Question

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: (a) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) (b) \(2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)\) (c) \(2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\)

Short answer

For the given reactions, increasing the partial pressure of H2 results in the following changes in ΔG: (a) ΔG increases (b) ΔG decreases (c) ΔG increases

Step-by-step solution

Identify the reaction quotient (Q)

In each reaction, the reaction quotient Q can be calculated by taking the ratio of the products to the reactants, each raised to the power of its stoichiometric coefficient. Since we are working with partial pressures, Q will be represented as Qp for each reaction: (a) Qp = {(\(P_{NH_3}\))²} / {(\(P_{N_2}\)) (\(P_{H_2}\))^3} (b) Qp = {(\(P_{H_2}\)) (\(P_{Br_2}\))} / {(\(P_{HBr}\))^2} (c) Qp = {(\(P_{C_2H_6}\))} / {(\(P_{H_2}\))^2 (\(P_{C_2H_2}\))} Now let's analyze how Qp will change when the partial pressure of H2 is increased for each reaction.

Determine the effect on ΔG for each reaction#a

(a) When the partial pressure of H2 (\(P_{H_2}\)) is increased, the denominator of the reaction quotient Qp for reaction (a) will increase. As a result, Qp decreases. Since ΔG is directly proportional to the natural logarithm of Q (ΔG = ΔG° + RT ln(Q)), a decrease in Qp means that ΔG will increase. In other words, if the partial pressure of H2 increases, ΔG for reaction (a) will increase.

Determine the effect on ΔG for each reaction#b

(b) In reaction (b), increasing the partial pressure of H2 will increase the numerator of Qp, which in turn, increases Qp. As ΔG is directly proportional to the natural logarithm of Q, an increase in Qp implies that ΔG will decrease. Therefore, if the partial pressure of H2 increases, ΔG for reaction (b) will decrease.

Determine the effect on ΔG for each reaction#c

(c) Increasing the partial pressure of H2 in reaction (c) affects the denominator of Qp. A higher partial pressure of H2 will increase the denominator of Qp, leading to a decrease in Qp. As ΔG is directly proportional to the natural logarithm of Q, a decrease in Qp results in an increase in ΔG. Thus, if the partial pressure of H2 increases, ΔG for reaction (c) will increase.

Present the results

For the given reactions, the effect of increasing the partial pressure of H2 on ΔG is as follows: (a) ΔG increases (b) ΔG decreases (c) ΔG increases