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.

Answer 2

This question gives an equation relating vapor pressures at two temperatures and asks which named law it represents. Checking what physical relationship each named equation actually describes points to the right one.

1. Clausius-Mossotti equation: This equation relates a material's dielectric constant to the polarizability of its molecules. It has nothing to do with vapor pressure or temperature, so it does not match the given equation.
2. BET equation: The BET equation describes how gas molecules build up in multiple layers on a solid surface as a function of relative pressure, used to calculate surface area. It does not involve the enthalpy of vaporization or a temperature-pressure relationship for a phase change.
3. Boltzmann-Planck equation: This equation connects entropy to the number of possible microscopic arrangements of a system, a concept from statistical mechanics. It is not concerned with vapor pressure changing with temperature.
4. Clausius-Clapeyron equation: This equation describes exactly how the vapor pressure of a substance changes between two temperatures during a phase change, in terms of the enthalpy (heat) of vaporization, \(\Delta H_v\), and the gas constant \(R\). The given equation, with \(P_1\), \(P_2\), \(T_1\), \(T_2\), and \(\Delta H_v\) arranged this way, is its standard logarithmic form.

Since the equation directly involves vapor pressures at two temperatures and the heat of vaporization, it matches the relationship the Clausius-Clapeyron equation describes.

So the correct answer is Clausius-Clapeyron equation.