The Clapeyron-Clausius equation can be used to calculate the...

The Clapeyron-Clausius equation can be used to calculate the equilibrium vapor pressure of a solid by writing $\Delta H_{\text {sub }}$ in place of $\Delta H_{\text {vap }}$. Given that $\Delta H_{\text {sub }}=$ $25.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ for $\mathrm{CO}_{2}(s)$ and that $P_{\mathrm{CO}_{2}}=1.0 \times 10^{2} \mathrm{kPa}$ at $-78.6^{\circ} \mathrm{C}$, calculate the equilibrium vapor pressure of $\mathrm{CO}_{2}(s)$ at $-100.0^{\circ} \mathrm{C}$. Compare your results to the experimental value of $14 \mathrm{kPa}$.

The Clapeyron-Clausius equation can be used to calculate the equilibrium vapor pressure of a solid by writing $\Delta H_{\text {sub }}$ in place of $\Delta H_{\text {vap }}$. Given that $\Delta H_{\text {sub }}=$ $25.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ for $\mathrm{CO}_{2}(s)$ and that $P_{\mathrm{CO}_{2}}=1.0 \times 10^{2} \mathrm{kPa}$
at $-78.6^{\circ} \mathrm{C}$, calculate the equilibrium vapor pressure of $\mathrm{CO}_{2}(s)$ at $-100.0^{\circ} \mathrm{C}$. Compare your results to the experimental value of $14 \mathrm{kPa}$.

Key Concepts

Clapeyron-Clausius Equation

This equation describes the relation between the change in pressure and temperature during a phase change, taking into account the latent heat of the transition and the volume change between phases. It is a fundamental tool for predicting how the equilibrium vapor pressure varies with temperature, and it can be adapted for different phase transitions, for example, using the enthalpy of sublimation when studying solid-to-gas transitions.

Phase Equilibrium and Vapor Pressure

Phase equilibrium refers to the state in which different phases of a substance coexist in balance, with no net change occurring between them. Vapor pressure is the pressure exerted by a vapor in equilibrium with its condensed phase (solid or liquid) at a given temperature. Understanding this concept is crucial for analyzing how and why the pressure of a gas above a solid or liquid changes with temperature.

Enthalpy of Sublimation

The enthalpy of sublimation is the energy required for a substance to transition directly from the solid phase to the gaseous phase without passing through the liquid phase. This thermodynamic quantity is a key parameter in the Clapeyron-Clausius equation when applied to sublimation, as it directly influences the equilibrium vapor pressure of a solid at various temperatures.

Temperature Dependence in Phase Transitions

The equilibrium vapor pressure of a substance is highly sensitive to changes in temperature. In phase transitions, particularly during sublimation, the exponential relationship predicted by the Clapeyron-Clausius equation illustrates how even small variations in temperature can lead to significant changes in the vapor pressure. This concept is fundamental for both theoretical calculations and experimental comparisons.

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