If C + CO2 <--> Co, when equilibirum is established at 1000 K, the total pressure in the system is 4.70 atm. If Kp= 1.72, what are the partial pressures of CO and CO2?
C(g) + CO2(g) ==> CO(g)
Kp = 1.72 = pCO/pCO2
I would set up an ICE chart where p = pressure of CO and 4.70 = pressure CO2 at equilibrium. Substitute into Kp expression and solve for p.
To determine the partial pressures of CO and CO2 in the given equilibrium reaction, you can use the equilibrium constant expression, Kp, along with the total pressure of the system.
The equilibrium constant expression for the given reaction is:
Kp = (P(Co) / P(C)) * (P(CO2) / P(CO))
Where P(Co), P(C), P(CO2), and P(CO) are the partial pressures of CO, C, CO2, and CO, respectively.
Given information:
Total pressure (P(total)) = 4.70 atm
Kp = 1.72
Since the total pressure is given, we know that P(total) is the sum of the partial pressures of all the gases in the system:
P(total) = P(Co) + P(C) + P(CO2) + P(CO)
Since C and CO2 are reactants, and Co is the product, we can assume that the partial pressures of C and CO2 are small compared to the total pressure and can be neglected. Therefore, we can rewrite the equation as:
P(total) ≈ P(Co) + P(CO)
Now, rearranging the Kp expression gives:
Kp = (P(Co) / P(C)) * (P(CO2) / P(CO))
1.72 = (P(Co) / P(CO)) * (P(CO2) / P(C))
Since P(Co) and P(CO) are the only nonzero partial pressures, we can set them equal to x for simplicity.
1.72 = (x / x) * (P(CO2) / P(C))
1.72 = P(CO2) / P(C)
Also, using the equation P(total) = P(Co) + P(CO), we have:
4.70 = x + x
4.70 = 2x
x = 4.70 / 2
x = 2.35
Now, substitute the value of x back into the equation:
1.72 = P(CO2) / P(C)
1.72 = P(CO2) / 2.35
Cross-multiplying:
1.72 * 2.35 = P(CO2)
4.04 = P(CO2)
Therefore, the partial pressure of CO2 is approximately 4.04 atm.
Since the total pressure is the sum of the partial pressures, you can find the partial pressure of CO by subtracting the partial pressure of CO2 from the total pressure:
P(CO) = P(total) - P(CO2)
P(CO) = 4.70 - 4.04
P(CO) = 0.66
Therefore, the partial pressure of CO is approximately 0.66 atm.
In summary, the partial pressure of CO is approximately 0.66 atm, and the partial pressure of CO2 is approximately 4.04 atm.