Chapter 3

Diborane, \(\mathrm{B}_{2} \mathrm{H}_{6}\), can be prepared by the following reaction: $$ 3 \mathrm{NaBH}_{4}(s)+4 \mathrm{BF}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{~B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{NaBF}_{4}(s) $$ (a) How many moles of \(\mathrm{NaBH}_{4}\) react with \(1.299 \mathrm{~mol}\) of \(\mathrm{BF}_{3} ?\) (b) How many moles of \(\mathrm{B}_{2} \mathrm{H}_{6}\) can be obtained from \(0.893 \mathrm{~mol}\) of \(\mathrm{NaBH}_{4} ?\) (c) If \(1.987 \mathrm{~mol}\) of \(\mathrm{B}_{2} \mathrm{H}_{6}\) is obtained, how many moles of \(\mathrm{NaBF}_{4}\) are produced? (d) How many moles of \(\mathrm{BF}_{3}\) are required to produce \(4.992 \mathrm{~mol}\) of \(\mathrm{NaBF}_{4} ?\)

One way to remove nitrogen oxide (NO) from smoke stack emissions is to react it with ammonia. $$ 4 \mathrm{NH}_{3}(g)+6 \mathrm{NO}(g) \longrightarrow 5 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ Calculate (a) the mass of water produced from \(0.839\) mol of ammonia. (b) the mass of NO required to react with \(3.402\) mol of ammonia. (c) the mass of ammonia required to produce \(12.0 \mathrm{~g}\) of nitrogen gas. (d) the mass of ammonia required to react with \(115 \mathrm{~g}\) of NO.

Phosphine gas reacts with oxygen according to the following equation: $$ 4 \mathrm{PH}_{3}(g)+8 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ Calculate (a) the mass of tetraphosphorus decaoxide produced from \(12.43 \mathrm{~mol}\) of phosphine. (b) the mass of \(\mathrm{PH}_{3}\) required to form \(0.739 \mathrm{~mol}\) of steam. (c) the mass of oxygen gas that yields \(1.000 \mathrm{~g}\) of steam. (d) the mass of oxygen required to react with \(20.50 \mathrm{~g}\) of phosphine.

The combustion of liquid chloroethylene, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), yields carbon dioxide, steam, and hydrogen chloride gas. (a) Write a balanced equation for the reaction. (b) How many moles of oxygen are required to react with \(35.00 \mathrm{~g}\) of chloroethylene? (c) If \(25.00 \mathrm{~g}\) of chloroethylene reacts with an excess of oxygen, how many grams of each product are formed?

Sand consists mainly of silicon dioxide. When sand is heated with an excess of coke (carbon), pure silicon and carbon monoxide are produced. (a) Write a balanced equation for the reaction. (b) How many moles of silicon dioxide are required to form \(12.72 \mathrm{~g}\) of silicon? (c) How many grams of carbon monoxide are formed when \(44.99 \mathrm{~g}\) of silicon is produced?

Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), is responsible for the effects of intoxication felt after drinking alcoholic beverages. When ethanol burns in oxygen, carbon dioxide, and water are produced. (a) Write a balanced equation for the reaction. (b) How many liters of ethanol \(\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\) will produce \(1.25 \mathrm{~L}\) of water \(\left(d=1.00 \mathrm{~g} / \mathrm{cm}^{3}\right) ?\) (c) A wine cooler contains \(4.5 \%\) ethanol by mass. Assuming that only the alcohol burns in oxygen, how many grams of wine cooler need to be burned to produce \(3.12 \mathrm{~L}\) of \(\mathrm{CO}_{2}\left(d=1.80 \mathrm{~g} / \mathrm{L}\right.\) at \(25^{\circ} \mathrm{C}, 1\) atm pressure) at the conditions given for the density?

A crude oil burned in electrical generating plants contains about \(1.2 \%\) sulfur by mass. When the oil burns, the sulfur forms sulfur dioxide gas: $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How many liters of \(\mathrm{SO}_{2}(d=2.60 \mathrm{~g} / \mathrm{L})\) are produced when \(1.00 \times 10^{4} \mathrm{~kg}\) of oil burns at the same temperature and pressure?

Oxygen masks for producing \(\mathrm{O}_{2}\) in emergency situations contain potassium superoxide, \(\mathrm{KO}_{2}\). It reacts with \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) in exhaled air to produce oxygen: $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)+4 \mathrm{CO}_{2}(g) \longrightarrow 4 \mathrm{KHCO}_{3}(s)+3 \mathrm{O}_{2}(g) $$

Consider the hypothetical reaction $$ 8 \mathrm{~A}_{2} \mathrm{~B}_{3}(s)+3 \mathrm{X}_{4}(g) \longrightarrow 4 \mathrm{~A}_{4} \mathrm{X}_{3}(s)+12 \mathrm{~B}_{2}(g) $$ When \(10.0 \mathrm{~g}\) of \(\mathrm{A}_{2} \mathrm{~B}_{3}(\mathrm{MM}=255 \mathrm{~g} / \mathrm{mol})\) react with an excess of \(\mathrm{X}_{4}, 4.00 \mathrm{~g}\) of \(\mathrm{A}_{4} \mathrm{X}_{3}\) are produced. (a) How many moles of \(A_{4} X_{3}\) are produced? (b) What is the molar mass of \(\mathrm{A}_{4} \mathrm{X}_{3}\) ?

When three moles of a metal oxide, \(\mathrm{MO}_{2}\), react with ammonia gas, the metal (M), water, and nitrogen gas are formed. (a) Write a balanced equation to represent the reaction. (b) When \(13.8 \mathrm{~g}\) of ammonia react with an excess of metal oxide, \(126 \mathrm{~g}\) of \(\mathrm{M}\) are formed. What is the molar mass for \(\mathrm{M}\) ? What is the identity of \(\mathrm{M} ?\)

A gaseous mixture containing \(4.15 \mathrm{~mol}\) of hydrogen gas and \(7.13 \mathrm{~mol}\) of oxygen gas reacts to form steam. (a) Write a balanced equation for the reaction. (b) What is the limiting reactant? (c) What is the theoretical yield of steam in moles? (d) How many moles of the excess reactant remain unreacted?

Aluminum reacts with sulfur gas to form aluminum sulfide. Initially, \(1.18\) mol of aluminum and \(2.25\) mol of sulfur are combined. (a) Write a balanced equation for the reaction. (b) What is the limiting reactant? (c) What is the theoretical yield of aluminum sulfide in moles? (d) How many moles of excess reactant remain unreacted?

When potassium chlorate is burned, potassium chloride and oxygen are formed. (a) Write a balanced equation for the reaction. (b) How much potassium chlorate must be burned to produce \(198.5 \mathrm{~g}\) of oxygen? The yield is found to be \(83.2 \%\).

When iron and steam react at high temperatures, the following reaction takes place. $$ 3 \mathrm{Fe}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{H}_{2}(g) $$ How much iron must react with excess steam to form \(897 \mathrm{~g}\) of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) if the reaction yield is \(69 \%\) ?

Oxyacetylene torches used for welding reach temperatures near \(2000^{\circ} \mathrm{C}\). The reaction involved in the combustion of acetylene is $$ 2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) Starting with \(175 \mathrm{~g}\) of both acetylene and oxygen, what is the theoretical yield, in grams, of carbon dioxide? (b) If \(68.5 \mathrm{~L}(d=1.85 \mathrm{~g} / \mathrm{L})\) of carbon dioxide is produced, what is the percent yield at the same conditions of temperature and pressure? (c) How much of the reactant in excess is unused? (Assume 100\% yield.)

The Space Shuttle uses aluminum metal and ammonium perchlorate in its reusable booster rockets. The products of the reaction are aluminum oxide, aluminum chloride, nitrogen oxide gas, and steam. The reaction mixture contains \(7.00 \mathrm{~g}\) of aluminum and \(9.32 \mathrm{~g}\) of ammonium perchlorate. (a) Write a balanced equation for the reaction. (b) What is the theoretical yield of aluminum oxide? (c) If \(1.56 \mathrm{~g}\) of aluminum oxide is formed, what is the percent yield? (d) How many grams of excess reactant are unused? (Assume \(100 \%\) yield.)

Aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\), is prepared by reacting salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\), with acetic anhydride, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\), in the reaction $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}(s)+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}(l) $$

A student prepares phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}\), by reacting solid phosphorus triodide with water. $$ \mathrm{PI}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{3}(s)+3 \mathrm{HI}(g) $$ The student needs to obtain \(0.250 \mathrm{~L}\) of \(\mathrm{H}_{3} \mathrm{PO}_{3}\left(d=1.651 \mathrm{~g} / \mathrm{cm}^{3}\right)\). The procedure calls for a \(45.0 \%\) excess of water and a yield of \(75.0 \%\). How much phosphorus triiodide should be weighed out? What volume of water \(\left(d=1.00 \mathrm{~g} / \mathrm{cm}^{3}\right)\) should be used?

Carbon tetrachloride, \(\mathrm{CCl}_{4}\), was a popular dry-cleaning agent until it was shown to be carcinogenic. It has a density of \(1.589 \mathrm{~g} / \mathrm{cm}^{3} .\) What volume of carbon tetrachloride will contain a total of \(6.00 \times 10^{25}\) molecules of \(\mathrm{CCl}_{4} ?\)

Some brands of salami contain \(0.090 \%\) sodium benzoate \(\left(\mathrm{NaC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) by mass as a preservative. If you eat \(6.00 \mathrm{oz}\) of this salami, how many atoms of sodium will you consume, assuming salami contains no other source of that element?

Most wine is prepared by the fermentation of the glucose in grape juice by yeast: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g) $$ How many grams of glucose should there be in grape juice to produce \(725 \mathrm{~mL}\) of wine that is \(11.0 \%\) ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\), by volume?

All the fertilizers listed below contribute nitrogen to the soil. If all these fertilizers are sold for the same price per gram of nitrogen, which will cost the least per 50 -lb bag? urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) ammonia, \(\mathrm{NH}_{3}\) ammonium nitrate, \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) guanidine, \(\mathrm{HNC}\left(\mathrm{NH}_{2}\right)_{2}\)

Perhaps the simplest way to calculate Avogadro's number is to compare the charge on the electron, first determined by Robert Millikan in 1909, with the charge on a mole of electrons, determined electrochemically (Chapter 18). These charges, in coulombs (C), are given in Appendix 1 . Use them to calculate Avogadro's number to five significant figures.

Given a pair of elements and their mass relation, answer the following questions. (a) The mass of 4 atoms of \(A=\) the mass of 6 atoms of \(B\). Which element has the smaller molar mass? (b) The mass of 6 atoms of \(C\) is less than the mass of 3 atoms of the element D. Which element has more atoms/gram? (c) Six atoms of \(\mathrm{E}\) have larger mass than six atoms of \(\mathrm{F}\). Which has more atoms/gram? (d) Six atoms of \(F\) have the same mass as 8 atoms of \(G .\) Which has more atoms/mole?

Nitrogen reacts with hydrogen to form ammonia. Represent each nitrogen atom by a square and each hydrogen atom with a circle. Starting with five molecules of both hydrogen and nitrogen, show pictorially what you have after the reaction is complete.

When \(4.0 \mathrm{~mol}\) of \(\mathrm{CCl}_{4}\) reacts with an excess of \(\mathrm{HF}, 3.0 \mathrm{~mol}\) of \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) (Freon) is obtained. The equation for the reaction is $$ \mathrm{CCl}_{4}(l)+2 \mathrm{HF}(g) \longrightarrow \mathrm{CCl}_{2} \mathrm{~F}_{2}(l)+2 \mathrm{HCl}(g) $$ State which of the statements are true about the reaction and make the false statements true. (a) The theoretical yield for \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) is \(3.0 \mathrm{~mol}\). (b) The theoretical yield for \(\mathrm{HCl}\) is \(71 \mathrm{~g}\). (c) The percent yield for the reaction is \(75 \%\). (d) The theoretical yield cannot be determined unless the exact amount of \(\mathrm{HF}\) is given. (e) From just the information given above, it is impossible to calculate how much HF is unreacted. (f) For this reaction, as well as for any other reaction, the total number of moles of reactants is equal to the total number of moles of product. (g) Half a mole of \(\mathrm{HF}\) is consumed for every mole of \(\mathrm{CCl}_{4}\) used. (h) At the end of the reaction, no \(\mathrm{CCl}_{4}\) is theoretically left unreacted.

Suppose that the atomic mass of \(\mathrm{C}-12\) is taken to be \(5.000 \mathrm{amu}\) and that a mole is defined as the number of atoms in \(5.000 \mathrm{~kg}\) of carbon-12. How many atoms would there be in one mole under these conditions? (Hint: There are \(6.022 \times 10^{23} \mathrm{C}\) atoms in \(12.00 \mathrm{~g}\) of \(\mathrm{C}-12 .\) )

97\. Answer the questions below, using LT (for is less than), GT (for is greater than), EQ (for is equal to), or MI (for more information required) in the blanks provided. (a) The mass (to three significant figures) of \(6.022 \times 10^{23}\) atoms of Na ______ 23.0 g. (b) Boron has two isotopes, B-10 (10.01 amu) and B-11 (11.01 amu). The abundance of B-10 _______the abundance of B-11. (c) If S-32 were assigned as the standard for expressing relative atomic masses and assigned an atomic mass of \(10.00 \mathrm{amu}\), the atomic mass for \(\mathrm{H}\) would be _____\(1.00 \mathrm{amu} .\) (d) When phosphine gas, \(\mathrm{PH}_{3}\), is burned in oxygen, tetraphosphorus decaoxide and steam are formed. In the balanced equation (using smallest whole-number coefficients) for the reaction, the sum of the coefficients on the reactant side is _______ \(7 .\) (e) The mass (in grams) of one mole of bromine molecules is _______ \(79.90\)

Determine whether the statements given below are true or false. (a) The mass of an atom can have the unit mole. (b) In \(\mathrm{N}_{2} \mathrm{O}_{4}\), the mass of the oxygen is twice that of the nitrogen. (c) One mole of chlorine atoms has a mass of \(35.45 \mathrm{~g}\). (d) Boron has an average atomic mass of \(10.81\) amu. It has two isotopes, \(\mathrm{B}-10(10.01\) amu \()\) and \(\mathrm{B}-11(11.01 \mathrm{amu}) .\) There is more naturally occurring B-10 than B-11. (e) The compound \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{2} \mathrm{~N}\) has for its simplest formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{ON}_{1 / 2}\). (f) A 558.5-g sample of iron contains ten times as many atoms as \(0.5200 \mathrm{~g}\) of chromium. (g) If \(1.00\) mol of ammonia is mixed with \(1.00\) mol of oxygen the following reaction occurs, $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ All the oxygen is consumed. (h) When balancing an equation, the total number of moles of reactant molecules must equal the total number of moles of product molecules.

Chlorophyll, the substance responsible for the green color of leaves, has one magnesium atom per chlorophyll molecule and contains \(2.72 \%\) magnesium by mass. What is the molar mass of chlorophyll?

By \(x\) -ray diffraction it is possible to determine the geometric pattern in which atoms are arranged in a crystal and the distances between atoms. In a crystal of silver, four atoms effectively occupy the volume of a cube \(0.409 \mathrm{~nm}\) on an edge. Taking the density of silver to be \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), calculate the number of atoms in one mole of silver.

A 5.025-g sample of calcium is burned in air to produce a mixture of two ionic compounds, calcium oxide and calcium nitride. Water is added to this mixture. It reacts with calcium oxide to form \(4.832 \mathrm{~g}\) of calcium hydroxide. How many grams of calcium oxide are formed? How many grams of calcium nitride?

A mixture of potassium chloride and potassium bromide weighing \(3.595 \mathrm{~g}\) is heated with chlorine, which converts the mixture completely to potassium chloride. The total mass of potassium chloride after the reaction is \(3.129 \mathrm{~g}\). What percentage of the original mixture was potassium bromide?

A sample of an oxide of vanadium weighing \(4.589 \mathrm{~g}\) was heated with hydrogen gas to form water and another oxide of vanadium weighing \(3.782 \mathrm{~g} .\) The second oxide was treated further with hydrogen until only \(2.573 \mathrm{~g}\) of vanadium metal remained. (a) What are the simplest formulas of the two oxides? (b) What is the total mass of water formed in the successive reactions?