Benzene has a heat of vaporization of 30.72 kJ/mol and a normal boiling point of 80.1 °C. At what temperature does benzene boil when the external pressure is 445 torr?

Verified step by step guidance

1. Identify the known values: the heat of vaporization (\(\Delta H_{vap} = 30.72 \text{ kJ/mol}\)), the normal boiling point (\(T_1 = 80.1 \degree C\)), and the normal pressure (\(P_1 = 760 \text{ torr}\)).
2. Convert the normal boiling point from Celsius to Kelvin: \(T_1 = 80.1 + 273.15\).
3. Use the Clausius-Clapeyron equation: \(\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)\), where \(P_2 = 445 \text{ torr}\) and \(R = 8.314 \text{ J/mol K}\).
4. Rearrange the Clausius-Clapeyron equation to solve for \(T_2\): \(T_2 = \left(\frac{1}{T_1} - \frac{R}{\Delta H_{vap}} \ln\left(\frac{P_2}{P_1}\right)\right)^{-1}\).
5. Substitute the known values into the equation and solve for \(T_2\) in Kelvin, then convert back to Celsius if needed.

Key Concepts

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without a change in temperature. For benzene, this value is 30.72 kJ/mol, indicating the energy needed to vaporize one mole of benzene at its boiling point under standard atmospheric pressure.

Boiling Point and External Pressure

The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure surrounding it. As external pressure increases, the boiling point of the liquid also increases. In this case, the boiling point of benzene will change when the external pressure is adjusted to 445 torr, which is lower than standard atmospheric pressure.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates the change in vapor pressure with temperature to the heat of vaporization. It can be used to calculate the new boiling point of a substance when the external pressure changes. This equation is essential for determining how the boiling point of benzene will shift from its normal boiling point of 80.1 °C at a pressure of 445 torr.