Problem 76 - Chemistry The Central Science In Si Units

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) \(\mathrm{H}_{2}(g)+\mathrm{NiO}(s) \longrightarrow \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{H}_{2}(g)+\mathrm{S}(s) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)\) (c) \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)\)

Step-by-Step Solution

Answer

(a) \( \Delta G \) decreases, (b) \( \Delta G \) decreases, (c) \( \Delta G \) increases.

Step 1: Understanding Gibbs Free Energy

Gibbs Free Energy, denoted as \( \Delta G \), is related to the equilibrium of a chemical reaction. It tells us whether a reaction proceeds spontaneously. \( \Delta G = \Delta G^\circ + RT\ln Q \), where \( Q \) is the reaction quotient.

Step 2: Relating Partial Pressure to Q

For gaseous reactions, the reaction quotient \( Q \) depends on the partial pressures of the reacting gases. Changing the partial pressure of reactants or products will affect the value of \( Q \). Increase in \( Q \) increases \( \Delta G \), which means the reaction becomes less spontaneous.

Step 3: Analyzing Reaction (a)

In reaction (a), \( \mathrm{H}_{2}(g) + \mathrm{NiO}(s) \rightarrow \mathrm{Ni}(s) + \mathrm{H}_{2} \mathrm{O}(g) \), \( Q = \frac{P_{\mathrm{H}_2\mathrm{O}}}{P_{\mathrm{H}_2}} \). Increasing \( P_{\mathrm{H}_2} \) decreases \( Q \), thus decreasing \( \Delta G \).

Step 4: Analyzing Reaction (b)

In reaction (b), \( \mathrm{H}_{2}(g) + \mathrm{S}(s) \rightarrow \mathrm{H}_{2} \mathrm{S}(g) \), \( Q = \frac{P_{\mathrm{H}_2\mathrm{S}}}{P_{\mathrm{H}_2}} \). Increasing \( P_{\mathrm{H}_2} \) also decreases \( Q \), decreasing \( \Delta G \).

Step 5: Analyzing Reaction (c)

In reaction (c), \( \mathrm{C}(s) + \mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}(g) + \mathrm{H}_{2}(g) \), \( Q = \frac{P_{\mathrm{CO}} P_{\mathrm{H}_2}}{P_{\mathrm{H}_2\mathrm{O}}} \). Increasing \( P_{\mathrm{H}_2} \) increases \( Q \), increasing \( \Delta G \).

Key Concepts

Reaction Quotient

The reaction quotient, represented as \( Q \), is a measure used in chemistry to determine the direction in which a reaction is moving at any point in time. It is similar to the equilibrium constant \( K \), but \( Q \) can be calculated at any stage of the reaction, not just at equilibrium. The general formula for the reaction quotient is:

• \( Q = \frac{\text{products}}{\text{reactants}} \)

Brain understanding can be enhanced by thinking of \( Q \) as a snapshot of the current state of a reaction.
When \( Q = K \), the reaction is at equilibrium.
When \( Q < K \), the reaction will proceed in the forward direction to reach equilibrium.
When \( Q > K \), the reaction will revert in the opposite direction to achieve equilibrium.
In the context of gaseous reactions, \( Q \) is often influenced by the partial pressures of the gases involved. Adjusting these pressures directly affects \( Q \) and, consequently, the spontaneity of the reaction.

Partial Pressure

Partial pressure is a crucial concept when dealing with gases in chemical reactions. It refers to the pressure that a single gas in a mixture of gases contributes to the total pressure. Each gas has its unique partial pressure, which is essential when calculating the reaction quotient \( Q \). It can be represented mathematically as:

• \( P_i = \frac{n_i}{n_{\text{total}}} \times P_{\text{total}} \)

Here, \( P_i \) is the partial pressure of gas \( i \), \( n_i \) is the mole fraction of gas \( i \), and \( P_{\text{total}} \) is the total pressure of the gas mixture.Changing the partial pressures of reactants or products in a reaction will alter \( Q \). For example, if the partial pressure of a reactant is increased, the denominator in \( Q \) becomes larger, decreasing \( Q \) and making the reaction more spontaneous. Conversely, increasing the partial pressure of a product increases \( Q \), making the reaction less spontaneous.Understanding partial pressures helps in predicting the effects of changes in conditions on the reaction dynamics and Gibbs Free Energy.

Chemical Equilibrium

Chemical equilibrium occurs in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant, although not necessarily equal. This balance is represented by the equilibrium constant \( K \).

• \( K = \frac{\text{products at equilibrium}}{\text{reactants at equilibrium}} \)

Equilibrium does not mean the reactants and products are present in equal amounts but rather that their rates of formation are balanced, resulting in no net change.
\( \Delta G \), the Gibbs Free Energy change, is zero at equilibrium, indicating no net energy change in the system. However, when a system is not at equilibrium, \( \Delta G \) will be either positive or negative, showing which direction the reaction will spontaneously move to reach equilibrium.Changes in pressure, concentration, or temperature can disturb equilibrium, though the system usually adjusts to regain balance. This adjustment is described by Le Chatelier’s Principle, which asserts that a system will modify itself to counteract applied changes. Understanding Chemical Equilibrium is vital for managing reactions and predicting how they respond to external changes.