If ethanol and chloroform are present in a molar ratio of 2:3 then what is the vapor pressure at 20° C if vapor pressures of pure liquids are 5.95 kPa and 21.17 kPa, respectively?

Options

A. 16.692 kPa
B. 15.082 kPa
C. 8.731 kPa
D. 12.038 kPa

Answer

To find the vapor pressure of a mixture of ethanol and chloroform at 20°C, we can use Raoult's Law, which states that the partial vapor pressure of each component in a mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Molar ratio of ethanol to chloroform = 2:3
- Vapor pressure of pure ethanol (P0_ethanol) = 5.95 kPa
- Vapor pressure of pure chloroform (P0_chloroform) = 21.17 kPa

2. **Calculate Total Moles:**
- Let the number of moles of ethanol = 2 (from the ratio)
- Let the number of moles of chloroform = 3 (from the ratio)
- Total moles = 2 + 3 = 5

3. **Calculate Mole Fractions:**
- Mole fraction of ethanol (X_ethanol) = Moles of ethanol / Total moles = 2 / 5 = 0.4
- Mole fraction of chloroform (X_chloroform) = Moles of chloroform / Total moles = 3 / 5 = 0.6

4. **Calculate Partial Pressures:**
- Partial pressure of ethanol (P_ethanol) = P0_ethanol × X_ethanol
\[ P_{\text{ethanol}} = 5.95 \, \text{kPa} \times 0.4 = 2.38 \, \text{kPa} \]
- Partial pressure of chloroform (P_chloroform) = P0_chloroform × X_chloroform
\[ P_{\text{chloroform}} = 21.17 \, \text{kPa} \times 0.6 = 12.702 \, \text{kPa} \]

5. **Calculate Total Vapor Pressure:**
- Total vapor pressure (P_total) = P_ethanol + P_chloroform
\[ P_{\text{total}} = 2.38 \, \text{kPa} + 12.702 \, \text{kPa} = 15.082 \, \text{kPa} \]

### Final Answer:
The vapor pressure at 20°C is **15.082 kPa**.