Gaseous indium dihydride is formed from the elements at elevated temperature: ln(g) + H2(g) ightarrow lnH2(g), Kp = 1.48 at 973 K. Partial pressures measured in a reaction vessel are: P_in = 0.0600 atm, P_H2 = 0.0350 atm, P_lnH2 = 0.0760 atm. (b) Determine the equilibrium partial pressures of all the gases.

Verified step by step guidance

1. Step 1: Write the expression for the equilibrium constant Kp for the reaction: \( \text{In}(g) + \text{H}_2(g) \rightleftharpoons \text{InH}_2(g) \). The expression is given by \( K_p = \frac{P_{\text{InH}_2}}{P_{\text{In}} \times P_{\text{H}_2}} \).
2. Step 2: Substitute the given partial pressures into the Kp expression: \( K_p = \frac{0.0760}{0.0600 \times 0.0350} \). Calculate this value to check if the system is at equilibrium.
3. Step 3: Compare the calculated Kp value with the given Kp (1.48). If they are equal, the system is at equilibrium. If not, determine the direction in which the reaction will shift to reach equilibrium.
4. Step 4: If the reaction is not at equilibrium, use an ICE (Initial, Change, Equilibrium) table to determine the changes in partial pressures needed to reach equilibrium. Define the change in pressure as \( x \) and adjust the initial pressures accordingly.
5. Step 5: Substitute the equilibrium expressions from the ICE table back into the Kp expression and solve for \( x \). Use this value to find the equilibrium partial pressures of all gases.

Key Concepts

Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a numerical value that expresses the ratio of the partial pressures of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction ln(g) + H2(g) ⇌ lnH2(g), Kp = 1.48 indicates the relationship between the partial pressures of indium dihydride and its constituent gases. Understanding Kp is essential for calculating the equilibrium state of the system.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. In this context, the partial pressures of indium (P_in), hydrogen (P_H2), and indium dihydride (P_lnH2) are crucial for determining the equilibrium state of the reaction. The total pressure of the gas mixture is the sum of the partial pressures, and these values are used to calculate the equilibrium concentrations.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In this case, if the partial pressures of the reactants or products are altered, the system will shift in the direction that minimizes the effect of that change, which is vital for predicting how the equilibrium will shift in response to changes in partial pressures.