Chapter 1

PRACTICE 1.1 Express the following quantities in scientific notation and then express the number and unit with the most appropriate prefix. (a) The diameter of an insulin molecule, \(0.000000005 \mathrm{~m}\) (b) The circumference of the Earth at the Equator, \(40,075,017 \mathrm{~m}\)

The melting point of table salt is \(1474^{\circ} \mathrm{F}\). What temperature is this on the Celsius and Kelvin scales?

The metal gallium has a relatively low melting point for a metal, \(302.91 \mathrm{~K}\). If the temperature in the cargo compartment carrying a shipment of gallium has a temperature of \(88{ }^{\circ} \mathrm{F}\), is the gallium in the solid or liquid state?

Chloroform, a substance once used as an anesthetic, has a density of \(1.483\) \(\mathrm{g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). How many milliliters would you use if you needed \(9.37 \mathrm{~g}\) ? \(\left(1 \mathrm{~mL}=1 \mathrm{~cm}^{3}\right)\)

You are beachcombing on summer vacation and find a silver bracelet. You take it to the jeweler and he tells you that it is silver plated and will give you $$\$ 10$$ for it. You do not want to be swindled so you take the bracelet to your chemistry lab and find its mass on a balance \((80.0 \mathrm{~g})\). To measure the volume you place the bracelet in a graduated cylinder (Figure 1.8) containing \(10.0 \mathrm{~mL}\) of water at \(20^{\circ} \mathrm{C}\). The final volume in the graduated cylinder after the bracelet has been added is \(17.61 \mathrm{~mL}\). The density of silver at \(20^{\circ} \mathrm{C}\) is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\) and \(1 \mathrm{~cm}^{3}=1 \mathrm{~mL}\). What can you conclude about the identity of the metal in the bracelet?

Some radioactive materials emit a type of radiation called alpha particles at high velocity. (a) What is the kinetic energy in joules of an alpha particle with a mass of \(6.6 \times 10^{-27} \mathrm{~kg}\) and a speed of \(1.5 \times 10^{\frac{1}{7}} \mathrm{~m} / \mathrm{s} ?\) Express the number in scientific notation. (b) Express the number and unit using an appropriate prefix.

A baseball with a mass of \(450 \mathrm{~g}\) has a kinetic energy of \(406 \mathrm{~J} .\) Calculate the velocity of the baseball in units of \(\mathrm{m} / \mathrm{s}\).

How many significant figures does each of the following quantities have? (a) \(76.600 \mathrm{~kJ}\) (b) \(4.50200 \times 10^{3} \mathrm{~g}\) (c) \(3000 \mathrm{~nm}\) (d) \(0.00300 \mathrm{~mL}\) (e) 18 students (f) \(3 \times 10^{-5} \mathrm{~g}\) (g) \(47.60 \mathrm{~mL}\) (h) \(2070 \mathrm{mi}\)

A \(1.000 \mathrm{~mL}\) sample of acetone, a common solvent used as a paint remover, was placed in a small vial whose mass was known to be \(4.002 \mathrm{~g}\). The following values were obtained when the acetone-filled vial was weighed: \(4.531 \mathrm{~g}, 4.525 \mathrm{~g}\), and, \(4.537 \mathrm{~g}\). How would you characterize the precision and accuracy of these measurements if the true mass of the acetone was \(0.7795 \mathrm{~g}\) ?

Carry out the following calculations, expressing each result with the correct number of significant figures: (a) \(24.567 \mathrm{~g}+0.04478 \mathrm{~g}=? \mathrm{~g}\) (b) \(4.6742 \mathrm{~g} \div 0.00371 \mathrm{~L}=? \mathrm{~g} / \mathrm{L}\) (c) \(0.378 \mathrm{~mL}+42.3 \mathrm{~mL}-1.5833 \mathrm{~mL}=? \mathrm{~mL}\)

A sodium chloride solution was prepared in the following manner: \- A \(25.0 \mathrm{~mL}\) volumetric flask (Figure \(1.8)\) was placed on an analytical balance and found to have a mass of \(35.6783 \mathrm{~g}\). \- Sodium chloride was added to flask and the mass of the solid \(+\) flask was \(36.2365 \mathrm{~g}\). \- The flask was filled to the mark with water and mixed well. Calculate the concentration of the sodium chloride solution in units of \(\mathrm{g} / \mathrm{mL}\) and give the answer in scientific notation with the correct number of significant figures.

Gemstones are weighed in carats, with 1 carat \(=200 \mathrm{mg}\) (exactly). What is the mass in grams of the Hope Diamond, the world's largest blue diamond at \(44.4\) carats? What is this mass in ounces? (See conversion on the inside back cover.)

(a) A 12 -inch pizza has an area of \(113.112\) square inches \(\left(\mathrm{in}^{2}\right)\). What is the area in units of \(\mathrm{cm}^{2}\) ? \((1\) inch \(=2.54 \mathrm{~cm}\), exactly \()\) (b) A can of soda has a volume of \(355 \mathrm{~mL}\). What is the volume expressed in SI units of \(\mathrm{m}^{3}\) ?

How large, in cubic centimeters, is the volume of a red blood cell (in \(\mathrm{cm}^{3}\) ) if the cell has a cylindrical shape with a diameter of \(6 \times 10^{-6} \mathrm{~m}\) and a height of \(2 \times 10^{-6} \mathrm{~m}\) ? What is the volume in pL?

Catalytic converters use nanoscale particles of precious metals such as platinum to change pollutants in automobile exhaust into less harmful gases. Calculate the following quantities for two different spherical particles of platinum with diameters of \(5.0 \mathrm{~nm}\) and \(5.0 \mu \mathrm{m}\). (a) surface area in units of \(\mu \mathrm{m}^{2}\left(S A=4 \pi r^{2}\right)\) (b) volume in units of \(\mu \mathrm{m}^{3}\left(V=\frac{4}{3} \pi r^{3}\right)\) (c) surface area to volume ratio in units of \(\mu \mathrm{m}^{-1}\) (d) How many times larger is the surface area to volume ratio of the \(5 \mathrm{~nm}\) particle than the \(5 \mu \mathrm{m}\) particle?

Platinum is an expensive and rare metal used in catalytic converters and other industrial applications. Much research has been devoted to maximizing reactive properties of other metals by shrinking them to nanoparticles in the hope that someday they will be an efficient and economic alternative to platinum. (a) Explain why changing the size of a metal particle influences its reactivity. (b) What is the economic benefit of using small particles? (c) What properties other than reactivity might you expect to change as the size of particle approaches the nanoscale?

Assume that you have two graduated cylinders, one with a capacity of \(5 \mathrm{~mL}\) (a) and the other with a capacity of \(50 \mathrm{~mL}\) (b). Draw a line in each, showing how much liquid you would add if you needed to measure \(2.64 \mathrm{~mL}\) of water. Which cylinder will give the more accurate measurement? Explain.

The following cylinder contains three liquids that do not mix with one another: water (density \(=1.0 \mathrm{~g} / \mathrm{mL}\) ), vegetable oil (density \(=0.93 \mathrm{~g} / \mathrm{mL})\), and mercury (density \(=13.5 \mathrm{~g} / \mathrm{mL})\). Which liquid is which?

The following statements pertain to the development of the theory of combustion by the French chemist Lavoisier in the eighteenth century. Match the statement with the appropriate step (observation, hypothesis, experiment designed to test hypothesis) in the scientific method. (a) A metal is burned in a closed container and the change in mass of the solid and volume of the gas is measured. (b) Oxygen gas combines with a substance during its combustion. (c) Combustion of a metal in a closed container ceases after a length of time.

The following statements pertain to the development of the theory of the structure of DNA. Match the statement with the appropriate step (observation, hypothesis, experiment designed to test hypothesis) in the scientific method. (a) Two strands of DNA wind around one another in a helical structure. (b) In a sample of DNA, there are equal amounts of the bases \(\mathrm{A}\) and \(\mathrm{T}\) and equal amounts of the bases \(\mathrm{C}\) and \(\mathrm{G}\). (c) Direct X-rays at a sample of crystallized DNA and interpret the diffraction pattern for structural information.

What is the difference between a hypothesis and theory? (a) A hypothesis provides an explanation for a phenomenon, but a theory does not. (b) A theory provides an explanation for a phenomenon, but hypothesis does not. (c) Both a theory and a hypothesis provide an explanation for a phenomenon, but a theory has been upheld by experimental observations.

Dr. DiMarchi proposed that switching the positions of two amino acids in human insulin would create an analog with a faster time profile. Is this a hypothesis or theory?

Label the following statements about insulin therapy for diabetics as quantitative or qualitative observations: (a) Insulin injections allow a diabetic patient to survive. (b) The peak in the time release profile for natural insulin is 90 minutes while the peak for injected insulin is 150 minutes.

Label the following statements about the world's largest gold bar as quantitative or qualitative observations. (This gold bar was worth approximately \(\$ 10.25\) million in 2013.) (a) The melting point of gold is \(1064.2^{\circ} \mathrm{C}\). (b) The volume of the gold bar is \(15,730 \mathrm{~cm}^{3}\). (c) Gold metal is a conductor of electricity. (d) The mass of the gold bar is \(250 \mathrm{~kg}\). (e) The gold bar is yellow and shiny.

Label the following statements as quantitative or qualitative observations. (a) An object weighs less on the moon than on Earth. (b) An object that weighs 50 pounds on Earth only weighs \(8.3\) pounds on the moon. (c) The freezing point of water is cold. (d) The freezing point of water is \(0{ }^{\circ} \mathrm{C}\).

What is the difference between mass and weight?

What is the difference between a derived SI unit and a fundamental SI unit? Give an example of each.

What SI units are used for measuring the following quantities? For derived units, express your answers in terms of the six fundamental units. (a) Mass (b) Length (c) Temperature (d) Volume (e) Energy (f) Density

What SI prefixes correspond to the following multipliers? (a) \(10^{3}\) (b) \(10^{-6}\) (c) \(10^{9}\) (d) \(10^{-12}\) (e) \(10^{-2}\)

Which is larger, a Fahrenheit degree or a Celsius degree? By how much?

What is the difference between a kelvin and a Celsius degree?

What is the difference between a cubic decimeter (SI) and a liter (metric)?

What is the difference between a cubic centimeter (SI) and a milliliter (metric)?

Which of the following statements use exact numbers? (a) \(1 \mathrm{ft}=12 \mathrm{in}\). (b) \(1 \mathrm{cal}=4.184 \mathrm{~J}\) (c) The height of Mt. Everest is \(29,035 \mathrm{ft}\). (d) The world record for the 1 mile run, set by Morocco's \(\mathrm{Hi}\) cham el Guerrouj in July, 1999 , is 3 minutes, \(43.13\) seconds.

What is the difference in mass between a nickel that weighs \(4.8 \mathrm{~g}\) and a nickel that weighs \(4.8673 \mathrm{~g}\) ?

Bottles of wine sometimes carry the notation "Volume \(=75 \mathrm{cL}\) " What does the unit cL mean?

What do the following abbreviations stand for? (a) dL (b) \(\mathrm{dm}\) (c) \(\mu \mathrm{m}\) (d) \(\mathrm{nL}\) (e) MJ

Which quantity in each of the following pairs is larger? (a) \(5.63 \times 10^{6} \mathrm{~cm}\) or \(6.02 \times 10^{1} \mathrm{~km}\) (b) \(46 \mu\) s or \(3.2 \times 10^{-2} \mathrm{~ms}\) (c) \(200,098 \mathrm{~g}\) or \(17 \times 10^{1} \mathrm{~kg}\)

Which quantity in each of the following pairs is smaller? (a) \(154 \mathrm{pm}\) or \(7.7 \times 10^{-9} \mathrm{~cm}\) (b) \(1.86 \times 10^{11} \mu \mathrm{m}\) or \(2.02 \times 10^{2} \mathrm{~km}\) (c) \(2.9 \mathrm{GA}\) or \(3.1 \times 10^{15} \mu \mathrm{A}\)

How many picograms are in \(1 \mathrm{mg} ?\) In \(35 \mathrm{ng}\) ?

How many microliters are in 1 L? In 20 mL?

Carry out the following conversions: (a) 5 pm = _______ cm = _______ nm (b) \(8.5 \mathrm{~cm}^{3}=\) _______ \(\mathrm{m}^{3}=\) _______ \(\mathrm{mm}^{3}\) (c) \(65.2 \mathrm{mg}=\) _______ \(\mathrm{g}=\) _______ pg

How many significant figures are in each of the following measurements? (a) \(35.0445 \mathrm{~g}\) (b) \(59.0001 \mathrm{~cm}\) (c) \(\begin{array}{lll}0.030 & 03 \mathrm{~kg}\end{array}\) (d) \(0.00450 \mathrm{~m}\) (e) \(67,000 \mathrm{~m}^{2}\) (f) \(3.8200 \times 10^{3} \mathrm{~L}\)

How many significant figures are in each of the following measurements? (a) \(\$ 130.95\) (b) \(2000.003 \mathrm{~g}\) (c) \(5 \mathrm{ft} 3\) in. (d) \(510 \mathrm{~J}\) (e) \(5.10 \times 10^{2} \mathrm{~J}\) (f) 10 students

The Vehicle Assembly Building at the John F. Kennedy Space Center in Cape Canaveral, Florida, is the largest building in the world, with a volume of \(3,666,500 \mathrm{~m}^{3}\). Round off this quantity to four significant figures; and then to two significant figures. Express the answers in scientific notation.

The diameter of the Earth at the equator is \(7926.381 \mathrm{mi}\). Round off this quantity to four significant figures; then to two significant figures. Express the answers in scientific notation.

Express the following measurements in scientific notation: (a) \(453.32 \mathrm{mg}\) (b) \(0.0000421 \mathrm{~mL}\) (c) \(667,000 \mathrm{~g}\)

Convert the following measurements from scientific notation to standard notation: (a) \(3.221 \times 10^{-3} \mathrm{~mm}\) (b) \(8.940 \times 10^{5} \mathrm{~m}\) (c) \(1.35082 \times 10^{-12} \mathrm{~m}^{3}\) (d) \(6.4100 \times 10^{2} \mathrm{~km}\)

Round off the following quantities to the number of significant figures indicated in parentheses: (a) \(35,670.06 \mathrm{~m}(4,6)\) (b) \(68.507 \mathrm{~g}(2,3)\) (c) \(4.995 \times 10^{3} \mathrm{~cm}(3)\) (d) \(2.30985 \times 10^{-4} \mathrm{~kg}(5)\)

Round off the following quantities to the number of significant figures indicated in parentheses: (a) \(7.0001 \mathrm{~kg}(4)\) (b) \(1.605 \mathrm{~km}(3)\) (c) \(13.2151 \mathrm{~g} / \mathrm{cm}^{3}(3)\) (d) \(2,300,000.1(7)\)