At 1500 K, the process I2(g) ⟶ 2 I(g) 10 atm 10 atm is not spontaneous. However

step 1 Okay, problem 24, we have this reaction and we change the pressure and one of them becomes spont

At 1500 K, the process I2(g) ⟶ 2 I(g) 10 atm ...

At $1500 \mathrm{~K}$, the process $$\begin{array}{c}\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{I}(g) \\ 10 \mathrm{~atm} \quad 10 \mathrm{~atm}\end{array}$$ is not spontaneous. However, the process $$\begin{array}{c}\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{I}(g) \\ 0.10 \mathrm{~atm} \quad 0.10 \mathrm{~atm}\end{array}$$ is spontaneous at $1500 \mathrm{~K}$. Explain.

At $1500 \mathrm{~K}$, the process
$$\begin{array}{c}\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{I}(g) \\
10 \mathrm{~atm} \quad 10 \mathrm{~atm}\end{array}$$
is not spontaneous. However, the process
$$\begin{array}{c}\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{I}(g) \\
0.10 \mathrm{~atm} \quad 0.10 \mathrm{~atm}\end{array}$$
is spontaneous at $1500 \mathrm{~K}$. Explain.

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic function that indicates the spontaneity of a process; a negative ?G means a process is spontaneous under constant temperature and pressure conditions. The relationship is given by ?G = ?G° + RT ln Q, where ?G° is the standard free energy change, R is the gas constant, T is the temperature, and Q is the reaction quotient, reflecting the effect of non-standard conditions on reaction spontaneity.

Reaction Quotient vs Equilibrium Constant

The reaction quotient (Q) represents the ratio of the products’ activities (or pressures for gases) to the reactants' at any given moment during the reaction. It is compared with the equilibrium constant (K) to predict the direction of the reaction’s shift towards equilibrium. When conditions such as pressure change, Q changes, which in turn affects the Gibbs free energy and thus the spontaneity of a reaction.

Pressure Dependence in Gas-phase Reactions

In gas-phase reactions, the partial pressures of the reactants and products play a crucial role in determining Q, and therefore the spontaneity. Changes in pressure can alter the value of Q through the logarithmic term in the Gibbs equation. For reactions with a change in the number of gas molecules, such as a dissociation reaction, lower total pressures result in a lower Q which can favor spontaneity, whereas high pressures can increase Q and make the process less spontaneous.

Effect of Temperature on Reaction Spontaneity

Temperature is a significant factor in determining the impact of the RT ln Q term in the Gibbs free energy equation. At high temperatures, even small changes in Q due to pressure variations can substantially influence ?G. In the described scenario, the reaction’s spontaneity is not solely dependent on temperature, but on the interplay between temperature, pressure, and the reaction quotient.

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