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Chapter 5: Problem 86
The boiling point of liquid nitrogen is \(-196^{\circ} \mathrm{C}\). On the basis of this information alone, do you think nitrogen is an ideal gas?
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What volume will 5.6 moles of sulfur hexafluoride (SF \(_{6}\) ) gas occupy if the temperature and pressure of the gas are \(128^{\circ} \mathrm{C}\) and \(9.4 \mathrm{~atm} ?\)
An ideal gas originally at 0.85 atm and \(66^{\circ} \mathrm{C}\) was allowed to expand until its final volume, pressure, and temperature were \(94 \mathrm{~mL}, 0.60 \mathrm{~atm},\) and \(45^{\circ} \mathrm{C},\) respectively. What was its initial volume?
Apply your knowledge of the kinetic theory of gases to these situations. (a) Does a single molecule have a temperature? (b) Two flasks of volumes \(V_{1}\) and \(V_{2}\left(V_{2}>V_{1}\right)\) contain the same number of helium atoms at the same temperature. (i) Compare the root- mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers (c) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right)\) (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (d) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume and the temperature of both gases is \(74^{\circ} \mathrm{C}\). Comment on the validity of these statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is \(1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}\).
A mixture of helium and neon gases is collected over water at \(28.0^{\circ} \mathrm{C}\) and \(745 \mathrm{mmHg}\). If the partial pressure of helium is \(368 \mathrm{mmHg}\), what is the partial pressure of neon? (Vapor pressure of water at \(28^{\circ} \mathrm{C}=\) \(28.3 \mathrm{mmHg} .)\)
In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g)$$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) On further heating the sample above \(43^{\circ} \mathrm{C}\), it is observed that the pressure of the gas increases much more rapidly than predicted based on the ideal gas equation. Explain.
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