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).
States of Matter
The substance that constitutes everything in the universe is known as matter. Matter comprises atoms which in turn are composed of electrons, protons, and neutrons. Different atoms combine together to give rise to molecules that act as a foundation for all kinds of substances. There are five states of matter based on their energies of attraction, namely solid, liquid, gases, plasma, and BEC (Bose-Einstein condensates).
Chemical Reactions and Equations
When a chemical species is transformed into another chemical species it is said to have undergone a chemical reaction. It consists of breaking existing bonds and forming new bonds by changing the position of electrons. These reactions are best explained using a chemical equation.
![**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:
\[ \ln \left( \frac{P_2}{760 \text{ mm Hg}} \right) = - \frac{31320 \text{ J/mole}}{8.314 \text{ J/mol·K}} \left( \frac{1}{298 \text{ K}} - \frac{1}{361 \text{ K}} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6746fa6f-1856-443b-addc-ecae5d9da9b9%2Fb4fd2384-c0f6-46da-aa4a-4452fa0eb8f5%2Fdyl3e8e.jpeg&w=3840&q=75)
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