Chapter 6

Explain why the constant \(a\) in the van der Waals equation generally increases with the molar mass of the gas.

Which noble gas is expected to deviate the most from ideal bchavior in a graph of \(P V / R T\) versus \(P ?\)

At high pressures, real gases do not behave ideally. (a) Use the van der Waals equation and data in the text to calculate the pressure exerted by \(40.0 \mathrm{g}\) of \(\mathrm{H}_{2}\) at \(20^{\circ} \mathrm{C}\) in a \(1.00 \mathrm{L}\) container. (b) Repeat the calculation, assuming that the gas behaves like an ideal gas.

(a) Calculate the pressure exerted by 1.00 mol of \(\mathrm{CO}_{2}\) in a \(1.00 \mathrm{L}\) vessel at \(300 \mathrm{K},\) assuming that the gas behaves ideally. (b) Repeat the calculation using the van der Waals equation.

The volume of a sample of propane gas at 12.5 atm is \(10.6 \mathrm{L}\) What volume does the gas occupy if the pressure is reduced to 1.05 atm and the temperature remains constant?

A 22.4 L sample of hydrogen chloride gas is heated from \(15^{\circ} \mathrm{C}\) to \(78^{\circ} \mathrm{C} .\) What volume does it occupy at the higher temperature if the pressure remains constant?

The temperature of a quantity of methane gas at a pressure of \(761 \mathrm{mmHg}\) is \(18.6^{\circ} \mathrm{C} .\) Predict the temperature of the gas if the pressure is reduced to 355 mmHg while the volume remains constant.

A souvenir soccer ball is partially deflated and then put into a suitcase. At a pressure of 0.947 atm and a temperature of \(27^{\circ} \mathrm{C},\) the ball has a volume of \(1.034 \mathrm{L} .\) What volume does it occupy during an airplane flight if the pressure in the baggage compartment is 0.235 atm and the temperature is \(-35^{\circ} \mathrm{C} ?\)

A gas mixture used experimentally for asthma treatments contains 17.5 mol of helium for every 0.938 mol of oxygen. What is the mole fraction of oxygen in the mixture?

A typical blood pressure in a resting adult is "120 over 80," meaning 120 mmHg with each beat of the heart and \(80 \mathrm{mmHg}\) of pressure between heartbeats. Express these pressures in the following units: (a) torr; (b) \(\operatorname{atm} ;(\text { c })\) bar; \((\text { d) } \mathrm{kPa}\).

Which noble gas effuses at about half the effusion rate of \(\mathrm{O}_{2} ?\)

One cotton ball soaked in ammonia and another soaked in hydrochloric acid were placed at opposite ends of a \(1.00 \mathrm{m}\) glass tube (Figure \(\mathrm{P} 6.160\) ). The vapors diffused toward the middle of the tube and formed a white ring of ammonium chloride where they met. a. Write the chemical equation for this reaction. b. Will the ammonium chloride ring form closer to the end of the tube with ammonia or the end with hydrochloric acid? Explain your answer. c. Calculate the distance from the ammonia end to the position of the ammonium chloride ring.

Students at the University of North Texas and the University of Washington built a car propelled by compressed nitrogen gas. The gas was obtained by boiling liquid nitrogen stored in a 182 - L tank. What volume of \(\mathrm{N}_{2}\) is released at 0.927 atm of pressure and \(25^{\circ} \mathrm{C}\) from a tank full of liquid \(\mathrm{N}_{2}(d=0.808 \mathrm{g} / \mathrm{mL}) ?\)

The pressure in an aerosol can is 1.5 atm at \(27^{\circ} \mathrm{C}\). The can will withstand a pressure of about 2 atm. Will it burst if heated in a campfire to \(450^{\circ} \mathrm{C} ?\)

Combustion of hydrogen supplies a great deal of energy per gram. One challenge in designing hydrogen-powered vehicles is storing hydrogen. The pressure limit for carbon fiber-reinforced gas cylinders is 10,000 psi \((1 \text { atm }=14.7 \text { psi }) .\) A fuel tank capable of holding up to \(10 \mathrm{kg}\) of \(\mathrm{H}_{2}\) is required to meet a reasonable driving range for a vehicle. If we limit the volume of the fuel tank to \(400 \mathrm{L}\), what pressure must the hydrogen be under at \(300 \mathrm{K} ?\) Does your answer conform to the safety requirements?

A sample of \(11.4 \mathrm{L}\) of an ideal gas at \(25.0^{\circ} \mathrm{C}\) and 735 torr is compressed and heated so that the volume is \(7.9 \mathrm{L}\) and the temperature is \(72.0^{\circ} \mathrm{C} .\) What is the pressure in the container?

A sample of argon gas at STP occupies \(15.0 \mathrm{L} .\) What mass of argon is present in the container?

A sample of a gas has a mass of \(2.889 \mathrm{g}\) and a volume of \(940 \mathrm{mL}\) at 735 torr and \(31^{\circ} \mathrm{C} .\) What is its molar mass?

A sample of \(\mathrm{N}_{2}(g)\) requires 240 s to diffuse through a porous plug. It takes 530 s for an equal number of moles of an unknown gas \(X\) to diffuse through the plug under the same conditions of temperature and pressure. What is the molar mass of gas X?

The rate of effusion of an unknown gas is \(0.10 \mathrm{m} / \mathrm{s}\) and the rate of effusion of \(\mathrm{SO}_{3}(g)\) is \(0.052 \mathrm{m} / \mathrm{s}\) under identical experimental conditions. What is the molar mass of the unknown gas?

Derive an equation that expresses the ratio of the densities \(\left(d_{1} \text { and } d_{2}\right)\) of a gas under two different combinations of temperature and pressure, \(\left(T_{1}, P_{1}\right)\) and \(\left(T_{2}, P_{2}\right)\).

In some aquatic ecosystems, nitrate (NO \(_{3}^{-}\) ) is converted to nitrite \(\left(\mathrm{NO}_{2}^{-}\right),\) which then decomposes to nitrogen and water. As an example of this second reaction, consider the decomposition of ammonium nitrite: $$ \mathrm{NH}_{4} \mathrm{NO}_{2}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ What would be the change in pressure in a sealed \(10.0 \mathrm{L}\) vessel due to the formation of \(\mathrm{N}_{2}\) gas when the ammonium nitrite in \(1.00 \mathrm{L}\) of \(1.0 \mathrm{MNH}_{4} \mathrm{NO}_{2}\) decomposes at \(25^{\circ} \mathrm{C} ?\)

When sulfur dioxide bubbles through a solution containing nitrite, chemical reactions that produce gaseous \(\mathrm{N}_{2} \mathrm{O}\) and NO may occur. a. How much faster, on average, would NO molecules be moving than \(\mathrm{N}_{2} \mathrm{O}\) molecules in such a reaction mixture? b. If these two nitrogen oxides were to be separated based on differences in their rates of effusion, would unreacted SO \(_{2}\) interfere with the separation? Explain your answer.

Using Wetlands to Treat Agricultural Waste Wetlands can play a significant role in removing fertilizer residues from rain runoff and groundwater; one way they do this is through denitrification, which converts nitrate ions to nitrogen gas: \(2 \mathrm{NO}_{3}^{-}(a q)+5 \mathrm{CO}(g)+2 \mathrm{H}^{+}(a q) \rightarrow \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell)+5 \mathrm{CO}_{2}(g)\) Suppose \(200.0 \mathrm{g}\) of \(\mathrm{NO}_{3}^{-}\) flows into a swamp each day. What volume of \(\mathrm{N}_{2}\) would be produced at \(17^{\circ} \mathrm{C}\) and 1.00 atm if the denitrification process were complete? What volume of \(\mathrm{CO}_{2}\) would be produced? Suppose the gas mixture produced by the decomposition reaction is trapped in a container at \(17^{\circ} \mathrm{C} ;\) what is the density of the mixture if we assume that \(P_{\text {total }}=1.00\) atm?

Generating hydrogen from water or methane is energy intensive. A non-natural enzymatic process has been developed that produces 12 moles of hydrogen per mole of glucose by the reaction: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 12 \mathrm{H}_{2}(g)+6 \mathrm{CO}_{2}(g)\) What volume of hydrogen could be produced from \(256 \mathrm{g}\) of glucose at STP?

The severity of a tropical storm is related to the depressed atmospheric pressure at its center. In August \(1985,\) Typhoon Odessa reached maximum winds of about \(90 \mathrm{mi} / \mathrm{h}\) and the pressure was 40 mbar lower at the center than normal atmospheric pressure. In contrast, the central pressure of Hurricane Andrew (Figure \(\mathrm{P} 6.179\) ) was 90 mbar lower than its surroundings when it hit southern Florida with winds as high as \(165 \mathrm{mi} / \mathrm{h}\). If a small weather balloon with a volume of \(50.0 \mathrm{L}\) at a pressure of 1.0 atmosphere was deployed above the center of Andrew, what was the volume of the balloon when it reached the surface of the ocean?

Here is the overall reaction in an automobile air bag: $$ \begin{aligned} 20 \mathrm{NaN}_{3}(s)+6 \mathrm{SiO}_{2}(s)+4 \mathrm{KNO}_{3}(s) & \rightarrow \\ 32 \mathrm{N}_{2}(g)+5 \mathrm{Na}_{4} \mathrm{SiO}_{4}(s)+\mathrm{K}_{4} \mathrm{SiO}_{4}(s) \end{aligned} $$ Calculate how many grams of sodium azide (NaN \(_{3}\) ) are needed to inflate a \(40 \times 40 \times 20 \mathrm{cm}\) bag to a pressure of 1.25 atm at a temperature of \(20^{\circ} \mathrm{C} .\) How much more sodium azide is needed if the air bag must produce the same pressure at \(10^{\circ} \mathrm{C} ?\)

\(0.200 \mathrm{L}\) of \(\mathrm{O}_{2}\) is collected over water at \(25.0^{\circ} \mathrm{C} .\) The atmospheric pressure is 750.0 torr. The vapor pressure of water at \(25.0^{\circ} \mathrm{C}\) is 24.0 torr. How many moles of \(\mathrm{O}_{2}\) have been collected?