Chapter 5

An intermediate reaction used in the production of nitrogencontaining fertilizers is that between ammonia and oxygen: $$ 4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ A \(150.0\) - \(\mathrm{L}\) reaction chamber is charged with reactants to the following partial pressures at \(500^{\circ} \mathrm{C}: P_{\mathrm{NH}_{3}}=1.3 \mathrm{~atm}, P_{\mathrm{O}_{2}}=1.5 \mathrm{~atm} .\) What is the limiting reactant?

A Porsche \(928 \mathrm{~S} 4\) engine has a cylinder volume of \(618 \mathrm{~cm}^{3}\). The cylinder is full of air at \(75^{\circ} \mathrm{C}\) and \(1.00\) atm. (a) How many moles of oxygen are in the cylinder? (Mole percent of oxygen in air \(=21.0\).) (b) Assume that the hydrocarbons in gasoline have an average molar mass of \(1.0 \times 10^{2} \mathrm{~g} / \mathrm{mol}\) and react with oxygen in a \(1: 12 \mathrm{~mole}\) ratio. How many grams of gasoline should be injected into the cylinder to react with the oxygen?

At \(25^{\circ} \mathrm{C}\) and \(380 \mathrm{~mm} \mathrm{Hg}\), the density of sulfur dioxide is \(1.31 \mathrm{~g} / \mathrm{L}\). The rate of effusion of sulfur dioxide through an orifice is \(4.48 \mathrm{~mL} / \mathrm{s}\). What is the density of a sample of gas that effuses through an identical orifice at the rate of \(6.78 \mathrm{~mL} / \mathrm{s}\) under the same conditions? What is the molar mass of the gas?

Glycine is an amino acid made up of carbon, hydrogen, oxygen, and nitrogen atoms. Combustion of a \(0.2036\) -g sample gives \(132.9 \mathrm{~mL}\) of \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) and \(0.122 \mathrm{~g}\) of water. What are the percentages of carbon and hydrogen in glycine? Another sample of glycine weighing \(0.2500 \mathrm{~g}\) is treated in such a way that all the nitrogen atoms are converted to \(\mathrm{N}_{2}(g)\). This gas has a volume of \(40.8 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\). What is the percentage of nitrogen in glycine? What is the percentage of oxygen? What is the empirical formula of glycine?

Consider a vessel with a movable piston. A reaction takes place in the vessel at constant pressure and a temperature of \(200 \mathrm{~K}\). When reaction is complete, the pressure remains the same and the volume and temperature double. Which of the following balanced equations best describes the reaction? (a) \(\mathrm{A}+\mathrm{B}_{2} \longrightarrow \mathrm{AB}_{2}\) (b) \(\mathrm{A}_{2}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB}\) (c) \(2 \mathrm{AB}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB}_{2}\) (d) \(2 \mathrm{AB}_{2} \longrightarrow \mathrm{A}_{2}+2 \mathrm{~B}_{2}\)

Consider three sealed tanks all at the same temperature, pressure, and volume Tank A contains \(\mathrm{SO}_{2}\) gas. Tank B contains \(\mathrm{O}_{2}\) gas. Tank C contains \(\mathrm{CH}_{4}\) gas.

Sketch a cylinder with ten molecules of helium (He) gas. 'The cylinder has a movable piston. Label this aketch before. Make an after abetch to represent (a) decrease in temperature at constant pressure. (b) a decrease in pressure fram \(1000 \mathrm{~mm} \mathrm{Hg}\) to \(500 \mathrm{~mm} \mathrm{Hg}\) at constant temperature. (c) five molecules of \(\mathrm{H}_{2}\) gas added at constant temperature and pressure.

Tank A has ammonis at \(300 \mathrm{~K}\), Tank B hes nitrogen gas at \(150 \mathrm{~K}\). Thaks A and B have the same volume. Compare the presrures in tanks \(A\) and \(B\) if (a) tank B has twice as many moles of nitrogen as tank \(A\) has of ammonia. (b) tank A has the same number of moles of ammonia as tank \(\mathrm{B}\) has of nitrogen. (Try to do this without a calculatorl)

Two tanks have the same volume and are kept at the same temperature. Compare the pressure in both tanks if (a) tank A has \(2.00\) mol of carbon dioxide and tank B has \(2.00\) mol of heltum. (b) tank \(A\) has \(2.00 \mathrm{~g}\) of carbon dioride and tank \(\mathrm{B}\) has \(2.00 \mathrm{~g}\) of heIfum. (Try to do this without a calculatorl)

E Consider an ideal gas that exerts a pressure of \(23.76 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\). Assuming \(n\) and \(V\) are held constant, what would its pressure be at \(40^{\circ} \mathrm{C}\) ? \(70^{\circ} \mathrm{C}^{2} 100^{\circ} \mathrm{C}\) ? Compare the numbers you have just calculated with the vapor pressures of water at these temperatures. Can you suggest a reason why the two sets of numbers are so different?

A tube \(5.0 \mathrm{ft}\) long is evacuated. Samples of \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\), at the same temperature and pressure, are introduced simultaneously through tiny openings at opposite ends of the tube. When the two gases meet, a white ring of \(\mathrm{NH}_{4} \mathrm{Cl}(s)\) forms. How far from the end at which ammonia was introduced will the ring form?

A \(0.2500-\mathrm{g}\) sample of an \(\mathrm{Al}-\mathrm{Zn}\) alloy reacts with \(\mathrm{HCl}\) to form hydro- gen gas: $$ \begin{aligned} &\mathrm{Al}(s)+3 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+\frac{3}{2} \mathrm{H}_{2}(g) \\ &\mathrm{Zn}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{H}_{2}(g) \end{aligned} $$ The hydrogen produced has a volume of \(0.147 \mathrm{~L}\) at \(25^{\circ} \mathrm{C}\) and \(755 \mathrm{~mm} \mathrm{Hg}\) What is the percentage of zinc in the alloy?

The buoyant force on a balloon is equal to the mass of air it displaces. The gravitational force on the balloon is equal to the sum of the masses of the balloon, the gas it contains, and the balloonist. If the balloon and the balloonist together weigh \(168 \mathrm{~kg}\), what would the diameter of a spherical hydrogen-filled balloon have to be in meters if the rig is to get off the ground at \(22^{\circ} \mathrm{C}\) and \(758 \mathrm{~mm} \mathrm{Hg}\) ? (Take \(\mathrm{MM}_{\text {air }}=29.0 \mathrm{~g} /\) mol.)

A mixture in which the mole ratio of hydrogen to oxygen is \(2: 1\) is used to prepare water by the reaction $$ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$ The total pressure in the container is \(0.950 \mathrm{~atm}\) at \(25^{\circ} \mathrm{C}\) before the reaction. What is the final pressure in the container at \(125^{\circ} \mathrm{C}\) after the reaction, assuming an \(88.0 \%\) yield and no volume change?

The volume fraction of a gas \(\mathrm{A}\) in a mixture is defined by the equation $$ \text { volume fraction } \mathrm{A}=\frac{V_{\mathrm{A}}}{V} $$ where \(V\) is the total volume and \(V_{A}\) is the volume that gas A would occupy alone at the same temperature and pressure. Assuming ideal gas behavior, show that the volume fraction is the same as the mole fraction. Explain why the volume fraction differs from the mass fraction.