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: $$ \begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } 2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)} \\ {\text { (c) } 2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)}\end{array} $$

Short answer

In summary, increasing the partial pressure of \(\mathrm{H}_{2}\) in the given reactions leads to the following changes in \(\Delta G\): (a) \(\Delta G\) decreases (b) \(\Delta G\) increases (c) \(\Delta G\) decreases

Step-by-step solution

Reaction (a)

Reaction (a) is given by: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) As per Le Chatelier's principle, if we increase the partial pressure of \(\mathrm{H}_{2}\), the system will respond by shifting the equilibrium to counteract this change. In this case, the equilibrium will shift to the right, favoring the formation of \(\mathrm{NH}_{3}\). This indicates a decrease in \(\Delta G\) because the reaction is becoming more spontaneous in the forward direction.

Reaction (b)

Reaction (b) is given by: \(2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)\) Here, if we increase the partial pressure of \(\mathrm{H}_{2}\), the equilibrium will shift to the left according to Le Chatelier's principle, which will favor the formation of \(\mathrm{HBr}\). This shift leads to an increase in \(\Delta G\), as the reaction is becoming less spontaneous in the forward direction.

Reaction (c)

Reaction (c) is given by: \(2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\) When we increase the partial pressure of \(\mathrm{H}_{2}\) in reaction (c), the equilibrium will shift to the right to counteract the change, as per Le Chatelier's principle. This will favor the formation of \(\mathrm{C}_{2} \mathrm{H}_{6}(g)\). This shift corresponds to a decrease in \(\Delta G\) because the reaction is becoming more spontaneous in the forward direction. In conclusion: For reaction (a), the \(\Delta G\) decreases. For reaction (b), the \(\Delta G\) increases. For reaction (c), the \(\Delta G\) decreases.

Key concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy, denoted as \( \Delta G \), is a key concept in thermodynamics that helps us predict whether a chemical reaction will occur spontaneously. Essentially, it represents the maximum amount of work that can be performed by a chemical process at constant temperature and pressure.

When \( \Delta G \) is negative, the reaction occurs spontaneously in the forward direction, releasing free energy. If \( \Delta G \) is positive, the reaction is non-spontaneous and may require external energy input to proceed. A \( \Delta G \) of zero indicates that the reaction is at equilibrium, with no net change in the concentrations of reactants and products.

Changes in reaction conditions, such as temperature, pressure, and concentration, can affect \( \Delta G \). According to Le Chatelier's principle, a system at equilibrium will shift in response to changes in these conditions, impacting \( \Delta G \). This is precisely why increasing the partial pressure of hydrogen \((\mathrm{H}_{2}\)) in the given reactions can alter the spontaneity of these reactions by affecting \( \Delta G \).

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no net change in the concentrations of reactants and products. At equilibrium, the system has reached a point where \( \Delta G \) is zero, meaning that the reaction does not favor the forward or reverse direction.

Achieving equilibrium does not mean the concentrations of reactants and products are equal but that their ratios remain constant over time. The position of equilibrium is given by the equilibrium constant \( K \), which indicates the ratio of product concentrations to reactant concentrations at equilibrium.

In the context of the given reactions, shifting the position of equilibrium by altering conditions like pressure can change the spontaneity and direction of the reaction. This shift is predicted by Le Chatelier's principle, which helps explain how \( \Delta G \) could increase or decrease when we tweak factors like partial pressure.

In reactions (a) and (c), increasing the partial pressure of \( \mathrm{H}_{2} \) shifts equilibrium towards product formation, decreasing \( \Delta G \), while for reaction (b), it shifts towards reactant formation, increasing \( \Delta G \).

Partial Pressure

Partial pressure is a concept used mainly in gases and is defined as the pressure exerted by a single gas in a mixture of gases. It contributes to the total pressure exerted by the gas mixture.

Partial pressures play a crucial role in chemical equilibrium, especially when dealing with gaseous reactions. According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases.

In chemical equilibria involving gases, changing the partial pressure of one component affects the equilibrium position. For instance, if you increase the partial pressure of \( \mathrm{H}_{2} \) in the reactions provided, it influences the direction in which the equilibrium shifts as per Le Chatelier's principle.

In reactions (a) and (c), higher partial pressure of hydrogen favors the forward reaction, resulting in more product formation and thus a more negative \( \Delta G \), indicating increased spontaneity. Conversely, in reaction (b), increased hydrogen partial pressure shifts equilibrium towards reactants, resulting in a more positive \( \Delta G \), indicating decreased spontaneity.