To determine the equilibrium partial pressures of carbon monoxide (CO) and carbon dioxide (CO2) in the reaction where iron(II) oxide (FeO) is reduced by CO, we can utilize the equilibrium constant expression and the initial conditions provided. The reaction can be represented as follows:
The Reaction and Equilibrium Constant
The balanced chemical equation is:
FeO (s) + CO (g) ⇌ Fe (s) + CO2 (g)
The equilibrium constant expression for this reaction is given by:
Kp = (P_CO2) / (P_CO)
Where:
- P_CO2 is the partial pressure of carbon dioxide at equilibrium.
- P_CO is the partial pressure of carbon monoxide at equilibrium.
Given that Kp = 0.265 atm at 1050 K, we can use this information along with the initial partial pressures to find the equilibrium values.
Initial Conditions
The initial partial pressures are:
- P_CO = 1.4 atm
- P_CO2 = 0 atm (since it is not mentioned, we assume it starts from zero)
Change in Partial Pressures
As the reaction proceeds towards equilibrium, let’s denote the change in the partial pressure of CO that reacts as x. Therefore, at equilibrium, we can express the partial pressures as:
- P_CO = 1.4 - x
- P_CO2 = 0 + x = x
Setting Up the Equation
Substituting these expressions into the equilibrium constant equation gives us:
Kp = (P_CO2) / (P_CO) = x / (1.4 - x)
Now, substituting the value of Kp:
0.265 = x / (1.4 - x)
Solving for x
To solve for x, we can cross-multiply:
0.265(1.4 - x) = x
Expanding this gives:
0.371 - 0.265x = x
Now, combine like terms:
0.371 = x + 0.265x
0.371 = 1.265x
Now, solve for x:
x = 0.371 / 1.265 ≈ 0.293 atm
Calculating Equilibrium Partial Pressures
Now that we have the value of x, we can find the equilibrium partial pressures:
- P_CO = 1.4 - x = 1.4 - 0.293 ≈ 1.107 atm
- P_CO2 = x = 0.293 atm
Final Results
At equilibrium, the partial pressures at 1050 K are approximately:
- P_CO ≈ 1.107 atm
- P_CO2 ≈ 0.293 atm
This analysis shows how the initial conditions and the equilibrium constant interact to determine the final state of the system. Understanding these relationships is crucial in chemical equilibrium and industrial processes like steel production.
