Given the data in Problem 18.78, calculate ∆G for the vaporization of benzene at:(a) 70 °CPredict whether benzene will boil at each of these temperatures and 1 atm pressure.

Verified step by step guidance

1. Identify the given data from Problem 18.78, which should include the enthalpy of vaporization (\( \Delta H_{vap} \)) and the entropy of vaporization (\( \Delta S_{vap} \)) for benzene.
2. Use the Gibbs free energy equation for vaporization: \( \Delta G = \Delta H_{vap} - T \Delta S_{vap} \), where \( T \) is the temperature in Kelvin.
3. Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature (70 °C + 273.15 = 343.15 K).
4. Substitute the values of \( \Delta H_{vap} \), \( T \), and \( \Delta S_{vap} \) into the Gibbs free energy equation to calculate \( \Delta G \).
5. Determine if benzene will boil at 70 °C and 1 atm by checking if \( \Delta G \) is less than or equal to zero, which indicates that the vaporization process is spontaneous.

Key Concepts

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is crucial for predicting the spontaneity of a process; a negative ∆G indicates a spontaneous reaction, while a positive ∆G suggests non-spontaneity. In the context of vaporization, calculating ∆G helps determine whether the phase change from liquid to gas is favorable under given conditions.

Vaporization and Boiling Point

Vaporization is the process by which a liquid turns into vapor, and the boiling point is the temperature at which this occurs at a specific pressure. For a substance to boil, its vapor pressure must equal the external pressure. Understanding the relationship between temperature, pressure, and vapor pressure is essential for predicting whether a liquid will boil at a given temperature and pressure, such as 1 atm.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation describes the relationship between the vapor pressure of a substance and its temperature, providing a way to calculate changes in vapor pressure with temperature. This equation is particularly useful for determining the boiling point of a liquid at different pressures and for calculating ∆G for phase transitions. It highlights how temperature influences the equilibrium between phases, which is critical for understanding the boiling behavior of substances like benzene.