Given the following vapor pressure data for a liquid metal at different temperatures, which method would you use to determine the enthalpy of vaporization (ΔH_vap)?Temperature (K): 400, 420, 440, 460Vapor Pressure (atm): 0.12, 0.22, 0.38, 0.65Choose the most appropriate approach:

• A. Plot vapor pressure versus Temperature and use the intercept to calculate ΔH_vap.
• B. Plot ln(Temperature) versus vapor pressure and use the slope to calculate ΔH_vap.
• C. Plot ln(vapor pressure) versus 1/Temperature and use the slope to calculate ΔH_vap.
• D. Plot Temperature versus vapor pressure and use the area under the curve to calculate ΔH_vap.

Answer: (C)

Verified step by step guidance

1. Recognize that the enthalpy of vaporization (\( \Delta H_{vap} \)) can be determined using the Clausius-Clapeyron equation, which relates vapor pressure and temperature:
2. \[ \ln P = -\frac{\Delta H_{vap}}{R} \cdot \frac{1}{T} + C \]
3. where \( P \) is the vapor pressure, \( T \) is the temperature in Kelvin, \( R \) is the gas constant, and \( C \) is a constant related to entropy.
4. To find \( \Delta H_{vap} \), rearrange the equation to the form of a straight line: plotting \( \ln P \) (natural logarithm of vapor pressure) on the y-axis versus \( \frac{1}{T} \) (inverse temperature) on the x-axis will yield a straight line.
5. The slope of this line is equal to \( -\frac{\Delta H_{vap}}{R} \). By determining the slope from the plot, you can calculate \( \Delta H_{vap} \) using:
6. \[ \Delta H_{vap} = - \text{slope} \times R \]