Question

Benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH},\) melts at \(122{ }^{\circ} \mathrm{C} .\) The density in the liquid state at \(130^{\circ} \mathrm{C}\) is \(1.08 \mathrm{~g} / \mathrm{cm}^{3}\). The density of solid benzoic acid at \(15^{\circ} \mathrm{C}\) is \(1.266 \mathrm{~g} / \mathrm{cm}^{3} .\) (a) In which of these two states is the average distance between molecules greater? (b) If you converted a cubic centimeter of liquid benzoic acid into a solid, would the solid take up more, or less, volume than the original cubic centimeter of liquid?

Short answer

Molecules are farther apart in the liquid state. A solid occupies less volume than the liquid form.

Step-by-step solution

Identify the Densities and Calculate Volume

The density of liquid benzoic acid at \(130^{\circ} \text{C}\) is \(1.08 \text{ g/cm}^3\), and the density of solid benzoic acid at \(15^{\circ} \text{C}\) is \(1.266 \text{ g/cm}^3\). To compare the average distances between molecules, remember that denser materials have molecules packed more closely together. Thus, the liquid is less dense than the solid, indicating that the average distance between molecules is greater in the liquid state.

Analyze Volume Change During Phase Transition

To determine how the volume changes when liquid benzoic acid solidifies, note that density is inversely proportional to volume. Since the solid is denser (\(1.266 \text{ g/cm}^3\)) compared to the liquid (\(1.08 \text{ g/cm}^3\)), a given mass of benzoic acid would occupy a smaller volume as a solid than as a liquid. Therefore, when a cubic centimeter of liquid benzoic acid freezes, it forms a solid taking up less than one cubic centimeter.

Key concepts

Molecular Distance and Density

In the realm of chemistry, the density of a substance provides a window into the spacing between its molecules. Density is defined as the mass per unit volume, typically given in grams per cubic centimeter for solids and liquids. When a substance is less dense, its molecules are spaced farther apart, and when it is more dense, its molecules are packed closer together.

The relationship between molecular distance and density is crucial in understanding how substances behave under different conditions. For example, in the context of benzoic acid, the density of the liquid state at a temperature of 130°C is 1.08 g/cm³, while in the solid state at 15°C, it is denser at 1.266 g/cm³. Thus, the molecules in the liquid state are farther apart compared to those in the solid state.

In simpler terms, when benzoic acid is in a liquid form, the molecules have more space to move freely, leading to a greater average molecular distance. Whereas in the solid form, the molecules are more tightly packed, resulting in a smaller average molecular distance. This comparison helps us visualize how closely packed the molecules are in each phase of benzoic acid.

Phase Transition in Benzoic Acid

A phase transition is a fascinating process where a substance changes from one state of matter to another, such as from solid to liquid or liquid to gas. The transition between the solid and liquid states of benzoic acid is driven by temperature changes.

As the temperature of benzoic acid rises to its melting point of 122°C, the molecules gain energy, which weakens the intermolecular forces holding them in a rigid structure. This loss of structure leads to the phase transition from a solid to a liquid. Conversely, when cooled, the liquid molecules lose energy, and the stronger attractive forces pull them into a tightly packed solid form.

Phase transitions are essential for understanding the physical behavior of substances under varying conditions. And these transitions are governed by the delicate balance of intermolecular forces: the stronger these forces relative to the thermal energy, the more energy is required to initiate a phase transition.

Volume Change During Phase Transition

The conversion of substances from one phase to another often involves a change in volume. In the case of benzoic acid transitioning from a liquid to a solid, the substance undergoes a notable volume change.

Using density, we identify how the volume of benzoic acid changes as it transitions phases. The liquid form has a lower density (1.08 g/cm³) compared to its solid form (1.266 g/cm³). When the liquid is cooled to form a solid, its increased density means that it takes up less space. Specifically, if we imagine converting exactly 1 cm³ of liquid benzoic acid to solid, the resulting solid will occupy less than 1 cm³.

This decrease in volume upon solidification is due to the rearrangement of molecules into a more efficient, tightly packed form, characteristic of denser solids. Such volume changes are part and parcel of many phase transitions, illustrating the transformation from a more disordered to a more ordered state.