Chapter 3

Calculate the mass ratio of a bromine atom to an atom of (a) neon (b) calcium (c) helium

Arrange the following in order of increasing mass. (a) a sodium ion (b) a selenium atom (c) a sulfur \(\left(\mathrm{S}_{8}\right)\) molecule (d) a scandium atom

Silicon is widely used in the semi-conductor industry. Its isotopes and their atomic masses are: Si-28 ( \(27.9769 \mathrm{amu}\) ), Si-29 ( \(28.9765 \mathrm{amu}\) ), and Si-30 ( \(29.9794\) amu). Which is the most abundant?

Strontium has four isotopes with the following masses: \(83.9134\) amu \((0.56 \%), 85.9094 \mathrm{amu}(9.86 \%), 86.9089 \mathrm{amu}(7.00 \%)\), and \(87.9056(82.58 \%)\) Calculate the atomic mass of strontium.

Oxygen consists of three isotopes with atomic masses \(16.00,17.00\), and \(18.00\) amu. Their abundances are \(99.76 \%, 0.04 \%\), and \(0.20 \%\), respectively. What is the atomic mass of oxygen?

Chromium (atomic mass \(=51.9961\) amu) has four isotopes. Their masses are \(49.94605 \mathrm{amu}, 51.94051 \mathrm{amu}, 52.94065 \mathrm{amu}\), and \(53.93888\) amu. The first two isotopes have a total abundance of \(87.87 \%\), and the last isotope has an abundance of \(2.365 \%\). What is the abundance of the third isotope? Estimate the abundances of the first two isotopes.

Chlorine has two isotopes, Cl-35 and Cl-37. Their abundances are \(75.53 \%\) and \(24.47 \%\), respectively. Assume that the only hydrogen isotope present is \(\mathrm{H}-1\). (a) How many different HCl molecules are possible? (b) What is the sum of the mass numbers of the two atoms in each molecule? (c) Sketch the mass spectrum for \(\mathrm{HCl}\) if all the positive ions are obtained by removing a single electron from an HCl molecule.

One chocolate chip used in making chocolate chip cookies has a mass of \(0.324 \mathrm{~g}\). (a) How many chocolate chips are there in one mole of chocolate chips? (b) If a cookie needs 15 chocolate chips, how many cookies can one make with a billionth \(\left(1 \times 10^{-9}\right)\) of a mole of chocolate chips? (A billionth of a mole is scientifically known as a nanomole.)

The meat from one hazelnut has a mass of \(0.985 \mathrm{~g}\). (a) What is the mass of a millionth of a mole \(\left(10^{-6}\right)\) of hazelnut meats? (A millionth of a mole is also called a micromole.) (b) How many moles are in a pound of hazelnut meats?

Lead is a heavy metal that remains in the bloodstream, causing mental retardation in children. It is believed that \(3 \times 10^{-7} \mathrm{~g}\) of \(\mathrm{Pb}\) in \(1.00 \mathrm{~mL}\) of blood is a health hazard. For this amount of lead (a) how many atoms of lead are there in one \(\mathrm{mL}\) of a child's blood? (b) how many moles of lead are in \(1.00 \mathrm{~L}\) of blood?

Determine (a) the mass of \(0.357\) mol of gold. (b) the number of atoms in \(0.357 \mathrm{~g}\) of gold. (c) the number of moles of electrons in \(0.357 \mathrm{~g}\) of gold.

How many protons are in (a) an atom of platinum? (b) one mole of platinum? (c) one gram of platinum?

The isotope Si-28 has a mass of \(27.977\) amu. For ten grams of Si-28, calculate (a) the number of moles. (b) the number of atoms. (c) the total number of protons, neutrons, and electrons.

Consider an isotope of yttrium, Y-90. This isotope is incorporated into cancer-seeking antibodies so that the cancer can be irradiated by the yttrium and destroyed. How many neutrons are in (a) twenty-five atoms of yttrium? (b) \(0.250\) mol of yttrium? (c) one nanogram \(\left(10^{-9} \mathrm{~g}\right)\) of yttrium?

A cylindrical piece of pure copper \(\left(d=8.92 \mathrm{~g} / \mathrm{cm}^{3}\right)\) has diameter \(1.15 \mathrm{~cm}\) and height \(4.00\) inches. How many atoms are in that cylinder? (Note: the volume of a right circular cylinder of radius \(r\) and height \(h\) is \(V=\pi r^{2} h .\) )

Calculate the molar masses (in grams per mole) of (a) cane sugar, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) (b) laughing gas, \(\mathrm{N}_{2} \mathrm{O}\). (c) vitamin A, \(\mathrm{C}_{20} \mathrm{H}_{30} \mathrm{O}\).

Calculate the molar masses (in grams per mole) of (a) gallium, Ga, a metal that literally melts in your hands. (b) plaster of paris, \(\mathrm{CaSO}_{4} \cdot \frac{1}{2} \mathrm{H}_{2} \mathrm{O}\), once used in making casts for broken bones. (c) benzoyl peroxide, \(\mathrm{C}_{14} \mathrm{H}_{10} \mathrm{O}_{4}\), the active ingredient in many lotions used to treat acne.

Convert the following to moles. (a) \(4.00 \times 10^{3} \mathrm{~g}\) of hydrazine, a rocket propellant (b) \(12.5 \mathrm{~g}\) of tin(II) fluoride, the active ingredient in fluoride toothpaste (c) \(13 \mathrm{~g}\) of caffeine, \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\)

Convert the following to moles. (a) \(35.00 \mathrm{~g}\) of \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\), a chlorofluorocarbon that destroys the ozone layer in the atmosphere (b) \(100.0 \mathrm{mg}\) of iron(II) sulfate, an iron supplement prescribed for anemia (c) \(2.00 \mathrm{~g}\) of Valium \(\left(\mathrm{C}_{15} \mathrm{H}_{13} \mathrm{ClN}_{2} \mathrm{O}-\right.\) diazepam \()\)

Calculate the mass in grams of \(2.688 \mathrm{~mol}\) of (a) chlorophyll, \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{~N}_{4} \mathrm{O}_{5} \mathrm{Mg}\), responsible for the green color of leaves. (b) sorbitol, \(\mathrm{C}_{9} \mathrm{H}_{14} \mathrm{O}_{6}\), an artificial sweetener. (c) indigo, \(\mathrm{C}_{16} \mathrm{H}_{10} \mathrm{~N}_{2} \mathrm{O}_{2}\), a blue dye.

Calculate the mass in grams of \(13.5 \mathrm{~mol}\) of (a) vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), the starting material for a plastic. (b) capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\), the substance that makes red chili peppers "hot." (c) stearic acid, \(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\), used in soaps.

Turquoise has the following chemical formula: \(\mathrm{CuAl}_{6}\left(\mathrm{PO}_{4}\right)_{4}(\mathrm{OH})_{8}\). \(4 \mathrm{H}_{2} \mathrm{O} .\) Calculate the mass percent of each element in turquoise.

The active ingredient of some antiperspirants is \(\mathrm{Al}_{2}(\mathrm{OH})_{5} \mathrm{Cl} .\) Calculate the mass percent of each element in this ingredient.

Deer ticks are known to cause Lyme disease. The presence of DEET (diethyltoluamide) in insect repellents protects the user from the ticks. The molecular formula for DEET is \(\mathrm{C}_{12} \mathrm{H}_{17} \mathrm{NO}\). How many grams of carbon can be obtained from \(127 \mathrm{~g}\) of DEET?

Allicin is responsible for the distinctive taste and odor of garlic. Its simple formula is \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{2} \mathrm{~S}\). How many grams of sulfur can be obtained from \(25.0 \mathrm{~g}\) of allicin?

A tablet of Tylenol \(^{\text {m }}\) has a mass of \(0.611 \mathrm{~g}\). It contains \(251 \mathrm{mg}\) of its active ingredient, acetaminophen, \(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2}\). (a) What is the mass percent of acetaminophen in a tablet of Tylenol? (b) Assume that all the nitrogen in the tablet is in the acetaminophen. How many grams of nitrogen are present in a tablet of Tylenol?

The active ingredient in Pepto-Bismol \(^{\text {m }}\) (an over-the-counter remedy for upset stomach) is bismuth subsalicylate, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}\). Analysis of a 1.500-g sample of Pepto-Bismol yields \(346 \mathrm{mg}\) of bismuth. What percent by mass is bismuth subsalicylate? (Assume that there is no other bismuthcontaining compound in Pepto-Bismol.)

Combustion analysis of \(1.00 \mathrm{~g}\) of the male sex hormone, testosterone, yields \(2.90 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.875 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). What are the mass percents of carbon, hydrogen, and oxygen in testosterone?

Hexachlorophene, a compound made up of atoms of carbon, hydrogen, chlorine, and oxygen, is an ingredient in germicidal soaps. Combustion of a \(1.000-\mathrm{g}\) sample yields \(1.407 \mathrm{~g}\) of carbon dioxide, \(0.134 \mathrm{~g}\) of water, and \(0.523 \mathrm{~g}\) of chlorine gas. What are the mass percents of carbon, hydrogen, oxygen, and chlorine in hexachlorophene?

A compound \(\mathrm{XCl}_{3}\) is \(70.3 \%\) (by mass) chlorine. What is the molar mass of the compound? What is the symbol and name of X?

A compound \(\mathrm{YO}_{2}\) is \(50.0 \%\) (by mass) oxygen. What is the identity of Y? What is the molar mass of \(\mathrm{YO}_{2} ?\)

Phosphorus reacts with oxygen to produce different kinds of oxides. One of these oxides is formed when \(1.347 \mathrm{~g}\) of phosphorus reacts with \(1.744 \mathrm{~g}\) of oxygen. What is the simplest formula of this oxide? Name the oxide.

Nickel reacts with sulfur to form a sulfide. If \(2.986 \mathrm{~g}\) of nickel reacts with enough sulfur to form \(5.433\) g of nickel sulfide, what is the simplest formula of the sulfide? Name the sulfide.

Determine the simplest formulas of the following compounds: (a) the food enhancer monosodium glutamate (MSG), which has the composition \(35.51 \%\) C, \(4.77 \% \mathrm{H}, 37.85 \% \mathrm{O}, 8.29 \% \mathrm{~N}\), and \(13.60 \% \mathrm{Na} .\) (b) zircon, a diamond-like mineral, which has the composition \(34.91 \%\) \(\mathrm{O}, 15.32 \% \mathrm{Si}\), and \(49.76 \% \mathrm{Zr}\) (c) nicotine, which has the composition \(74.0 \%\) C, \(8.65 \% \mathrm{H}\), and \(17.4 \% \mathrm{~N} .\)

Determine the simplest formulas of the following compounds: (a) saccharin, the artificial sweetener, which has the composition \(45.90 \% \mathrm{C}, 2.75 \% \mathrm{H}, 26.20 \% \mathrm{O}, 17.50 \% \mathrm{~S}\), and \(7.65 \% \mathrm{~N}\) (b) allicin, the compound that gives garlic its characteristic odor, which has the composition \(6.21 \% \mathrm{H}, 44.4 \% \mathrm{C}, 9.86 \% \mathrm{O}\), and \(39.51 \% \mathrm{~S}\). (c) sodium thiosulfate, the fixer used in developing photographic film, which has the composition \(30.36 \% \mathrm{O}, 29.08 \% \mathrm{Na}\), and \(40.56 \% \mathrm{~S}\).

Ibuprofen, the active ingredient in Advil \(^{\text {m }}\), is made up of carbon, hydrogen, and oxygen atoms. When a sample of ibuprofen, weighing \(5.000 \mathrm{~g}\), burns in oxygen, \(13.86 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(3.926 \mathrm{~g}\) of water are obtaine \(\mathrm{d} .\) What is the simplest formula of ibuprofen?

Methyl salicylate is a common "active ingredient" in liniments such as Ben-Gay \(^{\pi \prime}\). It is also known as oil of wintergreen. It is made up of carbon, hydrogen, and oxygen atoms. When a sample of methyl salicylate weighing \(5.287 \mathrm{~g}\) is burned in excess oxygen, \(12.24 \mathrm{~g}\) of carbon dioxide and \(2.505 \mathrm{~g}\) of water are formed. What is the simplest formula for oil of wintergreen?

WEB DDT (dichlorodiphenyltrichloroethane) was the first chlorinated insecticide developed. It was used extensively in World War II to eradicate the mosquitoes that spread malaria. Its use was banned in the United States in 1978 because of environmental concerns. DDT is made up of carbon, hydrogen, and chlorine atoms. When a \(5.000-\mathrm{g}\) sample of DDT is burned in oxygen, \(8.692 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(1.142 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are obtained. A second five-gram sample yields \(2.571 \mathrm{~g}\) of \(\mathrm{HCl}\). What is the simplest formula for DDT?

Riboflavin is one of the \(\mathrm{B}\) vitamins. It is also known as vitamin \(\mathrm{B}_{6}\) and is made up of carbon, hydrogen, nitrogen, and oxygen atoms. When \(10.00 \mathrm{~g}\) of vitamin \(\mathrm{B}_{6}\) is burned in oxygen, \(19.88 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(4.79 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are obtained. Another experiment shows that vitamin \(\mathrm{B}_{6}\) is made up of \(14.89 \% \mathrm{~N}\). What is the simplest formula for vitamin \(\mathrm{B}_{6}\) ?

Hexamethylenediamine (MM \(=116.2 \mathrm{~g} / \mathrm{mol}\) ), a compound made up of carbon, hydrogen, and nitrogen atoms, is used in the production of nylon. When \(6.315 \mathrm{~g}\) of hexamethylenediamine is burned in oxygen, \(14.36 \mathrm{~g}\) of carbon dioxide and \(7.832 \mathrm{~g}\) of water are obtained. What are the simplest and molecular formulas of this compound?

Dimethylhydrazine, the fuel used in the Apollo lunar descent module, has a molar mass of \(60.10 \mathrm{~g} / \mathrm{mol}\). It is made up of carbon, hydrogen, and nitrogen atoms. The combustion of \(2.859 \mathrm{~g}\) of the fuel in excess oxygen yields \(4.190 \mathrm{~g}\) of carbon dioxide and \(3.428 \mathrm{~g}\) of water. What are the simplest and molecular formulas for dimethylhydrazine?

A certain hydrate of potassium aluminum sulfate (alum) has the formula \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2} \cdot x \mathrm{H}_{2} \mathrm{O}\). When a hydrate sample weighing \(5.459 \mathrm{~g}\) is heated to remove all the water, \(2.583 \mathrm{~g}\) of \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2}\) remains. What is the mass percent of water in the hydrate? What is \(x ?\)

Epsom salts are hydrates of magnesium sulfate. The formula for Epsom salts is \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\). A \(7.834\) -g sample is heated until a constant mass is obtained indicating that all the water has been evaporated off. What is the mass of the anhydrous magnesium sulfate? What percentage of the hydrate is water?

Balance the following equations: (a) \(\mathrm{CaC}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g)\) (b) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(s) \longrightarrow \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{CH}_{3} \mathrm{NH}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Balance the following equations: (a) \(\mathrm{H}_{2} \mathrm{~S}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{S}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{HCN}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(l)+\mathrm{H}_{2} \mathrm{O}(g)\)

Write balanced equations for the reaction of sulfur with the following metals to form solids that you can take to be ionic when the anion is \(\mathrm{S}^{2-}\). (a) potassium (b) magnesium (c) aluminum (d) calcium (e) iron (forming \(\mathrm{Fe}^{2+}\) ions)

Write balanced equations for the reaction of aluminum metal with the following nonmetals: (a) sulfur (b) bromine (c) nitrogen (d) oxygen (forming \(\mathrm{O}^{2-}\) ions) (e) oxygen (forming \(\mathrm{O}_{2}{\underline{\phantom{xx}}}^{2-}\), or peroxide ions)

Write a balanced equation for (a) the combustion (reaction with oxygen gas) of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), to give carbon dioxide and water. (b) the reaction between xenon tetrafluoride gas and water to give xenon, oxygen, and hydrogen fluoride gases. (c) the reaction between aluminum and iron(III) oxide to give aluminum oxide and iron. (d) the formation of ammonia gas from its elements. (e) the reaction between sodium chloride, sulfur dioxide gas, steam, and oxygen to give sodium sulfate and hydrogen chloride gas.

Write a balanced equation for (a) the reaction between fluorine gas and water to give oxygen difluoride and hydrogen fluoride gases. (b) the reaction between oxygen and ammonia gases to give nitrogen dioxide gas and water. (c) the burning of gold(III) sulfide in hydrogen to give gold metal and dihydrogen sulfide gas. (d) the decomposition of sodium hydrogen carbonate to sodium carbonate, water, and carbon dioxide gas. (e) the reaction between sulfur dioxide gas and liquid hydrogen fluoride to give sulfur tetrafluoride gas and water.

Cyanogen gas, \(\mathrm{C}_{2} \mathrm{~N}_{2}\), has been found in the gases of outer space. It can react with fluorine to form carbon tetrafluoride and nitrogen trifluoride. $$ \mathrm{C}_{2} \mathrm{~N}_{2}(g)+7 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{CF}_{4}(g)+2 \mathrm{NF}_{3}(g) $$ (a) How many moles of fluorine react with \(1.37\) mol of cyanogen? (b) How many moles of \(\mathrm{CF}_{4}\) are obtained from \(13.75 \mathrm{~mol}\) of fluorine? (c) How many moles of cyanogen are required to produce \(0.8974 \mathrm{~mol}\) of \(\mathrm{NP}_{3} ?\) (d) How many moles of fluorine will yield \(4.981 \mathrm{~mol}\) of nitrogen trifluoride?