H₂ (g) + CO₂ (g) ⇌ H₂O (g) + CO (g)
Initially, a sealed vessel contained only H₂ (g) with a partial pressure of 6 atm and CO₂ (g) with a partial pressure of 4 atm. The reaction above was allowed to come to equilibrium at a temperature of 700 K. At equilibrium, the partial pressure due to CO (g) was found to be 2 atm. What is the value of the equilibrium constant, Kp, for the reaction?
..................H₂ (g) + CO₂ (g) ⇌ H₂O (g) + CO (g)
I.................6 atm........4...............0...............0
C................-p..............-p.............+p............+p
E.................6-p...........4-p..............p..............p
The problem tells you that at equilibrium p = 2; therefore, at equilibrium (the E line), H2 is 6-2 = 4; 4-2 = 2. Substitute these values into Kp expression and solve for Kp.
Post your work if you get stuck.
bibv
To find the value of the equilibrium constant, Kp, for the reaction, we need to use the equilibrium expression and the given partial pressures.
The equilibrium expression for this reaction is:
Kp = (P(H2O) * P(CO)) / (P(H2) * P(CO2))
Let's substitute the given values into the expression:
P(H2) = 6 atm
P(CO2) = 4 atm
P(H2O) = Unknown
P(CO) = 2 atm
Now, we can rearrange the equilibrium expression to solve for P(H2O):
P(H2O) * P(CO) = (P(H2) * P(CO2)) / Kp
Substituting the known values:
P(H2O) * 2 atm = (6 atm * 4 atm) / Kp
Simplifying further:
P(H2O) = (24 atm²) / (2 * Kp)
P(H2O) = (12 atm²) / Kp
Since we only need the value of Kp, we can set up a ratio:
Kp = (12 atm²) / P(H2O)
To find the value of P(H2O), we can use the total pressure expression.
Total pressure = P(H2) + P(CO2) + P(H2O) + P(CO)
Given that the initial total pressure is equal to the equilibrium total pressure:
6 atm + 4 atm + P(H2O) + 2 atm = total pressure
Since we don't know the total pressure, we can use the ideal gas law:
PV = nRT
Assuming the number of moles and volume remain constant, we can rewrite the equation as:
P = (nRT) / V
Therefore, the total pressure can be calculated using the ideal gas law with the given temperature of 700 K.
Once you find the total pressure, substitute it into the equation for P(H2O) to get its value. Finally, substitute P(H2O) into the equation for Kp to find its value.
Note: The unit of pressure should be consistent throughout the calculations (e.g., atm).