Chapter 1

How many significant figures are there in each of the following measurements? a) \(4.0100 \mathrm{mg}\) b) \(0.05930 \mathrm{~g}\) c) \(0.035 \mathrm{~mm}\) d) \(3.100 \mathrm{~s}\) e) \(8.91 \times 10^{1} \mathrm{~L}\) f) \(9.100 \times 10^{4} \mathrm{~cm}\)

The circumference of the earth at the equator is \(40,000 \mathrm{~km}\). This value is precise to two significant figures. Write this in scientific notation to express correctly the number of significant figures.

The astronomical unit equals the mean distance between the earth and the sun. This distance is \(150,000,000 \mathrm{~km},\) which is precise to three significant figures. Express this in scientific notation to the correct number of significant figures.

Assuming all numbers are measured quantities, do the indicated arithmetic and give the answer to the correct number of significant figures. a \(\frac{8.71 \times 0.0301}{0.031}\) b \(0.71+89.3\) c \(934 \times 0.00435+107\) d) \((847.89-847.73) \times 14673\)

Assuming all numbers are measured quantities, do the indicated arithmetic and give the answer to the correct number of significant figures. a \(\frac{08.71 \times 0.57}{5.871}\) b \(8.937-8.930\) c \(8.937+8.930\) d \(0.00015 \times 54.6+1.002\)

One sphere has a radius of \(4.52 \mathrm{~cm} ;\) another has a radius of \(4.72 \mathrm{~cm}\). What is the difference in volume (in cubic centimeters) between the two spheres? Give the answer to the correct number of significant figures. The volume of a sphere is \((4 / 3) \pi r^{3},\) where \(\pi=3.1416\) and \(r\) is the radius.

A solid circular cylinder of iron with a radius of \(1.500 \mathrm{~cm}\) has a ruler etched along its length. What is the volume of iron contained between the marks labeled \(3.20 \mathrm{~cm}\) and \(3.50 \mathrm{~cm} ?\) The volume of a circular cylinder is \(\pi r^{2} l,\) where \(\pi=3.1416, r\) is the radius, and \(l\) is the length.

Write the following measurements, without scientific notation, using the appropriate SI prefix. a \(5.89 \times 10^{-12} \mathrm{~s} \quad\) b \(0.2010 \mathrm{~m}\) c \(2.560 \times 10^{-9} \mathrm{~g}\) d \(6.05 \times 10^{3} \mathrm{~m}\)

Write the following measurements, without scientific notation, using the appropriate SI prefix. a \(4.851 \times 10^{-6} \mathrm{~g}\) b \(3.16 \times 10^{-2} \mathrm{~m}\) c \(2.591 \times 10^{-9} \mathrm{~s}\) d \(8.93 \times 10^{-12} \mathrm{~g}\)

Using scientific notation, convert: a \(6.15 \mathrm{ps}\) to \(\mathrm{s}\) b \(3.781 \mu \mathrm{m}\) to \(\mathrm{m}\) c \(1.546 \AA\) to \(\mathrm{m}\) d \(9.7 \mathrm{mg}\) to \(\mathrm{g}\)

Convert: a \(68^{\circ} \mathrm{F}\) to degrees Celsius b \(-23^{\circ} \mathrm{F}\) to degrees \(\mathrm{Celsius}\) c \(26^{\circ} \mathrm{C}\) to degrees Fahrenheit d \(-81^{\circ} \mathrm{C}\) to degrees Fahrenheit

Salt and ice are stirred together to give a mixture to freeze ice cream. The temperature of the mixture is \(-20.0^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit?

The reaction of oxygen and hydrogen is used to propel rockets. Liquid oxygen has a boiling point of \(-222.7^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit?

A certain sample of the mineral galena (lead sulfide) weighs \(12.4 \mathrm{~g}\) and has a volume of \(1.64 \mathrm{~cm}^{3}\). What is the density of galena?

A flask contains a \(30.0 \mathrm{~mL}\) sample of acetone (nail polish remover) that weighs 23.6 grams. What is the density of the acetone?

A liquid with a volume of \(8.5 \mathrm{~mL}\) has a mass of \(6.71 \mathrm{~g}\). The liquid is either octane, ethanol, or benzene, the densities of which are \(0.702 \mathrm{~g} / \mathrm{cm} 3,0.789 \mathrm{~g} / \mathrm{cm}^{3},\) and \(0.879 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. What is the identity of the liquid?

A mineral sample has a mass of \(5.94 \mathrm{~g}\) and a volume of \(0.73 \mathrm{~cm}^{3}\). The mineral is either sphalerite (density = \(4.0 \mathrm{~g} / \mathrm{cm}^{3}\) ), cassiterite (density \(=6.99 \mathrm{~g} / \mathrm{cm}^{3}\) ), or cinnabar (density \(=8.10 \mathrm{~g} / \mathrm{cm}^{3}\) ). Which is it?

Platinum has a density of \(21.4 \mathrm{~g} / \mathrm{cm}^{3}\). What is the mass of \(5.9 \mathrm{~cm}^{3}\) of this metal?

What is the mass of a \(43.8-\mathrm{mL}\) sample of gasoline, which has a density of \(0.70 \mathrm{~g} / \mathrm{cm}^{3} ?\)

Ethanol has a density of \(0.789 \mathrm{~g} / \mathrm{cm}^{3}\). What volume must be poured into a graduated cylinder to give \(19.8 \mathrm{~g}\) of alcohol?

Bromine is a red-brown liquid with a density of \(3.10 \mathrm{~g} / \mathrm{mL}\). A sample of bromine weighing \(88.5 \mathrm{~g}\) occupies what volume?

Sodium hydrogen carbonate, known commercially as baking soda, reacts with acidic materials such as vinegar to release carbon dioxide gas. An experiment calls for \(0.450 \mathrm{~kg}\) of sodium hydrogen carbonate. Express this mass in milligrams.

The acidic constituent in vinegar is acetic acid. \(\mathrm{A}\) \(10.0-\mathrm{mL}\) sample of a certain vinegar contains \(611 \mathrm{mg}\) of acetic acid. What is this mass of acetic acid expressed in micrograms?

The different colors of light have different wavelengths. The human eye is most sensitive to light whose wavelength is \(555 \mathrm{nm}\) (greenish- yellow). What is this wavelength in centimeters?

Water consists of molecules (groups of atoms). A water molecule has two hydrogen atoms, each connected to an oxygen atom. The distance between any one hydrogen atom and the oxygen atom is \(0.96 \AA\). What is this distance in millimeters?

The total amount of fresh water on earth is estimated to be \(3.73 \times 10^{8} \mathrm{~km}^{3}\). What is this volume in cubic meters? in liters?

A submicroscopic particle suspended in a solution has a volume of \(1.3 \mu \mathrm{m}^{3}\). What is this volume in liters?

How many grams are there in 3.58 short tons? Note that \(1 \mathrm{~g}=0.03527\) oz (ounces avoirdupois), \(1 \mathrm{lb}\) (pound) \(=\) 16 oz, and 1 short ton \(=2000\) lb. (These relations are exact.)

The calorie, the Btu (British thermal unit), and the joule are units of energy; 1 calorie \(=4.184\) joules (exact), - and \(1 \cdot \mathrm{Btu}=252.0\) calories. Convert 3.15 Btu to joules.

The first measurement of sea depth was made in 1840 in the central South Atlantic, where a plummet was lowered 2425 fathoms. What is this depth in meters? Note that 1 fathom \(=6 \mathrm{ft}, 1 \mathrm{ft}=12 \mathrm{in} .\), and \(1 \mathrm{in.}=2.54 \times 10^{-2} \mathrm{~m}\). (These relations are exact.)

The estimated amount of recoverable oil from the field at Prudhoe Bay in Alaska is \(1.3 \times 10^{10}\) barrels. What is this amount of oil in cubic meters? One barrel \(=42 \mathrm{gal}\) \((\) exact \(), 1 \mathrm{gal}=4\) qt (exact), and \(1 \mathrm{qt}=9.46 \times 10^{-4} \mathrm{~m}^{3}\).

A fish tank is 24.2 in. long, 15.9 in. deep, and 14.8 in. high. What is the maximum volume of water, in liters, that the fish tank can hold?

The population density of worms in a particular field is 33 worms per cubic meter of soil. How many worms would there be in the top meter of soil in a field that has dimensions of \(1.00 \mathrm{~km}\) by \(2.0 \mathrm{~km}\) ?

Sodium metal reacts vigorously with water. A piece of sodium weighing \(19.70 \mathrm{~g}\) was added to a beaker containing \(126.22 \mathrm{~g}\) of water. During reaction, hydrogen gas was produced and bubbled from the solution. The solution, containing sodium hydroxide, weighed \(145.06 \mathrm{~g} .\) How many grams of hydrogen gas were produced?

An antacid tablet weighing \(0.853 \mathrm{~g}\) contained calcium carbonate as the active ingredient, in addition to an inert binder. When an acid solution weighing \(56.519 \mathrm{~g}\) was added to the tablet, carbon dioxide gas was released, producing a fizz. The resulting solution weighed \(57.152 \mathrm{~g}\). How many grams of carbon dioxide were produced?

When a mixture of aluminum powder and iron(III) oxide is ignited, it produces molten iron and aluminum oxide. In an experiment, \(5.40 \mathrm{~g}\) of aluminum was mixed with \(18.50 \mathrm{~g}\) of iron(III) oxide. At the end of the reaction, the mixture contained \(11.17 \mathrm{~g}\) of iron, \(10.20 \mathrm{~g}\) of aluminum oxide, and an undetermined amount of unreacted iron(III) oxide. No aluminum was left. What is the mass of the iron(III) oxide?

When chlorine gas is bubbled into a solution of sodium bromide, the sodium bromide reacts to give bromine, a red-brown liquid, and sodium chloride (ordinary table salt). A solution was made by dissolving \(20.6 \mathrm{~g}\) of sodium bromide in \(100.0 \mathrm{~g}\) of water. After passing chlorine through the solution, investigators analyzed the mixture. It contained \(16.0 \mathrm{~g}\) of bromine and \(11.7 \mathrm{~g}\) of sodium chloride. How many grams of chlorine reacted?

A graduated cylinder weighed \(66.5 \mathrm{~g}\). To the cylinder was added \(58.2 \mathrm{~g}\) of water and \(5.279 \mathrm{~g}\) of sodium chloride. What was the total mass of the cylinder and the solution? Express the answer to the correct number of significant figures.

Describe each of the following as a physical or chemical property of each listed chemical substance. A baking soda reacts with vinegar B ice melts at \(0^{\circ} \mathrm{C}\) C graphite is a soft, black solid D hydrogen burns in air

Describe each of the following as a physical or chemical property of each listed chemical substance. A chlorine is a green gas B zinc reacts with acids C magnesium has a density of \(1.74 \mathrm{~g} / \mathrm{cm}^{3}\) D iron can rust

A cubic box measures \(39.3 \mathrm{~cm}\) on an edge. What is the volume of the box in cubic centimeters? Express the answer to the correct number of significant figures.

A cylinder with circular cross section has a radius of \(2.56 \mathrm{~cm}\) and a height of \(56.32 \mathrm{~cm}\). What is the volume of the cylinder? Express the answer to the correct number of significant figures.

An aquarium has a rectangular cross section that is 47.8 in. by 12.5 in.; it is 19.5 in. high. How many U.S. gallons does the aquarium contain? One U.S. gallon equals exactly \(231 \mathrm{in}^{3}\).

A spherical tank has a radius of 175.0 in. Calculate the volume of the tank in cubic inches; then convert this to Imperial gallons. The volume of a sphere is \((4 / 3) \pi r^{3},\) where \(r\) is the radius. One Imperial gallon equals 277.4 in \(^{3}\).

Obtain the difference in volume between two spheres, one of radius \(5.61 \mathrm{~cm},\) the other of radius \(5.85 \mathrm{~cm} .\) The volume \(V\) of a sphere is \((4 / 3) \pi r^{3},\) where \(r\) is the radius. Give the result to the correct number of significant figures.

What is the difference in surface area between two circles, one of radius \(7.98 \mathrm{~cm},\) the other of radius \(8.50 \mathrm{~cm} ?\) The surface area of a circle of radius \(r\) is \(\pi r^{2}\). Obtain the result to the correct number of significant figures.

Assuming all of the numbers are measured quantities, perform the following arithmetic setups and report the answers to the correct number of significant figures. a \(\frac{9.345-9.005}{9.811}\) b \(\frac{9.345+9.005}{9.811}\) c \((7.50+7.53) \times 3.71\) d) \(0.71 \times 0.36+17.36\)

For each of the following, write the measurement in terms of an appropriate prefix and base unit. A The mass of calcium per milliliter in a sample of blood serum is \(0.0912 \mathrm{~g}\). B The radius of an oxygen atom is about \(0.000000000066 \mathrm{~m}\). C A particular red blood cell measures \(0.0000071 \mathrm{~m}\). D The wavelength of a certain ultraviolet radiation is \(0.000000056 \mathrm{~m} .\)

For each of the following, write the measurement in terms of an appropriate prefix and base unit. a The mass of magnesium per milliliter in a sample of blood serum is \(0.0186 \mathrm{~g}\). b. The radius of a carbon atom is about \(0.000000000077 \mathrm{~m}\). c The hemoglobin molecule, a component of red blood cells, is \(0.0000000065 \mathrm{~m}\) in diameter. d. The wavelength of a certain infrared radiation is \(0.00000085 \mathrm{~m}\)

Write each of the following in terms of the SI base unit (that is, express the prefix as the power of 10 ). a \(1.07 \mathrm{ps}\) b \(5.8 \mu \mathrm{m}\) c \(319 \mathrm{nm}\) d \(15.3 \mathrm{~ms}\)