At 100 .^∘ C and 1.00 atm, ΔH^∘=40.6 kJ / mol for the vaporiza- tion of water. Estimate ΔG^∘ f

step 1 Problem 56, we have the vaporization of water, and we're given the delta H. It's given in kilojo

At 100 .^∘ C and 1.00 atm, ΔH^∘=40.6 kJ / mol for the...

At $100 .^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}, \Delta H^{\circ}=40.6 \mathrm{~kJ} / \mathrm{mol}$ for the vaporiza- tion of water. Estimate $\Delta G^{\circ}$ for the vaporization of water at $90 .{ }^{\circ} \mathrm{C}$ and $110 .{ }^{\circ} \mathrm{C}$. Assume $\Delta H^{\circ}$ and $\Delta S^{\circ}$ at $100 .{ }^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ do not depend on temperature.

At $100 .^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}, \Delta H^{\circ}=40.6 \mathrm{~kJ} / \mathrm{mol}$ for the vaporiza-
tion of water. Estimate $\Delta G^{\circ}$ for the vaporization of water at $90 .{ }^{\circ} \mathrm{C}$ and $110 .{ }^{\circ} \mathrm{C}$. Assume $\Delta H^{\circ}$ and $\Delta S^{\circ}$ at $100 .{ }^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ do not depend on temperature.

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Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic potential that indicates the maximum reversible work a system can perform at constant temperature and pressure. It determines whether a chemical process is spontaneous and is calculated using the equation ?G = ?H - T?S, where ?H is the enthalpy change, T is the temperature, and ?S is the entropy change.

Enthalpy

Enthalpy (?H) is a measure of the total heat content of a system and represents the energy change during a process at constant pressure. In the context of phase changes, enthalpy reflects the heat absorbed or released when a substance, such as water, vaporizes.

Entropy

Entropy (?S) quantifies the degree of disorder or randomness in a system. During vaporization, the entropy increases as the molecules in the gas phase are more disordered than those in the liquid phase, making ?S a critical factor in determining the Gibbs free energy.

Temperature Dependence in Thermodynamics

The effect of temperature on the spontaneity of a process is captured by the T?S term in the Gibbs free energy equation. Even when ?H and ?S are assumed constant over a limited temperature range, variations in temperature can significantly change the value of ?G, thereby influencing the equilibrium and favorability of phase transitions.

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