For the vaporization of benzene, ∆H_vap = 30.7 kJ/mol and ∆S_vap = 87.0 J/(K*mol). Calculate ∆S_surr and ∆S_total at: (a) 70 °C

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature: T(K) = 70 + 273.15.
2. Calculate the entropy change of the surroundings (\( \Delta S_{surr} \)) using the formula: \( \Delta S_{surr} = -\frac{\Delta H_{vap}}{T} \). Make sure to convert \( \Delta H_{vap} \) from kJ/mol to J/mol by multiplying by 1000.
3. Substitute the values into the formula: \( \Delta S_{surr} = -\frac{30.7 \times 1000}{T(K)} \).
4. Calculate the total entropy change (\( \Delta S_{total} \)) using the formula: \( \Delta S_{total} = \Delta S_{vap} + \Delta S_{surr} \).
5. Substitute the given \( \Delta S_{vap} \) and the calculated \( \Delta S_{surr} \) into the formula to find \( \Delta S_{total} \).

Key Concepts

Gibbs Free Energy and Spontaneity

Gibbs Free Energy (G) is a thermodynamic potential that helps predict whether a process will occur spontaneously at constant temperature and pressure. The change in Gibbs Free Energy (∆G) is calculated using the equation ∆G = ∆H - T∆S, where ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy. A negative ∆G indicates a spontaneous process.

Entropy Change of the Surroundings (∆S_surr)

The entropy change of the surroundings (∆S_surr) during a process can be calculated using the formula ∆S_surr = -∆H/T, where ∆H is the enthalpy change of the system and T is the temperature in Kelvin. This relationship shows how the heat exchanged with the surroundings affects the disorder or randomness of the surroundings, which is crucial for understanding the overall entropy changes in a thermodynamic process.

Total Entropy Change (∆S_total)

The total entropy change (∆S_total) of a system and its surroundings is the sum of the entropy change of the system (∆S_sys) and the entropy change of the surroundings (∆S_surr). It is given by the equation ∆S_total = ∆S_sys + ∆S_surr. For a process to be spontaneous, ∆S_total must be greater than zero, indicating an overall increase in disorder in the universe.