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In a study of the reaction

\[3Fe(s) + 4H_2O(g) \leftrightarrow Fe_3O_4(s) + 4H_2(g)\]

at 1200 K, it was observed that when the equilibrium partial pressure of water vapor is 15.0 torr, the total pressure at equilibrium is 36.3 torr.

Calculate the value of \(K_p\) for this reaction at 1200 K.

(Hint: Apply Dalton's law of partial pressures.)

Answer :

Final answer:

To calculate the equilibrium constant (Kp) for the reaction, we apply Dalton's law of partial pressures and use the given information on total and partial pressures. The equilibrium equation for this reaction is used to solve for Kp.

Explanation:

The question refers to the study of a reaction 3Fe(s) + 4H₂O(g)⇌Fe₃O₄(s) + 4H₂(g), and we are asked to calculate the equilibrium constant, Kp, at a certain temperature (1200K), using Dalton's law of partial pressures. The total pressure at equilibrium and the partial pressure of the water vapor are given.

Turning to Dalton's law says that the total pressure exerted by a mix of non-reacting gases is equal to the sum of the partial pressures of those gases. Hence, in this case, the partial pressure of H₂ can be found by subtracting the partial pressure of water from the total pressure: 36.3 torr - 15.0 torr = 21.3 torr.

With these values, we can build the equilibrium expression for Kp: Kp = (PFe3O4 * PH2^4) / (PFe^3 * PH2O^4). As the reaction does not explicitly produce Fe3O4, its partial pressure is considered to be zero. With substituted values, Kp = (21.3 torr)^4 / (15.0 torr)^4.

Solving this equation gives us the value of Kp at 1200 K.

Learn more about Equilibrium constants here:

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