Problem 12 - Chemistry Central Science

Question

(a) Both a liquid and a gas are moved to larger containers. How does their behavior differ? Explain the difference in molecular terms. (b) Although water and carbon tetrachloride, \(\mathrm{CCl}_{4}(l)\), do not mix, their vapors form homogeneous mixtures. Explain. (c) The densities of gases are generally reported in units of \(\mathrm{g} / \mathrm{L}\), whereas those for liquids are reported as \(\mathrm{g} / \mathrm{mL}\). Explain the molecular basis for this difference.

Step-by-Step Solution

Answer

(a) When a liquid is moved to a larger container, its behavior and volume remain essentially the same due to strong intermolecular forces. However, a gas expands to fill the larger container, because of weaker intermolecular forces allowing gas molecules to move freely. (b) Water and carbon tetrachloride don't mix in the liquid phase due to their difference in polarity. In the gas phase, their molecules disperse throughout the entire volume, overcoming the polarity difference, leading to a homogeneous vapor mixture. (c) The different density units for gases (\(\mathrm{g}/\mathrm{L}\)) and liquids (\(\mathrm{g}/\mathrm{mL}\)) are due to the difference in intermolecular distances, with gases having more dispersed molecules compared to liquids. These units provide a more comprehensible representation for each state of matter.

Step 1: (a) Behavior in larger containers

When a liquid is moved to a larger container, its behavior and volume remain essentially the same, because the intermolecular forces between molecules of the liquid are relatively strong, which allows the liquid to maintain its specific volume. However, the gas expands to fill the larger container, because the intermolecular forces between gas molecules are weak, so they have the ability to move freely and occupy the entire volume of their container. The behavior difference is primarily due to the difference in intermolecular forces between liquid and gas molecules.

Step 2: (b) Homogeneous vapors of water and carbon tetrachloride

The reason behind water and carbon tetrachloride not mixing in the liquid phase is due to their difference in polarity. Water is polar, whereas carbon tetrachloride is nonpolar - 'like dissolves like', meaning polar substances dissolve in polar substances and nonpolar dissolve in nonpolar. However, in the gas phase, the individual molecules of water and carbon tetrachloride are not close together, and there is no "mixing" or "dissolving" occurring. The molecules are simply dispersed throughout the entire volume, and the dispersion overcomes the issue of polarity difference, leading to a homogeneous vapor mixture.

Step 3: (c) Density units for gases and liquids

The molecular basis for the difference in density units for gases and liquids lies in the fact that gas molecules are much more dispersed and have a larger intermolecular distance compared to liquid molecules. Due to this, a much larger volume of gas is needed to compare the mass of the gas molecules to that of liquid molecules. Thus, using \(\mathrm{g}/\mathrm{L}\) for gases helps distinguish between the vast difference in densities between the two states of matter and provides a more comprehensible representation. For liquids, which have closely packed molecules, the mass of liquid per milliliter of the volume (g/mL) is higher, and using g/mL is a more convenient way of measuring and comparing densities for liquids.