Methane, CH4, reacts with I2 according to the reaction CH4(g) + I2(g) ⇌ CH3I(g) + HI(g). At 630 K, Kp for this reaction is 2.26 × 10^-4. A reaction was set up at 630 K with initial partial pressures of methane at 105.1 torr and I2 at 7.96 torr. Calculate the pressures, in torr, of all reactants and products at equilibrium.

Verified step by step guidance

Step 1: Write the expression for the equilibrium constant Kp for the reaction. For the reaction CH4(g) + I2(g) ⇌ CH3I(g) + HI(g), the expression is Kp = (P_CH3I * P_HI) / (P_CH4 * P_I2).

Step 2: Define the change in pressure for each species in terms of a variable, x. Assume that x is the change in pressure for CH4 and I2 as they react to form CH3I and HI. Therefore, the changes are: CH4: 105.1 - x, I2: 7.96 - x, CH3I: x, HI: x.

Step 3: Substitute the equilibrium pressures in terms of x into the Kp expression. This gives Kp = (x * x) / ((105.1 - x) * (7.96 - x)).

Step 4: Set the Kp expression equal to the given Kp value, 2.26 × 10^-4, and solve the resulting quadratic equation for x. This will involve expanding the equation and using the quadratic formula.

Step 5: Calculate the equilibrium pressures of all species using the value of x obtained from the quadratic equation. The pressures will be: P_CH4 = 105.1 - x, P_I2 = 7.96 - x, P_CH3I = x, P_HI = x.

Key Concepts

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

Equilibrium Constant (Kp)

The equilibrium constant, Kp, is a numerical value that expresses the ratio of the partial pressures of the products to the partial pressures of the reactants at equilibrium for a given reaction at a specific temperature. For the reaction CH4(g) + I2(g) ⇌ CH3I(g) + HI(g), Kp is calculated using the formula Kp = (P_CH3I * P_HI) / (P_CH4 * P_I2). A small Kp value indicates that at equilibrium, the reaction favors the reactants over the products.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. In the context of the reaction, the initial partial pressures of methane and iodine are given, and these values will change as the reaction progresses towards equilibrium. The total pressure of the system is the sum of the partial pressures of all gases present, and understanding how these pressures change is crucial for calculating equilibrium concentrations.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations (or pressures), the changes that occur as the reaction proceeds, and the equilibrium concentrations (or pressures) of the reactants and products. By setting up an ICE table for the given reaction, one can systematically determine how the initial pressures of CH4 and I2 change as the system reaches equilibrium, allowing for the calculation of the equilibrium pressures of all species involved.

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