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) Explain the difference in densities at the two temperatures in terms of the relative kinetic energies of the molecules.

Short answer

(a) The average distance between molecules is greater in the liquid state because the density of liquid benzoic acid ($1.08\frac{g}{c{m}^3}$) is lower than the density of solid benzoic acid ($1.266\frac{g}{c{m}^3}$). (b) The difference in densities between the solid and liquid states can be explained by the higher kinetic energy of the molecules in the liquid state. As the temperature increases, the kinetic energy of the molecules also increases, allowing them to move more freely and resulting in a lower density compared to the more tightly packed solid state.

Step-by-step solution

Understand the relationship between density and molecular distance

In general, density can be defined as the mass of a substance divided by its volume. In this particular case, a higher density means that the molecules are more closely packed together, whereas a lower density means that they are farther apart. Therefore, we can determine the average distance between molecules based on the given densities of solid and liquid benzoic acid.

Compare the densities of solid and liquid benzoic acid

We are given the following density values: - Solid benzoic acid at ${15}^{\circ }C$: $1.266\frac{g}{c{m}^3}$ - Liquid benzoic acid at ${130}^{\circ }C$: $1.08\frac{g}{c{m}^3}$ Comparing these two densities, we can see that the density of solid benzoic acid is greater than the density of liquid benzoic acid at their respective temperatures.

Determine which state has the greater average distance between molecules

Since the density of solid benzoic acid is greater than that of liquid benzoic acid, this means that the molecules in the solid state are more closely packed together. Therefore, the average distance between molecules is greater in the liquid state. So, the answer to part (a) is that the average distance between molecules is greater in the liquid state.

Understand the relationship between temperature, kinetic energy, and density

As temperature increases, the kinetic energy of a substance's molecules also increases. In general, when a substance is in its solid state, its molecules have lower kinetic energy than in its liquid state. As a result, the molecules in the solid state can lock into a more organized and tightly packed structure, thus having a higher density.

Explain the difference in densities in terms of kinetic energy

In the case of benzoic acid, when the temperature is increased from ${15}^{\circ }C$ (solid state) to ${130}^{\circ }C$ (liquid state), the kinetic energy of the molecules also increases. This added energy allows the molecules to move more freely, allowing the substance to transition to its liquid state. In the liquid state, the molecular structure becomes less organized, and the molecules can be farther apart, hence the lower density compared to solid benzoic acid. So, the answer to part (b) is that the difference in densities between the solid and liquid states can be explained by the higher kinetic energy of the molecules in the liquid state, which causes them to be farther apart and exhibit a lower density.

Key concepts

Molecular Distance

Density plays a crucial role in understanding molecular distance. When we say a substance has a higher density, it means that its molecules are closely packed together. Conversely, a lower density implies that molecules are more spread out.

In the case of solid and liquid benzoic acid, the given densities are key indicators of molecular distance. Solid benzoic acid at 15°C has a density of 1.266 g/cm³, while the liquid form at 130°C has a density of 1.08 g/cm³. This tells us that in the solid state, molecules are tightly packed, resulting in shorter average distances between them. In contrast, in the liquid state, molecules are farther apart due to increased spacing, indicating greater molecular distance.

Kinetic Energy

Kinetic energy is the energy that molecules possess due to their motion. As temperature rises, so does the kinetic energy of molecules. This increased energy affects how molecules behave and arrange themselves.

At higher temperatures, such as 130°C for the liquid state of benzoic acid, the kinetic energy is elevated, allowing molecules to move more freely. This increased movement causes them to spread out, reflecting a lower density compared to their solid state. While in the solid state at 15°C, the lower kinetic energy results in molecules staying organized and packed tightly, leading to a higher density.

Solid and Liquid States

Matter can exist in different states, notably solid and liquid, each possessing unique characteristics. Solids are known for their tightly packed molecular structure. This organized arrangement gives solids higher density and lesser molecular distance.

For benzoic acid, the solid state at 15°C showcases closely packed molecules held by lower kinetic energy. When benzoic acid is heated to 130°C, it transitions to a liquid state where its molecules gain the energy to move more freely. This results in less organized spacing and lower density, showcasing the change in properties as conditions shift.

Benzoic Acid Properties

Benzoic acid, with the chemical formula ${\mathrm{C}}_6{\mathrm{H}}_5\mathrm{COOH}$, is a common organic compound. Known for its preservative properties, it transforms at specific temperatures, providing a clear view of molecular behavior in different states.

In its solid form at 15°C, benzoic acid’s molecules align tightly, reflecting higher density. A temperature increase leads to melting at 122°C, transitioning it into a liquid with decreased density at 130°C due to increased molecular distance and kinetic activity. Understanding these properties is essential, especially in practical applications involving temperature and state changes.