Consider the vaporization of water: H2 O(1) ⟶H2 O(g) at...

Consider the vaporization of water: $\mathrm{H}_{2} \mathrm{O}(1) \longrightarrow$ $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $100^{\circ} \mathrm{C},$ with $\mathrm{H}_{2} \mathrm{O}(1)$ in its standard state, but with the partial pressure of $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $2.0 \mathrm{atm}$ Which of the following statements about this vaporization at $100^{\circ} \mathrm{C}$ are true? Explain. (a) $\Delta_{\mathrm{r}} G^{\circ}=0$ (b) $\Delta_{\mathrm{r}} G=0,$ (c) $\Delta_{\mathrm{r}} G^{\circ}>0,$ (d) $\Delta_{\mathrm{r}} G>0$

Consider the vaporization of water: $\mathrm{H}_{2} \mathrm{O}(1) \longrightarrow$ $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $100^{\circ} \mathrm{C},$ with $\mathrm{H}_{2} \mathrm{O}(1)$ in its standard state, but with the partial pressure of $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $2.0 \mathrm{atm}$ Which of the following statements about this vaporization at $100^{\circ} \mathrm{C}$ are true? Explain. (a) $\Delta_{\mathrm{r}} G^{\circ}=0$
(b) $\Delta_{\mathrm{r}} G=0,$ (c) $\Delta_{\mathrm{r}} G^{\circ}>0,$ (d) $\Delta_{\mathrm{r}} G>0$

Key Concepts

Phase Equilibrium and Boiling Point

At the boiling point of a liquid, the vapor pressure equals the ambient pressure for the vapor, meaning that the liquid and its vapor are in equilibrium. In the case of water at 100°C, this equilibrium occurs at a vapor pressure of 1 atm, where the free energy change for the phase transition is zero under standard conditions. Deviating from this equilibrium pressure, such as having a partial pressure of 2 atm for the vapor, disrupts the equilibrium and results in a non-zero Gibbs free energy change.

Standard Gibbs Free Energy Change

This concept refers to the change in free energy when a reaction is carried out under standard conditions, typically defined by a pressure of 1 atm for gases and a pure substance for liquids and solids. For a phase change reaction like the vaporization of water at its boiling point, the standard Gibbs free energy change (?rG°) is zero because the liquid and gas phases are in equilibrium under standard conditions.

Reaction Quotient and Non?Standard Conditions

The reaction quotient (Q) measures the ratio of the products’ activities (or pressures for gases) to those of the reactants under the actual conditions of a reaction. The relationship ?rG = ?rG° + RT ln Q is used to calculate the free energy change when the system is not at standard state. In the vaporization example, with water vapor at 2 atm instead of the standard 1 atm, Q is greater than one, which makes ?rG positive, indicating the process is not spontaneous under those conditions.

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