Chapter 2

When an iron object rusts, its mass increases. When a match burns, its mass decreases. Do these observations violate the law of conservation of mass? Explain.

A 0.406 g sample of magnesium reacts with oxygen, producing \(0.674 \mathrm{g}\) of magnesium oxide as the only product. What mass of oxygen was consumed in the reaction?

A 1.446 g sample of potassium reacts with 8.178 g of chlorine to produce potassium chloride as the only product. After the reaction, 6.867 g of chlorine remains unreacted. What mass of potassium chloride was formed?

When a solid mixture consisting of \(10.500 \mathrm{g}\) calcium hydroxide and \(11.125 \mathrm{g}\) ammonium chloride is strongly heated, gaseous products are evolved and \(14.336 \mathrm{g}\) of a solid residue remains. The gases are passed into \(62.316 \mathrm{g}\) water, and the mass of the resulting solution is \(69.605 \mathrm{g}\). Within the limits of experimental error, show that these data conform to the law of conservation of mass.

Within the limits of experimental error, show that the law of conservation of mass was obeyed in the following experiment: \(10.00 \mathrm{g}\) calcium carbonate (found in limestone) was dissolved in 100.0 mL hydrochloric acid \((d=1.148 \mathrm{g} / \mathrm{mL}) .\) The products were \(120.40 \mathrm{g}\) solution (a mixture of hydrochloric acid and calcium chloride) and 2.22 L carbon dioxide gas \((d=1.9769 \mathrm{g} / \mathrm{L})\)

In Example \(2-1,\) we established that the mass ratio of magnesium to magnesium oxide is 0.455 g magnesium/ \(0.755 \mathrm{g}\) magnesium oxide. (a) What is the ratio of oxygen to magnesium oxide, by mass? (b) What is the mass ratio of oxygen to magnesium in magnesium oxide? (c) What is the percent by mass of magnesium in magnesium oxide?

Samples of pure carbon weighing \(3.62,5.91,\) and \(7.07 \mathrm{g}\) were burned in an excess of air. The masses of carbon dioxide obtained (the sole product in each case) were \(13.26,21.66,\) and \(25.91 \mathrm{g},\) respectively. (a) Do these data establish that carbon dioxide has a fixed composition? (b) What is the composition of carbon dioxide, expressed in \% C and \% O, by mass?

In one experiment, 2.18 g sodium was allowed to react with \(16.12 \mathrm{g}\) chlorine. All the sodium was used up, and 5.54 g sodium chloride (salt) was produced. In a second experiment, 2.10 g chlorine was allowed to react with \(10.00 \mathrm{g}\) sodium. All the chlorine was used up, and 3.46 g sodium chloride was produced.Show that these results are consistent with the law of constant composition.

When \(3.06 \mathrm{g}\) hydrogen was allowed to react with an excess of oxygen, \(27.35 \mathrm{g}\) water was obtained. In a second experiment, a sample of water was decomposed by electrolysis, resulting in \(1.45 \mathrm{g}\) hydrogen and 11.51 g oxygen. Are these results consistent with the law of constant composition? Demonstrate why or why not.

In one experiment, the burning of \(0.312 \mathrm{g}\) sulfur produced 0.623 g sulfur dioxide as the sole product of the reaction. In a second experiment, \(0.842 \mathrm{g}\) sulfur dioxide was obtained. What mass of sulfur must have been burned in the second experiment?

In one experiment, the reaction of \(1.00 \mathrm{g}\) mercury and an excess of sulfur yielded \(1.16 \mathrm{g}\) of a sulfide of mercury as the sole product. In a second experiment, the same sulfide was produced in the reaction of \(1.50 \mathrm{g}\) mercury and \(1.00 \mathrm{g}\) sulfur. (a) What mass of the sulfide of mercury was produced in the second experiment? (b) What mass of which element (mercury or sulfur) remained unreacted in the second experiment?

Sulfur forms two compounds with oxygen. In the first compound, \(1.000 \mathrm{g}\) sulfur is combined with \(0.998 \mathrm{g}\) oxygen, and in the second, \(1.000 \mathrm{g}\) sulfur is combined with \(1.497 \mathrm{g}\) oxygen. Show that these results are consistent with Dalton's law of multiple proportions

Phosphorus forms two compounds with chlorine. In the first compound, \(1.000 \mathrm{g}\) of phosphorus is combined with \(3.433 \mathrm{g}\) chlorine, and in the second, \(2.500 \mathrm{g}\) phosphorus is combined with \(14.308 \mathrm{g}\) chlorine. Show that these results are consistent with Dalton's law of multiple proportions.

The following radioactive isotopes have applications in medicine. Write their symbols in the form \(\&\) E. (a) cobalt- \(60 ;\) (b) phosphorus- \(32 ;\) (c) iron-59; (d) radium-226.

For the atom \(^{108}\) Pd with mass 107.90389 u, determine (a) the numbers of protons, neutrons, and electrons in the atom; (b) the ratio of the mass of this atom to that of an atom of \(^{12}_{6} \mathrm{H}\)

For the ion \(^{228} \mathrm{Ra}^{2+}\) with a mass of 228.030 u, determine (a) the numbers of protons, neutrons, and electrons in the ion; (b) the ratio of the mass of this ion to that of an atom of \(^{16} \mathrm{O}\) (refer to page 47 ).

The following data on isotopic masses are from a chemical handbook. What is the ratio of each of these masses to that of\(^{12}_{6} \mathrm{c}\) ?\( \)^{17}_{35} \mathrm{CL}\( , 34.96885 \mathrm{u} ;\) (b) \(_{12}^{26} \mathrm{Mg}\) 25.98259 u ;\(^{86}_{222} \mathrm{Rn}\) , 222.0175 u.

Which of the following species has (a) equal numbers of neutrons and electrons; (b) protons, neutrons, and electrons in the ratio 9: 11: 8 ; (c) a number of neutrons equal to the number of protons plus one-half the number of electrons? \(^{24} \mathrm{Mg}^{2+},^{47} \mathrm{Cr},^{60} \mathrm{Co}^{3+},^{35} \mathrm{Cl}^{-},^{124} \mathrm{Sn}^{2+},^{226} \mathrm{Th},^{90} \mathrm{Sr}\)

An isotope with mass number 44 has four more neutrons than protons. This is an isotope of what element?

Identify the isotope \(X\) that has one more neutron than protons and a mass number equal to nine times the charge on the ion \(X^{3+}\)

Iodine has many radioactive isotopes. Iodine-123 is a radioactive isotope used for obtaining images of the thyroid gland. Iodine-123 is administered to patients in the form of sodium iodide capsules that contain \(123 \mathrm{I}^{-}\) ions. Determine the number of neutrons, protons, and electrons in a single \(^{123} \mathrm{I}^{-}\) ion.

Iodine-131 is a radioactive isotope that has important medical uses. Small doses of iodine-131 are used for treating hyperthyroidism (overactive thyroid) and larger doses are used for treating thyroid cancer. Iodine-131 is administered to patients in the form of sodium iodide capsules that contain \(^{131} \mathrm{I}^{-}\) ions. Determine the number of neutrons, protons, and electrons in a single \(^{131} \mathrm{I}^{-}\) ion.

Americium-241 is a radioactive isotope that is used in high-precision gas and smoke detectors. How many neutrons, protons, and electrons are there in an atom of americium-241?

Some foods are made safer to eat by being exposed to gamma rays from radioactive isotopes, such as cobalt-60. The energy from the gamma rays kills bacteria in the food. How many neutrons, protons, and electrons are there in an atom of cobalt-60?

Which statement is probably true concerning the masses of individual chlorine atoms: All have, some have, or none has a mass of 35.4527 u? Explain.

The mass of a carbon-12 atom is taken to be exactly 12 u. Are there likely to be any other atoms with an exact integral (whole number) mass, expressed in u? Explain.

There are three naturally occurring isotopes of magnesium. Their masses and percent natural abundances are \(23.985042 \mathrm{u}, 78.99 \% ; 24.985837 \mathrm{u}, 10.00 \% ;\) and \(25.982593 \mathrm{u}, 11.01 \% .\) Calculate the weighted-average atomic mass of magnesium.

\begin{tabular}{l} There are four naturally occurring isotopes of \\ \hline \end{tabular} chromium. Their masses and percent natural abundances are \(49.9461 \mathrm{u}, 4.35 \% ; 51.9405 \mathrm{u}, 83.79 \% ; 52.9407 \mathrm{u}\) \(9.50 \% ;\) and \(53.9389 \mathrm{u}, 2.36 \% .\) Calculate the weightedaverage atomic mass of chromium.

Bromine has two naturally occurring isotopes. One of them, bromine-79, has a mass of 78.918336 u and a natural abundance of \(50.69 \% .\) What must be the mass and percent natural abundance of the other isotope, bromine-81?

A mass spectrum of germanium displayed peaks at mass numbers \(70,72,73,74,\) and \(76,\) with relative heights of \(20.5,27.4,7.8,36.5,\) and \(7.8,\) respectively. (a) In the manner of Figure \(2-14,\) sketch this mass spectrum. (b) Estimate the weighted-average atomic mass of germanium, and state why this result is only approximately correct.

Hydrogen and chlorine atoms react to form simple diatomic molecules in a 1: 1 ratio, that is, \(\mathrm{HCl}\). The natural abundances of the chlorine isotopes are \(75.77 \%^{35} \mathrm{Cl}\) and \(24.23 \%^{37} \mathrm{Cl} .\) The natural abundances of \(^{2} \mathrm{H}\) and \(^{3} \mathrm{H}\) are \(0.015 \%\) and less than \(0.001 \%,\) respectively. (a) How many different HCl molecules are possible, and what are their mass numbers (that is, the sum of the mass numbers of the H and Cl atoms)? (b) Which is the most abundant of the possible HCl molecules? Which is the second most abundant?

Refer to the periodic table inside the front cover and identify (a) the element that is in group 14 and the fourth period (b) one element similar to and one unlike sulfur (c) the alkali metal in the fifth period (d) the halogen element in the sixth period

Refer to the periodic table inside the front cover and identify (a) the element that is in group 11 and the sixth period (b) an element with atomic number greater than 50 that has properties similar to the element with atomic number 18 (c) the group number of an element \(\mathrm{E}\) that forms an ion \(\mathrm{E}^{2-}\) (d) an element \(M\) that you would expect to form the ion \(\mathrm{M}^{3+}\)

Assuming that the seventh period of the periodic table has 32 members, what should be the atomic number of (a) the noble gas following radon (Rn); (b) the alkali metal following francium (Fr)?

What is the total number of atoms in (a) 15.8 mol \(\mathrm{Fe}\); (b) \(0.000467 \mathrm{mol} \mathrm{Ag} ;\) (c) \(8.5 \times 10^{-11} \mathrm{mol} \mathrm{Na} ?\)

Determine (a) the number of moles of \(\mathrm{Zn}\) in a \(415.0 \mathrm{g}\) sample of zinc metal (b) the number of \(\mathrm{Cr}\) atoms in \(147.4 \mathrm{kg}\) chromium (c) the mass of a one-trillion-atom \(\left(1.0 \times 10^{12}\right)\) sample of metallic gold (d) the mass of one fluorine atom

Determine (a) the number of \(\mathrm{Kr}\) atoms in a 5.25 -mg sample of krypton (b) the molar mass, \(M,\) and identity of an element if the mass of a \(2.80 \times 10^{22}\) -atom sample of the element is \(2.09 \mathrm{g}\) (c) the mass of a sample of phosphorus that contains the same number of atoms as \(44.75 \mathrm{g}\) of magnesium

How many atoms are present in a \(75.0 \mathrm{cm}^{3}\) sample of plumber's solder, a lead-tin alloy containing \(67 \% \mathrm{Pb}\) by mass and having a density of \(9.4 \mathrm{g} / \mathrm{cm}^{3} ?\)

How many \(^{204} \mathrm{Pb}\) atoms are present in a piece of lead weighing \(215 \mathrm{mg} ?\) The percent natural abundance of \(204 \mathrm{Pb}\) is \(1.4 \%\)

Without doing detailed calculations, determine which of the following samples has the greatest number of atoms: (a) a cube of iron with a length of \(10.0 \mathrm{cm}\) \(\left(d=7.86 \mathrm{g} / \mathrm{cm}^{3}\right)\) (b) \(1.00 \mathrm{kg}\) of hydrogen contained in a \(10,000 \mathrm{L}\) balloon (c) a mound of sulfur weighing \(20.0 \mathrm{kg}\) (d) a 76 lb sample of liquid mercury \((d=13.5 \mathrm{g} / \mathrm{mL})\)

Without doing detailed calculations, determine which of the following samples occupies the largest volume: (a) 25.5 mol of sodium metal \(\left(d=0.971 \mathrm{g} / \mathrm{cm}^{3}\right)\) (b) 0.725 L of liquid bromine \((d=3.12 \mathrm{g} / \mathrm{mL})\) (c) \(1.25 \times 10^{25}\) atoms of chromium metal \(\left(d=9.4 \mathrm{g} / \mathrm{cm}^{3}\right)\) (d) \(2.15 \mathrm{kg}\) of plumber's solder \(\left(d=9.4 \mathrm{g} / \mathrm{cm}^{3}\right), \mathrm{a}\) lead-tin alloy with a 2: 1 atom ratio of lead to tin

William Prout (1815) proposed that all other atoms are built up of hydrogen atoms, suggesting that all elements should have integral atomic masses based on an atomic mass of one for hydrogen. This hypothesis appeared discredited by the discovery of atomic masses, such as 24.3 u for magnesium and 35.5 u for chlorine. In terms of modern knowledge, explain why Prout's hypothesis is actually quite reasonable.

Use fundamental definitions and statements from Chapters 1 and 2 to establish the fact that \(6.022 \times 10^{23} \mathrm{u}=1.000 \mathrm{g}\)

In each case, identify the element in question. (a) The mass number of an atom is 234 and the atom has \(60.0 \%\) more neutrons than protons. (b) An ion with a \(2+\) charge has \(10.0 \%\) more protons than electrons. (c) An ion with a mass number of 110 and a \(2+\) charge has \(25.0 \%\) more neutrons than electrons.

Determine the only possible \(2+\) ion for which the following two conditions are both satisfied: \(\bullet\) The net ionic charge is one-tenth the nuclear charge. \(\bullet\) The number of neutrons is four more than the number of electrons.

Determine the only possible isotope (E) for which the following conditions are met: \(\bullet\)The mass number of \(\mathrm{E}\) is 2.50 times its atomic number. \(\bullet\)The atomic number of \(\mathrm{E}\) is equal to the mass number of another isotope (Y). In turn, isotope Y has a neutron number that is 1.33 times the atomic number of \(Y\) and equal to the neutron number of selenium- 82 .

Germanium has three major naturally occurring isotopes: \(^{70}\) Ge \((69.92425 \mathrm{u}, 20.85 \%),^{72} \mathrm{Ge}(71.92208 \mathrm{u},\) \(27.54 \%),^{74} \mathrm{Ge}(73.92118 \mathrm{u}, 36.29 \%) .\) There are also two minor isotopes: \(^{73}\) Ge \(\left(72.92346 \text { u) and }^{76} \mathrm{Ge}\right.\) (75.92140 u). Calculate the percent natural abundances of the two minor isotopes. Comment on the precision of these calculations.

From the densities of the lines in the mass spectrum of krypton gas, the following observations were made: \bullet Somewhat more than \(50 \%\) of the atoms were krypton-84. \(\bullet\) The numbers of krypton- 82 and krypton- 83 atoms were essentially equal. \(\bullet\) The number of krypton-86 atoms was 1.50 times as great as the number of krypton- 82 atoms. \(\bullet\) The number of krypton-80 atoms was \(19.6 \%\) of the number of krypton- 82 atoms. \(\bullet\) The number of krypton- 78 atoms was \(3.0 \%\) of the number of krypton- 82 atoms. The masses of the isotopes are \(^{78} \mathrm{Kr}, 77.9204 \mathrm{u} \quad^{80} \mathrm{Kr}, 79.9164 \mathrm{u} \quad^{82} \mathrm{Kr}, 81.9135 \mathrm{u}\) \(^{83} \mathrm{Kr}, 82.9141 \mathrm{u} \quad^{84} \mathrm{Kr}, 83.9115 \mathrm{u} \quad^{86} \mathrm{Kr}, 85.9106 \mathrm{u}\) The weighted-average atomic mass of \(\mathrm{Kr}\) is \(83.80 .\) Use these data to calculate the percent natural abundances of the krypton isotopes.

How many atoms are present in a \(1.00 \mathrm{m}\) length of 20-gauge copper wire? A 20-gauge wire has a diameter of 0.03196 in., and the density of copper is \(8.92 \mathrm{g} / \mathrm{cm}^{3}\)

Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics industry. A particular alloy with a density of \(8.80 \mathrm{g} / \mathrm{cm}^{3}\) and containing \(0.022 \%\) Si by mass is used to make a rectangular plate \(15.0 \mathrm{cm}\) long, \(12.5 \mathrm{cm}\) wide, \(3.00 \mathrm{mm}\) thick, and has a \(2.50 \mathrm{cm}\) diameter hole drilled through its center. How many silicon- 30 atoms are found in this plate? The mass of a silicon- 30 atom is \(29.97376 \mathrm{u}\) and the percent natural abundance of silicon- 30 is 3.10\%.