Chapter 8

A certain flexible weather balloon contains helium gas at a volume of \(855\) \(\mathrm{L}\). Initially, the balloon is at sea level where the temperature is \(25^{\circ} \mathrm{C}\) and the barometric pressure is \(730\) torr. The balloon then rises to an altitude of \(6000 \mathrm{ft}\), where the pressure is \(605\) torr and the temperature is \(15^{\circ} \mathrm{C}\). What is the change in volume of the balloon as it ascends from sea level to \(6000 \mathrm{ft} ?\)

A large flask with a volume of \(936 \mathrm{mL}\) is evacuated and found to have a mass of \(134.66 \mathrm{g}\). It is then filled to a pressure of 0.967 atm at \(31^{\circ} \mathrm{C}\) with a gas of unknown molar mass and then reweighed to give a new mass of 135.87 g. What is the molar mass of this gas?

A \(20.0\) -\(\mathrm{L}\) nickel container was charged with \(0.859\) atm of xenon gas and \(1.37\) atm of fluorine gas at \(400^{\circ} \mathrm{C}\). The xenon and fluorine react to form xenon tetrafluoride. What mass of xenon tetrafluoride can be produced assuming \(100 \%\) yield?

Consider the unbalanced chemical equation below: $$\mathrm{CaSiO}_{3}(s)+\mathrm{HF}(g) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l)$$ Suppose a \(32.9-\mathrm{g}\) sample of \(\mathrm{CaSiO}_{3}\) is reacted with \(31.8 \mathrm{L}\) of \(\mathrm{FH}\) at \(27.0^{\circ} \mathrm{C}\) and \(1.00\) atm. Assuming the reaction goes to completion, calculate the mass of the \(\mathrm{SiF}_{4}\) and \(\mathrm{H}_{2} \mathrm{O}\) produced in the reaction.

Consider separate \(1.0-\mathrm{L}\) gaseous samples of \(\mathrm{He}, \mathrm{N}_{2},\) and \(\mathrm{O}_{2}\) all at \(\mathrm{STP}\) and all acting ideally. Rank the gases in order of increasing average kinetic energy and in order of increasing average velocity.

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant. b. If the temperature of a gas increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

A chemist weighed out \(5.14 \mathrm{g}\) of a mixture containing unknown amounts of \(\mathrm{BaO}(s)\) and \(\mathrm{CaO}(s)\) and placed the sample in a \(1.50\) -\(\mathrm{L}\) flask containing \(\mathrm{CO}_{2}(g)\) at \(30.0^{\circ} \mathrm{C}\) and \(750 .\) torr. After the reaction to form \(\mathrm{BaCO}_{3}(s)\) and \(\mathrm{CaCO}_{3}(s)\) was completed, the pressure of \(\mathrm{CO}_{2}(g)\) remaining was \(230 .\) torr. Calculate the mass percentages of \(\mathrm{CaO}(s)\) and \(\mathrm{BaO}(s)\) in the mixture.

A mixture of chromium and zinc weighing \(0.362 \mathrm{g}\) was reacted with an excess of hydrochloric acid. After all the metals in the mixture reacted, \(225 \mathrm{mL}\) dry of hydrogen gas was collected at \(27^{\circ} \mathrm{C}\) and \(750 .\) torr. Determine the mass percent of \(\mathrm{Zn}\) in the metal sample. [Zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas; chromium reacts with hydrochloric acid to produce chromium(III) chloride and hydrogen gas.]

You have an equimolar mixture of the gases \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\), along with some He, in a container fitted with a piston. The density of this mixture at STP is \(1.924\) \(\mathrm{g/L}\). Assume ideal behavior and constant temperature and pressure. a. What is the mole fraction of He in the original mixture? b. The \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) react to completion to form \(\mathrm{SO}_{3}\). What is the density of the gas mixture after the reaction is complete?

Methane \(\left(\mathrm{CH}_{4}\right)\) gas flows into a combustion chamber at a rate of \(200 .\) L/min at \(1.50\) atm and ambient temperature. Air is added to the chamber at 1.00 atm and the same temperature, and the gases are ignited. a. To ensure complete combustion of \(\mathrm{CH}_{4}\) to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g),\) three times as much oxygen as is necessary is reacted. Assuming air is \(21\) mole percent \(\mathrm{O}_{2}\) and \(79\) mole percent \(\mathrm{N}_{2}\), calculate the flow rate of air necessary to deliver the required amount of oxygen. b. Under the conditions in part a, combustion of methane was not complete as a mixture of \(\mathrm{CO}_{2}(g)\) and \(\mathrm{CO}(g)\) was produced. It was determined that \(95.0 \%\) of the carbon in the exhaust gas was present in \(\mathrm{CO}_{2}\). The remainder was present as carbon in \(\mathrm{CO}\). Calculate the composition of the exhaust gas in terms of mole fraction of \(\mathrm{CO}, \mathrm{CO}_{2}, \mathrm{O}_{2}, \mathrm{N}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). Assume \(\mathrm{CH}_{4}\) is completely reacted and \(\mathrm{N}_{2}\) is unreacted.

A steel cylinder contains \(5.00\) moles of graphite (pure carbon) and \(5.00\) moles of \(\mathrm{O}_{2}\). The mixture is ignited and all the graphite reacts. Combustion produces a mixture of \(\mathrm{CO}\) gas and \(\mathrm{CO}_{2}\) gas. After the cylinder has cooled to its original temperature, it is found that the pressure of the cylinder has increased by \(17.0 \% .\) Calculate the mole fractions of \(\mathrm{CO}, \mathrm{CO}_{2},\) and \(\mathrm{O}_{2}\) in the final gaseous mixture.

The total mass that can be lifted by a balloon is given by the difference between the mass of air displaced by the balloon and the mass of the gas inside the balloon. Consider a hot-air balloon that approximates a sphere \(5.00 \mathrm{m}\) in diameter and contains air heated to \(65^{\circ} \mathrm{C}\). The surrounding air temperature is \(21^{\circ} \mathrm{C}\). The pressure in the balloon is equal to the atmospheric pressure, which is \(745\) torr. a. What total mass can the balloon lift? Assume that the average molar mass of air is \(29.0 \mathrm{g} / \mathrm{mol}\). (Hint: Heated air is less dense than cool air. b. If the balloon is filled with enough helium at \(21^{\circ} \mathrm{C}\) and \(745\) torr to achieve the same volume as in part a, what total mass can the balloon lift? c. What mass could the hot-air balloon in part a lift if it were on the ground in Denver, Colorado, where a typical atmospheric pressure is \(630 .\) torr?

You have a sealed, flexible balloon filled with argon gas. The atmospheric pressure is \(1.00\) atm and the temperature is \(25^{\circ} \mathrm{C}\). Assume that air has a mole fraction of nitrogen of \(0.790\), the rest being oxygen. a. Explain why the balloon would float when heated. Make sure to discuss which factors change and which remain constant, and why this matters. b. Above what temperature would you heat the balloon so that it would float?

You have a helium balloon at \(1.00\) atm and \(25^{\circ} \mathrm{C}\). You want to make a hot-air balloon with the same volume and same lift as the helium balloon. Assume air is \(79.0 \%\) nitrogen and \(21.0 \%\) oxygen by volume. The "lift" of a balloon is given by the difference between the mass of air displaced by the balloon and the mass of gas inside the balloon. a. Will the temperature in the hot-air balloon have to be higher or lower than \(25^{\circ} \mathrm{C} ?\) Explain. b. Calculate the temperature of the air required for the hotair balloon to provide the same lift as the helium balloon at \(1.00\) atm and \(25^{\circ} \mathrm{C}\). Assume atmospheric conditions are \(1.00\) atm and \(25^{\circ} \mathrm{C}\).

We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions.

Nitrogen gas \(\left(\mathrm{N}_{2}\right)\) reacts with hydrogen gas \(\left(\mathrm{H}_{2}\right)\) to form ammonia gas \(\left(\mathrm{NH}_{3}\right) .\) You have nitrogen and hydrogen gases in a \(15.0\)-\(\mathrm{L}\) container fitted with a movable piston (the piston allows the container volume to change so as to keep the pressure constant inside the container). Initially the partial pressure of each reactant gas is \(1.00\) atm. Assume the temperature is constant and that the reaction goes to completion. a. Calculate the partial pressure of ammonia in the container after the reaction has reached completion. b. Calculate the volume of the container after the reaction has reached completion.

Calculate \(w\) and \(\Delta E\) when \(1\) mole of a liquid is vaporized at its boiling point \(\left(80 .^{\circ} \mathrm{C}\right)\) and \(1.00\) atm pressure. \(\Delta H\) for the vaporization of the liquid is \(30.7 \mathrm{kJ} / \mathrm{mol}\) at \(80 .^{\circ} \mathrm{C}\). Assume the volume of \(1\) mole of liquid is negligible as compared to the volume of \(1\) mole of gas at \(80 .^{\circ} \mathrm{C}\) and \(1.00\) atm.

The preparation of \(\mathrm{NO}_{2}(g)\) from \(\mathrm{N}_{2}(g)\) and \(\mathrm{O}_{2}(g)\) is an endothermic reaction: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) \quad \text { (unbalanced) }$$ The enthalpy change of reaction for the balanced equation (with lowest whole-number coefficients) is \(\Delta H=67.7 \mathrm{kJ} .\) If \(2.50 \times\) \(10^{2} \mathrm{mL} \mathrm{N}_{2}(g)\) at \(100 .^{\circ} \mathrm{C}\) and \(3.50\) atm and \(4.50 \times 10^{2} \mathrm{mL} \mathrm{O}_{2}(g)\) at \(100 .^{\circ} \mathrm{C}\) and \(3.50\) atm are mixed, what amount of heat is necessary to synthesize the maximum yield of \(\mathrm{NO}_{2}(g) ?\)

In the presence of nitric acid, \(UO\) \(^{2+}\) undergoes a redox process. It is converted to \(\mathrm{UO}_{2}^{2+}\) and nitric oxide (NO) gas is produced according to the following unbalanced equation: $$\begin{aligned}\mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)+\mathrm{UO}^{2 *}(a q) & \longrightarrow \\\\\mathrm{NO}(g)+& \mathrm{UO}_{2}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{aligned}$$ If \(2.55 \times 10^{2} \mathrm{mL} \mathrm{NO}(g)\) is isolated at \(29^{\circ} \mathrm{C}\) and \(1.5 \mathrm{atm}\), what amount (moles) of \(UO\) \(^{2+}\) was used in the reaction? (Hint: Balance the reaction by the oxidation states method.)

Silane, \(\mathrm{SiH}_{4},\) is the silicon analogue of methane, \(\mathrm{CH}_{4} .\) It is prepared industrially according to the following equations: $$\begin{aligned} \mathrm{Si}(s)+3 \mathrm{HCl}(g) & \longrightarrow \mathrm{HSiCl}(i)+\mathrm{H}_{2}(g) \\\4 \mathrm{HSiCl}_{3}(l) & \longrightarrow \mathrm{SiH}_{4}(g)+3 \mathrm{SiCl}_{4}(l)\end{aligned}$$ a. If \(156 \mathrm{mL} \mathrm{HSiCl}_{3}(d=1.34 \mathrm{g} / \mathrm{mL})\) is isolated when \(15.0 \mathrm{L}\) HCl at \(10.0\) atm and \(35^{\circ} \mathrm{C}\) is used, what is the percent yield of HSiCl_? b. When \(156 \mathrm{mL}\) \(HSiCl_{3}\)is heated, what volume of \(\mathrm{SiH}_{4}\) at \(10.0\) atm and \(35^{\circ} \mathrm{C}\) will be obtained if the percent yield of the reaction is \(93.1 \% ?\)

Natural gas is a mixture of hydrocarbons, primarily methane \(\left(\mathrm{CH}_{4}\right)\) and ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right) .\) A typical mixture might have \(\chi_{\text {mathane }}=\) 0.915 and \(\chi_{\text {ethane }}=0.085 .\) What are the partial pressures of the two gases in a \(15.00\) -\(\mathrm{L}\) container of natural gas at \(20 .^{\circ} \mathrm{C}\) and \(1.44\) atm? Assuming complete combustion of both gases in the natural gas sample, what is the total mass of water formed?

Consider an equimolar mixture (equal number of moles) of two diatomic gases \(\left(A_{2} \text { and } B_{2}\right)\) in a container fitted with a piston. The gases react to form one product (which is also a gas) with the formula \(A_{x} B_{y}\). The density of the sample after the reaction is complete (and the temperature returns to its original state) is \(1.50\) times greater than the density of the reactant mixture. a. Specify the formula of the product, and explain if more than one answer is possible based on the given data. b. Can you determine the molecular formula of the product with the information given or only the empirical formula?