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The enthalpy of vaporization is a crucial concept when discussing phase changes between liquid and gas for substances. It represents the amount of energy required to convert one mole of a liquid to its gaseous form at a constant pressure, usually at the liquid's boiling point. For benzene, at its normal boiling point of 80.09°C, the molar enthalpy of vaporization is given as 30.72 kJ/mol.

This value indicates the strength of intermolecular forces that need to be overcome for the phase change to occur. When these forces are strong, a higher enthalpy of vaporization is required, meaning more energy is needed for vaporization. In calculations related to Gibbs free energy, this enthalpy value plays a significant role because it is directly used in the equation to determine the spontaneity of the vaporization process.

Enthalpy of vaporization is temperature dependent, though in many calculations, it is often assumed to be constant unless stated otherwise. This assumption simplifies calculations while still providing an accurate enough depiction of the thermodynamic behavior of the studied system.

Entropy, symbolized as \(\Delta S\), is a measure of the disorder or randomness in a system. The entropy change associated with vaporization, \(\Delta_{\mathrm{vap}} \bar{S}\), is significant because moving from the ordered structure of a liquid to the disordered state of a gas results in an increase in entropy.

To calculate entropy change during vaporization, we use the equation:

• \(\Delta_{\mathrm{vap}} \bar{S} = \frac{\Delta_{\mathrm{vap}} \bar{H}}{T}\)

where \(T\) is the absolute temperature in Kelvin at which the phase change occurs. This relationship stems from the understanding that at equilibrium (the boiling point), \(\Delta_{\mathrm{vap}} \bar{G} = 0\).

For benzene, the calculated entropy change at its boiling point is approximately 0.08696 kJ/molâ‹…K, indicating an increase in randomness as the liquid benzene evaporates. This measure of entropy is crucial in assessing the energy distribution in a system and is integral in determining the directionality of a process under different temperatures.

The spontaneity of vaporization is an essential factor in understanding whether a liquid will naturally convert to vapor at a given temperature. This spontaneity is determined using the Gibbs free energy change equation for vaporization, \(\Delta_{\mathrm{vap}} \bar{G} = \Delta_{\mathrm{vap}} \bar{H} - T \Delta_{\mathrm{vap}} \bar{S}\).

The sign of \(\Delta_{\mathrm{vap}} \bar{G}\) indicates the spontaneity:

• If \(\Delta_{\mathrm{vap}} \bar{G} > 0\), vaporization is non-spontaneous at that temperature.
• If \(\Delta_{\mathrm{vap}} \bar{G} = 0\), the system is at equilibrium, meaning no net change occurs. This typically happens at the boiling point.
• If \(\Delta_{\mathrm{vap}} \bar{G} < 0\), vaporization is spontaneous, indicating that the process will occur naturally without any additional input of energy.

Calculations show that for benzene above 80.09°C, vaporization becomes spontaneous, while below this temperature, it is non-spontaneous. This knowledge is vital in many practical applications, such as designing industrial processes where controlled phase changes are required.