A system at equilibrium contains I2(g) at a pressure of 0.21 atm and I(g) at a pressure of 0.23 atm. The system is then compressed to half its volume. Find the pressure of each gas when the system returns to equilibrium.

Verified step by step guidance

Identify the initial equilibrium condition and the equilibrium constant expression for the reaction: \( \text{I}_2(g) \rightleftharpoons 2\text{I}(g) \).

Calculate the initial equilibrium constant \( K_p \) using the initial pressures: \( K_p = \frac{(P_{\text{I}})^2}{P_{\text{I}_2}} \).

Determine the effect of compression on the system: halving the volume doubles the initial pressures of both gases.

Set up the new equilibrium expression using the doubled initial pressures and introduce a change variable \( x \) to account for the shift in equilibrium.

Solve the equilibrium expression for \( x \) to find the new equilibrium pressures of \( \text{I}_2(g) \) and \( \text{I}(g) \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change. In this case, compressing the system affects the pressures of the gases, prompting a shift in equilibrium to restore balance.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates the pressure, volume, and temperature of an ideal gas. In this scenario, the initial pressures and the change in volume due to compression will influence the final pressures of I2 and I, allowing us to calculate the new equilibrium state.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) for a reaction involving gases is defined in terms of the partial pressures of the reactants and products at equilibrium. Understanding Kp helps predict how the pressures of I2 and I will adjust after the system is compressed and reaches a new equilibrium.

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Equilibrium Constant Expressions

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