An unknown liquid has a heat of vaporization of 31.32 kJ/mole. If the normal boiling point is 88, what is vapor pressure (in torr) of this liquid at room temperature of 25 degrees C? HINT: Normal boiling point occurs when the vapor pressure of the liquid is the same as atmospheric pressure (1 atm or 760 mm Hg).

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**Determining the Vapor Pressure of an Unknown Liquid**

**Problem Statement:**
An unknown liquid has a heat of vaporization of 31.32 kJ/mole. If the normal boiling point is 88°C, what is the vapor pressure (in torr) of this liquid at room temperature of 25°C? 

**Hint:**
Normal boiling point occurs when the vapor pressure of the liquid is the same as atmospheric pressure (1 atm or 760 mm Hg).

**Explanation:**
To solve this problem, we use the Clausius-Clapeyron equation which relates the vapor pressure of a substance at two different temperatures. 

The Clausius-Clapeyron equation can be written as:

\[ \ln \left( \frac{P_2}{P_1} \right) = - \frac{\Delta H_\text{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]

Where: 
- \( P_1 \) is the initial vapor pressure (760 mm Hg at the boiling point).
- \( P_2 \) is the vapor pressure at the new temperature.
- \( \Delta H_\text{vap} \) is the heat of vaporization (31.32 kJ/mole).
- \( R \) is the ideal gas constant (8.314 J/mol·K).
- \( T_1 \) is the initial temperature in Kelvin (88°C = 361 K).
- \( T_2 \) is the new temperature in Kelvin (25°C = 298 K). 

Solve for \( P_2 \):

1. Convert the heat of vaporization from kJ/mole to J/mole:
\[ \Delta H_\text{vap} = 31.32 \text{ kJ/mole} \times 1000 \text{ J/kJ} = 31320 \text{ J/mole} \]

2. Substitute the values into the Clausius-Clapeyron equation:
\[ \ln \left( \frac{P_2}{760 \text{ mm Hg}} \right) = - \frac{31320 \text{ J/mole}}{8.314 \text{ J/mol·K}} \left( \frac{1}{298 \text{ K}} - \frac{1}{361 \text{ K}} \
Transcribed Image Text:**Determining the Vapor Pressure of an Unknown Liquid** **Problem Statement:** An unknown liquid has a heat of vaporization of 31.32 kJ/mole. If the normal boiling point is 88°C, what is the vapor pressure (in torr) of this liquid at room temperature of 25°C? **Hint:** Normal boiling point occurs when the vapor pressure of the liquid is the same as atmospheric pressure (1 atm or 760 mm Hg). **Explanation:** To solve this problem, we use the Clausius-Clapeyron equation which relates the vapor pressure of a substance at two different temperatures. The Clausius-Clapeyron equation can be written as: \[ \ln \left( \frac{P_2}{P_1} \right) = - \frac{\Delta H_\text{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \] Where: - \( P_1 \) is the initial vapor pressure (760 mm Hg at the boiling point). - \( P_2 \) is the vapor pressure at the new temperature. - \( \Delta H_\text{vap} \) is the heat of vaporization (31.32 kJ/mole). - \( R \) is the ideal gas constant (8.314 J/mol·K). - \( T_1 \) is the initial temperature in Kelvin (88°C = 361 K). - \( T_2 \) is the new temperature in Kelvin (25°C = 298 K). Solve for \( P_2 \): 1. Convert the heat of vaporization from kJ/mole to J/mole: \[ \Delta H_\text{vap} = 31.32 \text{ kJ/mole} \times 1000 \text{ J/kJ} = 31320 \text{ J/mole} \] 2. Substitute the values into the Clausius-Clapeyron equation: \[ \ln \left( \frac{P_2}{760 \text{ mm Hg}} \right) = - \frac{31320 \text{ J/mole}}{8.314 \text{ J/mol·K}} \left( \frac{1}{298 \text{ K}} - \frac{1}{361 \text{ K}} \
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