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Chapter 16: Problem 24

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

Short Answer

Expert verified
At 1500 K, the process \(I_{2}(g) \longrightarrow 2I(g)\) is spontaneous at 0.1 atm but non-spontaneous at 10 atm due to the effect of pressure on the Gibbs free energy change (∆G). As pressure decreases, the chemical potential difference between products and reactants (∆µ) decreases, resulting in a more negative ∆G, which makes the process spontaneous. In contrast, at higher pressures, the change in Gibbs free energy (∆G) becomes less negative (or even positive) causing the process to be non-spontaneous.

Step by step solution

01

Write Down the Reaction Equation

The given reaction is: \( I_{2}(g) \longrightarrow 2I(g) \) This reaction involves dissociation of an iodine molecule into two iodine atoms at two different pressures and the same temperature, 1500 K.
02

Write Down the Equation for Gibbs Free Energy

The equation for Gibbs free energy is: ∆G = ∆H - T∆S
03

Consider the Effects of Pressure on the Reaction Spontaneity

In this specific problem, both ∆H and ∆S do not change with pressure. Therefore, to analyze the effect of pressure on reaction spontaneity, we must turn our attention to the parameter of Gibbs free energy that's related to pressure: chemical potential. The equation for chemical potential, µ, is: µ = µ° + RT ln(P) Where µ° is the standard chemical potential, R is the gas constant, T is the temperature in Kelvin, and P is the pressure.
04

Analyze the Effects of Pressure on the Chemical Potential

As pressure decreases, the natural logarithm term in the chemical potential equation (ln(P)) also decreases, making the chemical potential for products lower. Consequently, the difference in the chemical potential between products and reactants (∆µ) will be smaller at lower pressures as compared to higher pressures.
05

Relate the Chemical Potential Difference to Gibbs Free Energy Change

Because the change in Gibbs free energy is proportional to the difference in chemical potential between products and reactants (∆G = -n∆µ), a smaller ∆µ will lead to a smaller ∆G. Therefore, at lower pressures, the change in Gibbs free energy for the given reaction will be more negative compared to the one at the higher pressure.
06

Explain the Spontaneity at Two Different Pressures

At lower pressure (0.1 atm), the change in Gibbs free energy (∆G) becomes more negative as compared to the reaction at a higher pressure (10 atm), leading to a spontaneous process. On the other hand, at higher pressure (10 atm), the Gibbs free energy change (∆G) is less negative (or even positive), making the process non-spontaneous.

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Most popular questions from this chapter

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