Problem 117
Consider a gas sample consisting of molecules with radius \(r\). (a) Determine the excluded volume defined by two molecules and (b) calculate the excluded volume per mole \((b)\) for the gas. Compare the excluded volume per mole with the volume actually occupied by a mole of the molecules.
Problem 118
Determine the excluded volume per mole and the total volume of the molecules in a mole for a gas consisting of molecules with radius 165 picometers (pm). [Note: To obtain the volume in liters, we must express the radius in decimeters (dm).]
Problem 119
Because the van der Waals constant \(b\) is the excluded volume per mole of a gas, we can use the value of \(b\) to estimate the radius of a molecule or atom. Consider a gas that consists of molecules, for which the van der Waals constant \(b\) is \(0.0315 \mathrm{~L} / \mathrm{mol}\). Estimate the molecular radius in pm. Assume that the molecules are spherical.
Problem 121
The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the Northern Hemisphere to be higher in the summer or winter? Explain.
Problem 122
(a) What volume of air at 1.0 atm and \(22^{\circ} \mathrm{C}\) is needed to fill a \(0.98-\mathrm{L}\) bicycle tire to a pressure of \(5.0 \mathrm{~atm}\) at the same temperature? (Note that the 5.0 atm is the gauge pressure, which is the difference between the pressure in the tire and atmospheric pressure. Before filling, the pressure in the tire was \(1.0 \mathrm{~atm} .\) ) (b) What is the total pressure in the tire when the gauge pressure reads 5.0 atm? (c) The tire is pumped by filling the cylinder of a hand pump with air at 1.0 atm and then, by compressing the gas in the cylinder, adding all the air in the pump to the air in the tire. If the volume of the pump is 33 percent of the tire's volume, what is the gauge pressure in the tire after three full strokes of the pump? Assume constant temperature.
Problem 123
At what temperature will He atoms have the same \(u_{\mathrm{rms}}\) value as \(\mathrm{N}_{2}\) molecules at \(25^{\circ} \mathrm{C} ?\)
Problem 124
Estimate the distance (in \(\mathrm{nm}\) ) between molecules of water vapor at \(100^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm} .\) Assume ideal behavior. Repeat the calculation for liquid water at \(100^{\circ} \mathrm{C},\) given that the density of water is \(0.96 \mathrm{~g} / \mathrm{cm}^{3}\) at that temperature. Comment on your results. (Assume each water molecule to be a sphere with a diameter of \(0.3 \mathrm{nm} .\) ) (Hint: First calculate the number density of water molecules. Next, convert the number density to linear density, that is, the number of molecules in one direction.)
Problem 125
Which of the noble gases would not behave ideally under any circumstance? Why?
Problem 126
A \(5.72-\mathrm{g}\) sample of graphite was heated with \(68.4 \mathrm{~g}\) of \(\mathrm{O}_{2}\) in a \(8.00-\mathrm{L}\) flask. The reaction that took place was $$ \mathrm{C} \text { (graphite) }+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) $$ After the reaction was complete, the temperature in the flask was \(182^{\circ} \mathrm{C}\). What was the total pressure inside the flask?
Problem 127
A 6.11-g sample of a Cu-Zn alloy reacts with \(\mathrm{HCl}\) acid to produce hydrogen gas. If the hydrogen gas has a volume of \(1.26 \mathrm{~L}\) at \(22^{\circ} \mathrm{C}\) and \(728 \mathrm{mmHg},\) what is the percent of Zn in the alloy? (Hint: Cu does not react with HCl.)
