Chapter 8

More challonging questions are indicated by an asterisk '. Note: For some questions, data will be needed from tables within the chapter and from the Periodic Table on the inside front cover. \(3.036 \mathrm{g}\) of a gas occupy a volume of \(426 \mathrm{cm}^{3}\) at \(273 \mathrm{K}\) and 1.00 atm pressure. Calculate the molar mass of the gas. (Section 8.2)

A sample of gas has a volume of \(346 \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\) when the pressure is 1.00 atm. What volume will it occupy if the conditions are changed to \(35^{\circ} \mathrm{C}\) and 1.25 atm? (Section 8.2)

Incandescent light bulbs, which have been phased out in favour of less energy- consuming lighting, are filled with an inert gas to prevent the filament from burning. Find the mass of argon needed to fill a \(75.0 \mathrm{cm}^{3}\) light bulb to a pressure of 1.05 atm at \(25.0^{\circ} \mathrm{C} .(\text { Section } 8.2)\)

A vessel of volume \(50.0 \mathrm{dm}^{3}\) contains \(2.50 \mathrm{mol}\) of argon and \(1.20 \mathrm{mol}\) of nitrogen at \(273.15 \mathrm{K}\) (i) Calculate the partial pressure in bar of each gas. (ii) Calculate the total pressure in bar. (iii) How many additional moles of nitrogen must be pumped into the vessel in order to raise the pressure to 5 bar? (Sections \(8.2 \text { and } 8.3)\)

Two bulbs \(A\) and \(B\), with volumes \(V_{A}=1.00 \mathrm{dm}^{3}\) and \(V_{B}\) \(=5.00 \mathrm{dm}^{3},\) are connected via a tap. The volume of the connecting tubing is negligible. Bulb A contains gas at a pressure of 6.00 bar while bulb \(\mathrm{B}\) contains a vacuum. (a) The temperature of the whole apparatus is maintained at \(298 \mathrm{K}\). If the tap is opened, calculate the pressure of gas in the system after opening the tap. (b) The tap is closed and bulb \(\mathrm{B}\) is then immersed in an oil bath at a temperature of \(423 \mathrm{K}\) while the temperature of bulb \(\mathrm{A}\) is maintained at \(298 \mathrm{K}\). Calculate the resulting pressures in each bulb. (c) The tap is opened again. What is the final pressure and the number of moles of gas in each bulb? (Section 8.2)

Divers' "bends' are caused by the formation of bubbles of nitrogen in blood as the solubility reduces when the diver returns to the surface. The solubility of nitrogen in water at 1.00 atm pressure is \(13.0 \mathrm{mg} \mathrm{kg}^{-1}\) at body temperature of \(37^{\circ} \mathrm{C}\) and increases linearly with pressure. In water, the pressure increases at the rate of 1.00 atm per \(10 \mathrm{m}\) depth. Estimate the volume of gas that comes out of solution when a diver who has \(4.5 \mathrm{kg}\) of blood rapidly ascends from a depth of \(50 \mathrm{m}\) of water to the surface. Assume the solubility of nitrogen in blood is the same as in water. (Section 8.2)

A mixture of nitrogen and carbon dioxide contains \(38.4 \% \mathrm{N}_{2}\) by mass. What is the mole fraction of nitrogen in the mixture? If the total pressure is 1.2 atm, what is the partial pressure of each gas in Pa? (Section 8.3)

How much faster is the rate of effusion of helium than that of carbon dioxide, when both gases are at the same temperature? (Section 8.5)

Two identical flasks contain nitrogen gas at the same pressure. Each has an identical pin-hole. One flask is kept at \(25^{\circ} \mathrm{C}\) while the other is heated to \(125^{\circ} \mathrm{C}\). Calculate the relative rates of effusion of nitrogen from the two flasks. (Section 8.5 )

An evacuated flask is filled with dry air and weighed. The same flask is filled at the same temperature to the same pressure with moist air on a humid day. Will it weigh more, less, or the same? Explain your answer. (Section 8.2)

The equation for the complete combustion of methane is $$\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ What volume of oxygen at SATP is needed to react exactly with \(10 g\) of methane? (Section 8.2 )

The average (root mean square) speed of an oxygen molecule is \(425 \mathrm{ms}^{-1}\) at \(0^{\circ} \mathrm{C}\). Calculate the average speed at \(100^{\circ} \mathrm{C}\). (Section \(8.5)\)

The atmosphere of a spacecraft with volume \(27 \mathrm{m}^{3}\) consists of \(80 \%\) helium and \(20 \%\) oxygen by volume. The gases continually escape by effusion through small leaks in the walls. The leak amounts to 1000 Pa per day. The temperature inside the spacecraft is \(20^{\circ} \mathrm{C}\). What masses of helium and oxygen must be carried to replace the gas that leaks during a 10 -day mission? (Section 8.5)

(a) State (i) the ideal gas equation (ii) the van der Waals equation of state. Explain how the additional terms in the van der Waals equation account for the actual behaviour of real gases. (b) Without performing any numerical calculations, show that, in the limit of high temperatures and low pressures, the van der Waals and ideal gas equations are identical. (Section 8.6)

Dry air with the following composition is used to fill a SCUBA cylinder for a dive. (Section 8.6) $$\begin{array}{lc} \hline \text { Gas } & \text { Composition of dry air by volume } \\ \hline \mathrm{N}_{2} & 78 \% \\ \mathrm{O}_{2} & 21 \% \\ \mathrm{Ar} & 1 \% \\ \hline \end{array}$$ (a) At \(10 \mathrm{m}\) depth, a diver experiences an external pressure of 2 atm. Write an expression for the total pressure of the air in terms of the partial pressures of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{Ar}\). (b) What is the molar percentage of oxygen in the air inhaled at 2 atm? (c) What is the partial pressure of \(\mathrm{O}_{2}\) in air inhaled at: (1) \(1 \mathrm{atm}\); (ii) 2 atm? How does the number of molecules of \(\mathrm{O}_{2}\) inhaled per breath at \(10 \mathrm{m}\) depth compare with the number inhaled per breath at sea level? Suggest why some deep-sea divers dive with a gas mixture containing \(10 \%\) oxygen.

A \(10 \mathrm{dm}^{3}\) SCUBA cylinder is filled with air to a pressure of \(\left.300 \text { atm at a temperature of } 20^{\circ} \mathrm{C}(293 \mathrm{K}) . \text { (Section } 8.6\right)\) (a) Calculate the amount in moles of gas in the cylinder, assuming the air behaves as an ideal gas. (b) When the diver jumps into cold water at \(278 \mathrm{K}\), the pressure gauge shows an alarming drop in pressure. Explain the reason why and calculate the new pressure inside the cylinder. (c) In fact, the compressed gases do not behave as ideal gases. Explain why. Use the van der Waals equation (for air, \(a=0.137 \mathrm{Pam}^{6} \mathrm{mol}^{-2}\) and \(b=3.7 \times 10^{-5} \mathrm{m}^{3} \mathrm{mol}^{-1}\) ) to show that the amount of air in the cylinder is 115 mol. In view of your answer to part (a) above, what are the implications of this for divers?

Sketch graphs to show how the distribution of molecular speeds differs between (Section 8.5): (a) helium at \(100 \mathrm{K}\) and helium at \(300 \mathrm{K}\) (b) helium at \(100 \mathrm{K}\) and xenon at \(100 \mathrm{K}\)

Consider the following gases at SATP (Section 8.6): argon, krypton, nitrogen, methane, hydrogen chloride, chlorine, carbon dioxide, helium. (a) Which gas would be expected to most closely follow ideal behaviour? (b) Which gas would deviate most from ideal behaviour? (c) Which gas would have the highest and lowest root mean square speeds? (d) Which gas would effuse most slowty?

The molecular speeds in a sample of 100 molecules are distributed as follows (Section 8.5): Number of molecules \(10 \quad 20 \quad 40 \quad 15 \quad 10 \quad 5\) Speed/ms \(^{-1}\) \(\begin{array}{llllll}60 & 80 & 100 & 120 & 140 & 160\end{array}\) (a) What is the most probable speed? (b) Calculate the mean speed of the molecules in the sample. (c) Calculate the ms speed of the molecules in the sample.

"The density of nitrogen gas in a container at \(300 \mathrm{K}\) and 1.0 bar pressure is \(1.25 \mathrm{g} \mathrm{dm}^{-3}\) (Section 8.5 ). (a) Calculate the rms speed of the molecules. (b) At what the temperature will the ms speed be twice as fast?

(a) Explain how the fact that gases such as nitrogen or carbon dioxide can be liquefied by applying high pressures shows that the ideal gas equation can only be an approximation. (b) Why is a lower pressure needed to liquefy \(\mathrm{CO}_{2}\) than for \(\mathrm{N}_{2}\) ? (Section 8.6)

Calculate the temperature at which 20.0 mol of helium would exert a pressure of 120 atm in a \(10.0 \mathrm{dm}^{3}\) cylinder, using (a) the ideal gas equation and (b) the van der Waals equation. For He, \(a=0.034 \mathrm{dm}^{6}\) atm \(\mathrm{mol}^{-2}\) and \(b=0.024 \mathrm{dm}^{3} \mathrm{mol}^{-1}\). (Section 8.6)