Clausius-Clapeyron Equation gives accurate result, when the Vapour pressure is relatively low and the temperature does not vary over wide limits. Vapour obeys the ideal gas law and the latent heat of vaporisation is constant. Volume in the liquid state is negligible compared with that in the vapour state. All (A), (B), and (C)
The correct answer and explanation is :
The Clausius-Clapeyron equation is a key relationship in thermodynamics that describes how the vapor pressure of a substance changes with temperature. It’s especially useful when studying phase transitions, such as the transition from liquid to vapor during boiling or evaporation. The equation is given by:
[
\ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_1} – \frac{1}{T_2} \right)
]
Where:
- (P_1) and (P_2) are the vapor pressures at temperatures (T_1) and (T_2),
- (\Delta H_{\text{vap}}) is the latent heat of vaporization,
- (R) is the universal gas constant,
- (T_1) and (T_2) are the absolute temperatures in Kelvin.
Assumptions of the Clausius-Clapeyron Equation
The equation assumes several ideal conditions that allow it to provide accurate results:
- Relatively Low Vapor Pressure: The equation is most accurate when the vapor pressure is not too high, as deviations from ideal behavior become more significant at higher pressures.
- Small Temperature Variations: The equation assumes that temperature changes are not large. When the temperature varies widely, the latent heat of vaporization may not be constant, and the equation becomes less reliable. A large temperature difference can introduce errors since the temperature-dependence of (\Delta H_{\text{vap}}) becomes more pronounced.
- Ideal Gas Law: The equation assumes that the vapor behaves ideally. This is a reasonable assumption for many substances at low to moderate pressures, where intermolecular forces between gas molecules are minimal. However, at very high pressures, the real behavior of the vapor can deviate significantly from ideal gas behavior.
- Negligible Liquid Volume: The equation assumes that the volume of the liquid phase is negligible compared to the volume of the vapor. This is generally true because the liquid is much denser than the vapor, so the volume of liquid doesn’t significantly affect the overall change in volume during vaporization.
Conclusion
The Clausius-Clapeyron equation works accurately under the assumption that vapor pressure is low, temperature changes are moderate, the vapor behaves ideally, and the volume of the liquid is negligible. When these conditions are met, the equation provides a reliable estimate of how vapor pressure changes with temperature.