (e) \(523 \mathrm{~K}\) to \({ }^{\circ} \mathrm{C}\) (f) \(38^{\circ} \mathrm{C}\) to \({ }^{\circ} \mathrm{F}\)

A student takes three measurements of the mass of an object. If the actual mass is \(8.54 \mathrm{~g}\), indicate whether each set of measurements is precise but not accurate, accurate but not precise, both accurate and precise, or neither accurate nor precise: (a) \(6.38 \mathrm{~g}, 9.23 \mathrm{~g}, 4.36 \mathrm{~g}\) (b) \(8.53 \mathrm{~g}, 8.59 \mathrm{~g}, 8.55 \mathrm{~g}\) (c) \(9.53 \mathrm{~g}, 8.54 \mathrm{~g}, 7.54 \mathrm{~g}\) (d) \(6.25 \mathrm{~g}, 6.27 \mathrm{~g}, 6.26 \mathrm{~g}\)

A block of metal measuring \(3.0 \mathrm{~cm} \times 4.0 \mathrm{~cm} \times 5.0 \mathrm{~cm}\) has a mass of \(470.0\) g. What is the density of the metal in grams per cubic centimeter?

A student measures the mass of an object three times and reports the numeric average of her measurements. If her three measurements are \(212 \mathrm{~g}\), \(260 \mathrm{~g}\), and \(233 \mathrm{~g}\) and the actual mass is \(235 \mathrm{~g}\), which of the following statements is true: (a) The student is accurate but not precise. (b) The student is precise but not accurate. (c) The student is both accurate and precise. (d) It is impossible to tell whether the student is accurate and \(/\) or precise without knowing how she determined the mass.

The density of an irregularly shaped object is determined by immersing the object in water. If the mass of the object is \(8.34 \mathrm{~g}\) and the water level rises from \(25.00 \mathrm{~mL}\) to \(28.10 \mathrm{~mL}\), what is the density of the object in grams per milliliter?

The specific heat of copper is \(0.385 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). How much heat energy in kilojoules is required to raise the temperature of \(454 \mathrm{~g}\) of copper from \(40.0{ }^{\circ} \mathrm{C}\) to \(75.0^{\circ} \mathrm{C} ?\)

Express \(23,000,000\) in scientific notation having: (a) Two significant figures (b) Three significant figures (c) Five significant figures (d) Six significant figures (e) Eight significant figures

Dieters are often told that drinking ice-cold water burns more energy than drinking roomtemperature water. Why is this true?

If a graduated cylinder has markings that indicate \(0.01 \mathrm{~mL}\), what is the uncertainty in any volumes determined using this graduated cylinder?

The density of gold is \(19.3 \mathrm{~g} / \mathrm{mL}\), that of lead is \(11.4 \mathrm{~g} / \mathrm{mL}\), that of iron \(7.8 \mathrm{~g} / \mathrm{mL}\), and that of aluminum \(2.7 \mathrm{~g} / \mathrm{mL}\). A student is given separate samples of three substances \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), along with a graduated cylinder containing \(50.0 \mathrm{~mL}\) of water. Each sample has a mass of \(200.0 \mathrm{~g}\), and the student finds that the volumes of the samples are A, \(25.64 \mathrm{~mL} ; \mathrm{B}, 10.36 \mathrm{~mL} ;\) and \(\mathrm{C}, 17.54 \mathrm{~mL}\). What is the identity of each substance?

When \(10 \mathrm{~kJ}\) of heat energy is added to a beaker containing \(250 \mathrm{~g}\) of water initially at \(23.0{ }^{\circ} \mathrm{C}\), what is the final temperature of the water?

Indicate the uncertainty in: (a) \(74.8 \mathrm{~m}\) (b) \(0.0026 \mathrm{~g}\) (c) \(1.250 \times 10^{3} \mathrm{~L}\) (d) \(18 \mathrm{~cm}\) (e) 18 pennies

Round each number to three significant digits and express the answer in scientific notation: (a) \(0.592861\) (b) 438932 (c) \(0.000073978\) (d) \(0.235469\) (e) \(82.550\) (f) \(529.8\)

Explain the relationship between a calorie and a Calorie.

Do the following calculations and express each answer in scientific notation: (a) \(\left(5.03 \times 10^{2}\right)+\left(8.1 \times 10^{1}\right)\) (b) \(\left(8.32 \times 10^{-5}\right) \times\left(0.53 \times 10^{4}\right)\) (c) \(\frac{6.02 \times 10^{23}}{3}\), where the 3 is an exact number (d) \(\left(3.960 \times 10^{3}\right)-\left(4.62 \times 10^{2}\right)\)

A block measures \(6.0 \mathrm{~cm}\) on each side. What is the volume of the block in cubic meters?

The mass of an average neon atom is \(20.2\) atomic mass units (amu), where 1 amu \(=1.66 \times 10^{-24} \mathrm{~g}\). (a) What is the mass in atomic mass units of 20 neon atoms? (b) What is the mass in grams of 20 neon atoms? (c) What is the mass in grams of \(6.022 \times 10^{23}\) neon atoms?

If the same amount of heat energy is added to a beaker containing \(100 \mathrm{~mL}\) of ethanol and a beaker containing \(100 \mathrm{~mL}\) of water, which liquid experiences the greater rise in temperature?

Indicate whether the trailing zero in each value is significant, not significant, or possibly significant: (a) \(540 \pm 0.5\) (b) \(540 \pm 5\) (c) \(0.540\) (d) \(0.000540\) (e) 540

Indicate the number of significant figures in: (a) \(0.503200 \mathrm{~mL}\) (b) \(2000 \pm 5\) (c) \(2000 \pm 50\) (d) \(2000 \pm 0.5\) (e) \(200.1\)

True or false? If any statement is false, rewrite it to make it true. (a) When multiplying or dividing a series of measured values, the number of significant figures in the answer is determined by the measured value having the fewest significant figures. (b) When adding or subtracting a series of measured values, the number of significant figures in the answer is determined by the measured value having the fewest significant figures.

Convert to cal \(/ \mathrm{g} \cdot{ }^{\circ} \mathrm{C}:\) (a) \(1.04 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (the specific heat of nitrogen gas) (b) \(0.84 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (the specific heat of carbon dioxide gas)

A one-semester chemistry course meets for \(1-\mathrm{h}\) sessions three times a week for 15 weeks. How many milliseconds will a student with perfect attendance spend in class during the semester?

Describe how the uncertainty in a measured value is determined.

Write each number in scientific notation, taking all trailing zeros to be nonsignificant: (a) 502,000 (b) \(0.000038402\) (c) \(436,000,000\) (d) 8470 (e) \(0.00591\) (f) \(0.658\)

A company wants 800 square feet of carpet, but the carpet store sells only by the square meter. How many square meters does the company need to buy? \((1 \mathrm{~m}=39.37\) in. \()\)

If 1 U.S. dollar is worth \(1.54\) Canadian dollars, how many U.S. dollars are needed to purchase an item that costs 350 Canadian dollars?

Which contains more matter: a \(50-\mathrm{g}\) block of lead or a \(50-\mathrm{g}\) block of gold? Explain.

Indicate the number of significant zeros in each value: (a) \(2.300\) (b) \(2.3003\) (c) \(0.0023\) (d) 2300 (e) \(23.000\)

Is reporting a measured mass as \(580 . \mathrm{g}\) the same as reporting it as \(580 \mathrm{~g}\) ? Explain.

Which is larger, a Kelvin or a Celsius degree? Explain.

A student reports a series of five length measurements that are accurate but not precise. Is it more likely that his laboratory technique is very good but the measuring instrument is bad, or that his laboratory technique is bad? Explain.

Write each number in standard notation: (a) \(1.79 \times 10^{-2}\) (b) \(8.76 \times 10^{-9}\) (c) \(4.88 \times 10^{10}\) (d) \(7.52 \times 10^{1}\) (e) \(8.37 \times 10^{\circ}\) (f) \(4.184 \times 10^{4}\)

(a) If \(25.0 \mathrm{~cm}^{3}\) of an unknown substance has a mass of \(195 \mathrm{~g}\), what is the density of the substance in grams per cubic centimeter? (b) How many cubic centimeters does \(500.0 \mathrm{~g}\) of the substance occupy? (c) Does this substance sink or float in mercury, which has a density of \(13.6 \mathrm{~g} / \mathrm{mL} ?\)

Express each mass in grams, both in standard notation and in scientific notation: (a) \(536 \mathrm{mg}\) (b) \(8.26 \mathrm{dg}\) (c) \(0.0057 \mu \mathrm{g}\) (d) \(139 \mathrm{~kg}\) (e) \(836 \mathrm{ng}\) (f) \(0.073 \mathrm{Mg}\)

At \(25^{\circ} \mathrm{C}\), air has a density of \(1.3 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\). What is this density in (a) kilograms per liter and (b) pounds per gallon?

On a hot summer day, you want to cool two glasses of warm lemonade, but have no ice. Not wanting to wait until you can make some, you place two small metal blocks in the freezer. One block is pure iron, the other pure aluminum, and each has a mass of exactly \(50 \mathrm{~g}\). After both have cooled to \(-10^{\circ} \mathrm{C}\), you put them into separate glasses and add \(200 \mathrm{~mL}\) of warm lemonade to each. After a few minutes, both blocks have warmed up to \(+10{ }^{\circ} \mathrm{C}\). At this point, is the lemonade in one glass cooler than the lemonade in the other glass? If so, which is cooler and why? (Despite all the numerical information, you should be able to use specific heat values from Table \(2.5\) to answer without doing any calculations.)

Use a scientific calculator to do the following calculations. Express each answer in scientific notation and to the correct number of significant figures. (a) \(9.865 \times 10^{3}+8.61 \times 10^{2}\) (b) \(\frac{\left(6.626 \times 10^{23}\right) \times\left(3.00 \times 10^{8}\right)}{4.5 \times 10^{-7}}\) (c) \(\frac{5.6200 \times 10^{-9}}{3.821 \times 10^{9}}\) (d) \(\frac{4.5600 \times 10^{3}-2.91 \times 10^{1}}{5}\), where the 5 is an exact number

What mass of each substance occupies a volume of \(50.0 \mathrm{~mL} ?\) (Densities are shown in parentheses.) (a) Lead \((11.4 \mathrm{~g} / \mathrm{mL})\) (b) Ethanol \((0.785 \mathrm{~g} / \mathrm{mL})\) (c) Oxygen gas \(\left(1.4 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\right)\) (d) Hydrogen gas \(\left(8.4 \times 10^{-5} \mathrm{~g} / \mathrm{mL}\right)\) (e) Mercury (13.6 g/mL) (f) Gold \((19.3 \mathrm{~g} / \mathrm{mL})\)