Chapter 1

Perform the indicated calculations, and express the answer to the correct number of significant figures. Use scientific notation where appropriate. (a) \(13.51+0.0459\) (b) \(16.45 / 32.0+10\) (c) \(3.14 \times 10^{4}-15.0\) (d) \(7.18 \times 10^{3} \div 1.51 \times 10^{5}\)

Perform the indicated calculations, and express the answer to the correct number of significant figures. Use scientific notation where appropriate. (a) \(1.88 \times 36.305\) (b) \(1.04 \times 3.114 / 42\) (c) \(28.5+4.43+0.073\) (d) \(3.10 \times 10^{2}-5.1 \times 10^{1}\)

The following expressions involve multiplication/division and addition/subtraction operations of measured values in the same problem. Evaluate each, and express the answer to the correct number of significant figures. (a) \(\frac{(25.12-1.75) \times 0.01920}{(24.339-23.15)}\) (b) \(\frac{55.4}{(26.3-18.904)}\) (c) \((0.921 \times 27.977)+(0.470 \times 28.976)+\) \((3.09 \times 29.974)\)

Calculate the following to the correct number of significant figures. Assume that all these numbers are measurements. (a) \(x=17.2+65.18-2.4\) (b) \(x=\frac{13.0217}{17.10}\) (c) \(x=(0.0061020)(2.0092)(1200.00)\) (d) \(x=0.0034+\frac{\sqrt{(0.0034)^{2}+4(1.000)\left(6.3 \times 10^{-4}\right)}}{2(1.000)}\)

A Calculate the result of the following equation, and use the convention of significant figures to express the answer correctly. $$ x=\frac{10^{121}}{10^{-121}} \times 1.01 $$

A Calculate the result of the following equation, and use the convention of significant figures to express the uncertainty in the answer. $$ x=\frac{2.05 \times 10^{-65}}{3.4 \times 10^{51}}+1.9 \times 10^{-3} $$

What base SI unit is used to express each of the following quantities? (a) The mass of a person (b) The distance from London to New York City (c) The boiling point of water (d) The duration of a movie

\- What base SI unit is used to express each of the following quantities? (a) The mass of a bag of flour (b) The distance from the Earth to the Sun (c) The temperature of a sunny August day (d) The time it takes to run a marathon ( 26.2 miles)

Write two conversion factors between micrometers ( \(\mu \mathrm{m}\) ) and meters \((\mathrm{m})\).

Write two conversion factors between grams \((\mathrm{g})\) and megagrams \((\mathrm{Mg})\)

Write two conversion factors between milliliters (mL) and kiloliters (kL).

Write two conversion factors between nanoseconds (ns) and milliseconds (ms).

A What is the conversion factor that will convert, in one calculation, from \(\mathrm{km} / \mathrm{hr}\) to \(\mathrm{ft} / \mathrm{s}\)

The speed of sound in air at sea level is \(340 \mathrm{~m} / \mathrm{s}\). Express this speed in miles per hour.

The area of the 48 contiguous states is \(3.02 \times 10^{6} \mathrm{mi}^{2}\). Assume that these states are completely flat (no mountains and no valleys). What volume of water, in liters, would cover these states with a rainfall of two inches?

(a) A light-year, the distance light travels in 1 year, is a unit used by astronomers to measure the great distances between stars. Calculate the distance, in miles, represented by 1 light-year. Assume that the length of a year is 365.25 days, and that light travels at a rate of \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (b) The distance to the nearest star (other than the Sun) is 4.36 light-years. How many meters is this? Express the result in scientific notation and with all the zeros.

Carry out each of the following conversions: (a) \(25.5 \mathrm{~m}\) to \(\mathrm{km}\) (b) \(36.3 \mathrm{~km}\) to \(\mathrm{m}\) (c) \(487 \mathrm{~kg}\) to \(\mathrm{g}\) (d) \(1.32 \mathrm{~L}\) to \(\mathrm{mL}\) (e) \(55.9 \mathrm{dL}\) to \(\mathrm{L}\) (f) \(6251 \mathrm{~L}\) to \(\mathrm{cm}^{3}\)

Perform the conversions needed to fill in the blanks. Use scientific notation where appropriate. Do the operations first without a calculator or spreadsheet, to check your understanding of SI prefixes. (a) \(6.39 \mathrm{~cm}=\mathrm{m}=\stackrel{\mathrm{mm}}=\underline{\mathrm{nm}}\) (b) \(55.0 \mathrm{~cm}^{3}=\mathrm{dm}^{3}=\overline{\mathrm{mL}}=\underline{\mathrm{L}}=\underline{\mathrm{m}^{3}}\) (c) \(23.1 \mathrm{~g}=\underline{\mathrm{mg}}=\) \(-\mathrm{kg}\) (d) \(98.6^{\circ} \mathrm{F}=\quad{ }^{\circ} \mathrm{C}=\) \(\mathrm{K}\)

I Perform the conversions needed to fill in the blanks. Use scientific notation where appropriate. Do the operations first without a calculator or spreadsheet, to check your understanding of SI prefixes. (a) \(45 \mathrm{~s}=\underline{\mathrm{ms}}=\) minutes (b) \(550 \mathrm{nm}=\mathrm{cm}=\mathrm{m}\) (c) \(4^{\circ} \mathrm{C}=\underline{\mathrm{K}}=\underline{ }^{\circ} \mathrm{F}\) (d) \(2.00 \mathrm{~L}=\) \(-\mathrm{cm}^{3}=\underline{\mathrm{m}^{3}}=\underline{\mathrm{qt}}\)

The \(1500-\mathrm{m}\) race is sometimes called the metric mile. Express this distance in miles.

A standard sheet of paper in the United States is \(8.5 \times 11\) inches. Express the area of this sheet of paper in square centimeters.

Wine is sold in \(750-\mathrm{mL}\) bottles. How many quarts of wine are in a case of 12 bottles?

The speed limit on limited-access roads in Canada is 100 \(\mathrm{km} / \mathrm{h}\). How fast is this in miles per hour? In meters per second?

Wine sold in Europe has its volume labeled in centiliters (cL). If wine is sold in 750 -mL bottles, how many centiliters is this?

Derive an equation, including units, to make conversions from degrees Fahrenheit to kelvins.

(a) Helium has the lowest boiling point of any substance; it boils at \(4.21 \mathrm{~K}\). Express this temperature in degrees Celsius and degrees Fahrenheit. (b) The oven temperature for a roast is \(400^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius.

(a) The boiling point of octane is \(126^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit and in kelvins? (b) Potatoes are cooked in oil at a temperature of \(350{ }^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius.

The melting point of sodium chloride, table salt, is \(801^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit and in kelvins?

At what temperature does a Celsius thermometer give the same numerical reading as a Fahrenheit thermometer?

The density of benzene at \(25.0^{\circ} \mathrm{C}\) is \(0.879 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the volume, in liters, of \(2.50 \mathrm{~kg}\) benzene?

Ethyl acetate, one of the compounds in nail polish remover, has a density of \(0.9006 \mathrm{~g} / \mathrm{cm}^{3} .\) Calculate the volume of \(25.0 \mathrm{~g}\) ethvl acetate.

Lead has a density of \(11.4 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the mass, in kilograms, of a lead brick measuring \(8.50 \times 5.10 \times 3.20 \mathrm{~cm} ?\)

What is the radius, \(r\), of a copper sphere (density = \(\left.8.92 \mathrm{~g} / \mathrm{cm}^{3}\right)\) whose mass is \(3.75 \times 10^{3} \mathrm{~g} ?\) 'The volume, \(V_{2}\) of a sphere is given by the equation \(V=(4 / 3) \pi r^{3}\).

An irregularly shaped piece of metal with a mass of \(147.8 \mathrm{~g}\) is placed in a graduated cylinder containing \(30.0 \mathrm{~mL}\) water. The water level rises to \(48.5 \mathrm{~mL}\). What is the density of the metal in \(\mathrm{g} / \mathrm{cm}^{3} ?\)

A solid with an irregular shape and a mass of \(11.33 \mathrm{~g}\) is added to a graduated cylinder filled with water \((d=\) \(1.00 \mathrm{~g} / \mathrm{mL}\) ) to the \(35.0-\mathrm{mL}\) mark. After the solid sinks to the bottom, the water level is read to be at the \(42.3-\mathrm{mL}\) mark. What is the density of the solid?

\(\mathbf{x}\) How many square meters will \(4.0 \mathrm{~L}\) (about 1 gal) of paint cover if it is applied to a uniform thickness of \(8.00 \times 10^{-2} \mathrm{~mm}(\) volume \(=\) thickness \(\times\) area \() ?\)

A A package of aluminum foil with an area of \(75 \mathrm{ft}^{2}\) weighs 12 ounces avdp. Use the density of aluminum, \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\), to find the average thickness of this foil, in nanometers (volume \(=\) thickness \(\times\) area \()\).

In describing the phase of a substance, is it possible that a substance can have two phases at the same time, say, solid and liquid phase? Give examples or circumstances to support your answer.

A Gold leaf, which is used for many decorative purposes, is made by hammering pure gold into very thin sheets. Assuming that a sheet of gold leaf is \(1.27 \times 10^{-5} \mathrm{~cm}\) thick, how many square feet of gold leaf could be obtained from \(28.35 \mathrm{~g}\) gold? The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\).

The speed of light is \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Assuming that the distance from the Earth to the Sun is 93,000,000 miles, (a) how many light-years is this (see question 1.71 )? (b) How many minutes does it take for light to reach the Earth from the Sun?

The mass of a piece of metal is \(134.412 \mathrm{~g}\). It is placed in a graduated cylinder that contains \(12.35 \mathrm{~mL}\) water. The volume of the metal and water in the cylinder is found to be \(19.40 \mathrm{~mL}\). Calculate the density of the metal.

A Consider two liquids: liquid \(A\), with a density of \(0.98 \mathrm{~g} / \mathrm{mL}\), and liquid \(\mathrm{B}\), with a density of \(1.03 \mathrm{~g} / \mathrm{mL}\). Notice that one density is known to have two significant figures and the other to have three. Calculate the volume of liquid \(A\) in a sample that weighs \(9.9132 \mathrm{~g}\); be sure to express your result to the proper number of significant digits. Calculate the volume of the same mass of liquid \(\mathrm{B}\), again making sure that you have the appropriate number of significant figures. Recording the number of significant figures is only one way to estimate the uncertainty. Repeat the calculations of volume by using the minimum and maximum values of density to calculate maximum and minimum volumes. The range between the two is also a measure of uncertainty. Compare the estimated uncertainties in the two liquids as measured by the two techniques. Do all estimates give the same answer? Should they? Explain any disagreements.

A scientific oven is programmed to change temperature from \(80.0{ }^{\circ} \mathrm{F}\) to \(215.0{ }^{\circ} \mathrm{F}\) in 1 minute. Express the rate of change in degrees Celsius per second, and use the convention of significant digits to express the uncertainty in the rate.

The average body temperature of a cow is about \(101.5^{\circ} \mathrm{F}\). Express this in degrees Celsius and in kelvins, using the correct number of significant figures.

"No two substances can have the same complete set of physical and chemical properties." Present arguments for and against this statement.

A The main weapon on a military tank is a cannon that fires a blunt projectile specially designed to cause a shock wave when it hits another tank. The projectile fits into a finned casing that improves its accuracy. Calculate the mass of the projectile, assuming it is a cylinder of uranium (density \(\left.=19.05 \mathrm{~g} / \mathrm{cm}^{3}\right)\) that is \(105 \mathrm{~mm}\) in diameter and \(30 \mathrm{~cm}\) in height. The volume of a cylinder is given by the equation \(V=\pi r^{2} b\).

The U.S. debt in 2008 was \(\$ 9.2\) trillion. (a) Estimate the height, in kilometers, of a stack of 9.2 trillion \(\$ 1\) bills. Assume that a \(\$ 1\) bill has a thickness of \(0.166 \mathrm{~mm}\). (b) Estimate the mass of this stack if a \(\$ 1\) bill has a mass of \(1.01 \mathrm{~g}\)