At standard temperature and pressure the molar volume of \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) gases are \(22.06 \mathrm{~L}\) and \(22.40 \mathrm{~L},\) respectively (a) Given the different molecular weights, dipole moments, and molecular shapes, why are their molar volumes nearly the same? (b) \(\mathrm{On}\) cooling to \(160 \mathrm{~K}\), both substances form crystalline solids. Do you expect the molar volumes to decrease or increase on cooling to \(160 \mathrm{~K} ?\) (c) The densities of crystalline \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) at \(160 \mathrm{~K}\) are \(2.02 \mathrm{~g} / \mathrm{cm}^{3}\) and \(0.84 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. Calculate their molar volumes. (d) Are the molar volumes in the solid state as similar as they are in the gaseous state? Explain. (e) Would you expect the molar volumes in the liquid state to be closer to those in the solid or gaseous state?

(a) At STP, the molar volumes of gases are determined by the ideal gas law, which depends only on temperature and pressure. Therefore, the nearly equal molar volumes of \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) gases at STP can be explained by the fact that both substances are at the same temperature and pressure, regardless of molecular weight, dipole moment, or molecular shape. (b) When the substances cool to 160 K and form crystalline solids, we expect the molar volumes to decrease due to increased intermolecular interactions in the solid state. (c) The molar volumes of solid \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) at 160 K are \(0.035\) L/mol and \(0.0203\) L/mol, respectively. (d) The molar volumes in the solid state are not as similar as in the gaseous state since they are more dependent on the molecular structure and crystalline lattice arrangement of particles. (e) We expect the molar volumes in the liquid state to be closer to those in the solid state because there are more significant intermolecular interactions compared to the gaseous state, but not as strong as in the solid state.