Question

The equation \[ \log \left( \frac{P_1}{P_2} \right) = \frac{2.303 \cdot \Delta H_v \cdot (T_2 - T_1)}{R \cdot T_1 \cdot T_2} \] is related to:

• A. Clausius-Mossotti equation
• B. BET equation
• C. Boltzmann-Planck equation
• D. Clausius-Clapeyron equation

Hint:

The Clausius-Clapeyron equation is crucial for determining enthalpy of vaporization and is used in evaluating drug stability and storage conditions.

Answer 1

The Correct Option is D

The given equation is a form of the Clausius-Clapeyron equation, which describes the relationship between vapor pressure and temperature for a pure substance undergoing phase change (typically liquid to vapor). This equation is widely used in physical pharmacy to determine the heat of vaporization (\ΔH\_v) of a substance. The logarithmic form of the Clausius-Clapeyron equation is: \[ \log \left( \frac{P_1}{P_2} \right) = \frac{2.303 \cdot \Delta H_v \cdot (T_2 - T_1)}{R \cdot T_1 \cdot T_2} \] Where: - \( P_1, P_2 \) = vapor pressures at temperatures \( T_1 \) and \( T_2 \) respectively
- \( \Delta H_v \) = enthalpy (heat) of vaporization
- \( R \) = gas constant
- \( T_1, T_2 \) = temperatures in Kelvin
Explanation of options: - (a) Clausius-Mossotti equation relates to dielectric constants and polarizability.
- (b) BET equation deals with multilayer adsorption on solid surfaces.
- (c) Boltzmann-Planck equation relates to statistical mechanics and entropy.
- (d) Clausius-Clapeyron equation is correct as it explains the change in vapor pressure with temperature.