Benzoic acid, C6H5COOH, melts at 122 °C. The density in the liquid state at 130 °C is 1.08 g/cm3. The density of solid benzoic acid at 15 °C is 1.266 g/cm3. (a) In which of these two states is the average distance between molecules greater?

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Understand that density is inversely related to the average distance between molecules. A lower density indicates a greater average distance between molecules.

Identify the densities given in the problem: liquid benzoic acid at 130 °C has a density of 1.08 g/cm³, and solid benzoic acid at 15 °C has a density of 1.266 g/cm³.

Compare the densities: since 1.08 g/cm³ (liquid) is less than 1.266 g/cm³ (solid), the average distance between molecules is greater in the liquid state.

Consider the physical states: in general, molecules in a liquid state are less tightly packed than in a solid state, contributing to a greater average distance between molecules.

Conclude that the average distance between molecules is greater in the liquid state at 130 °C compared to the solid state at 15 °C.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molecular Distance and State of Matter

The average distance between molecules varies with the state of matter. In solids, molecules are closely packed in a fixed arrangement, resulting in shorter average distances. In liquids, molecules are more loosely arranged and can move past one another, leading to greater average distances between them.

Density and Molecular Arrangement

Density is defined as mass per unit volume and is influenced by the arrangement of molecules. A higher density indicates that molecules are packed more closely together, while a lower density suggests more space between them. In this case, the solid benzoic acid has a higher density than the liquid, indicating that its molecules are more closely packed.

Phase Transition and Temperature Effects

Phase transitions, such as melting, involve changes in temperature and molecular arrangement. As a substance transitions from solid to liquid, the increase in temperature allows molecules to gain energy, move apart, and occupy a larger volume, which typically results in a decrease in density and an increase in the average distance between molecules.

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At standard temperature and pressure, the molar volumes of Cl₂ and NH₃ gases are 22.06 and 22.40 L, respectively (b) On cooling to 160 K, both substances form crystalline solids. Do you expect the molar volumes to decrease or increase on cooling the gases to 160 K?

Textbook Question

At standard temperature and pressure, the molar volumes of Cl₂ and NH₃ gases are 22.06 and 22.40 L, respectively. (c) The densities of crystalline Cl₂ and NH₃ at 160 K are 2.02 and 0.84 g/cm³, respectively. Calculate their molar volumes.

Textbook Question

At standard temperature and pressure, the molar volumes of Cl₂ and NH₃ gases are 22.06 and 22.40 L, respectively (d) Are the molar volumes in the solid state as similar as they are in the gaseous state? Explain.

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Textbook Question

Benzoic acid, C₆H₅COOH, melts at 122 °C. The density in the liquid state at 130 °C is 1.08 g/cm³. The density of solid benzoic acid at 15 °C is 1.266 g/cm³. (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?

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Textbook Question

(a) Which type of intermolecular attractive force operates between all molecules?

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Textbook Question

(b) Which type of intermolecular attractive force operates only between polar molecules?

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