The enthalpy of vaporization of Substance X is 16.0kJmol and its normal boiling point is 27.°C. Calculate the vapor pressure of X at −63.°C.
Round your answer to 2 significant digits.

To calculate the vapor pressure of a substance at a different temperature, we can use the **Clausius-Clapeyron equation**. This equation relates the vapor pressure at two different temperatures to the enthalpy of vaporization (\(\Delta H_{\text{vap}}\)):

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

where:
- \(P_1\) = vapor pressure at the boiling point (known, equal to 1 atm at normal boiling point),
- \(P_2\) = vapor pressure at the temperature we are interested in (to be calculated),
- \(\Delta H_{\text{vap}}\) = enthalpy of vaporization in J/mol (convert from kJ/mol),
- \(R\) = gas constant = 8.314 J/(mol·K),
- \(T_1\) = temperature at boiling point in Kelvin,
- \(T_2\) = temperature at which we want to calculate the vapor pressure, in Kelvin.

### Given:
- \(\Delta H_{\text{vap}} = 16.0 \, \text{kJ/mol} = 16.0 \times 10^3 \, \text{J/mol}\),
- Boiling point \(T_1 = 27^{\circ}C = 27 + 273.15 = 300.15 \, \text{K}\),
- Temperature of interest \(T_2 = -63^{\circ}C = -63 + 273.15 = 210.15 \, \text{K}\),
- \(P_1 = 1 \, \text{atm}\) (normal pressure at boiling point).

Let's plug in these values to find \(P_2\).The vapor pressure of Substance X at \(-63^\circ\text{C}\) is approximately \(0.064 \, \text{atm}\), rounded to two significant digits.

Would you like further details on the process or have any questions?

Here are five related questions to explore:
1. How does the vapor pressure of a substance change with temperature?
2. What assumptions does the Clausius-Clapeyron equation make?
3. How is the enthalpy of vaporization determined experimentally?
4. What is the significance of the boiling point in vapor pressure calculations?
5. How would the vapor pressure change if the enthalpy of vaporization were different?

**Tip:** Always ensure temperatures are converted to Kelvin in thermodynamic calculations to avoid errors.

The enthalpy of vaporization of Substance X is 16.0 kJ/mol and its normal boiling point is 27°C. Calculate the vapor pressure of X at −63°C. Round your answer to 2 significant digits.

Calculate the vapor pressure of Substance X at -63°C using the Clausius-Clapeyron equation. This problem involves thermodynamic concepts such as enthalpy of vaporization and phase transitions. Suitable for students in Grades 11-12.

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