Given the vapor pressures of a pure organic compound and its solution, which of the following equations correctly relates the enthalpy of vaporization (ΔH_{vap}) to the change in vapor pressure with temperature?

• A. ln(P_2/P_1) = -ΔH_{vap}/R (1/T_2 - 1/T_1)
• B. ΔH_{vap} = P_2 - P_1 / (T_2 - T_1)
• C. ΔH_{vap} = R (T_2 - T_1) / ln(P_2/P_1)
• D. P_{solution} = P_{solvent} + ΔH_{vap}

Answer: (A)

Verified step by step guidance

1. Recognize that the problem involves the relationship between vapor pressure and temperature, which is described by the Clausius-Clapeyron equation.
2. Recall the Clausius-Clapeyron equation in its integrated form: \(\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)\), where \(P_1\) and \(P_2\) are vapor pressures at temperatures \(T_1\) and \(T_2\), \(\Delta H_{vap}\) is the enthalpy of vaporization, and \(R\) is the gas constant.
3. Understand that this equation shows how the natural logarithm of the ratio of vapor pressures at two temperatures relates to the enthalpy of vaporization and the inverse of the temperatures.
4. Note that the other given equations do not correctly represent this relationship: the difference in vapor pressures divided by temperature difference is not equal to \(\Delta H_{vap}\), nor is the vapor pressure of a solution simply the sum of solvent vapor pressure and \(\Delta H_{vap}\).
5. Therefore, the correct equation to relate \(\Delta H_{vap}\) to vapor pressure changes with temperature is the integrated Clausius-Clapeyron equation: \(\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)\).