Pure phosgene gas (COCl2), .03mole, was placed in a 1.5 L container. It was heated to 800k, and at equilibrium the pressure of CO was found to be .497 atm. Calculate the equilibrium constant Kp for the reaction
CO(g) + Cl2(g) = COCL2(g)
Never mind I got it. I was just not seeing the PV=nRT relationship here lol. Thanks anyways.
Ah! I have the same question. Could you explain it?
Paul--I worked this problem further up the board for Adam. Go to 1:53 PM and post by Adam (chemistry) to find it.
To calculate the equilibrium constant Kp for the given reaction, we need to know the number of moles of CO(g) and Cl2(g) present at equilibrium.
First, let’s find the number of moles of CO(g) using the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
Rearranging the equation to solve for n, we have:
n = PV/(RT)
Given:
Pressure of CO(g) = 0.497 atm
Volume = 1.5 L
Temperature = 800 K
Now let’s calculate the number of moles of CO(g):
nCO = (0.497 atm) * (1.5 L) / (0.0821 L·atm/(mol·K) * 800 K)
nCO = 0.00925 moles
Since the stoichiometry of the reaction states that the ratio of CO:Cl2:COCl2 is 1:1:1, we can conclude that the moles of CO(g) equals the moles of COCl2(g) at equilibrium. Therefore, the number of moles of COCl2(g) is also 0.00925 moles.
Now that we have the moles of CO(g) and COCl2(g) at equilibrium, we can calculate Kp.
Kp is defined as the ratio of the partial pressures of the products raised to their stoichiometric coefficients to the partial pressures of the reactants raised to their stoichiometric coefficients, each raised to the power of their respective coefficients.
Kp = (P(COCl2))^1 / (P(CO))^1 * (P(Cl2))^1
Given:
P(COCl2) = 0.497 atm (from the problem statement)
P(CO) = 0.497 atm (since moles of CO(g) equals moles of COCl2(g))
P(Cl2) = unknown
To calculate P(Cl2), we can use the ideal gas law equation again:
n(Cl2) = PV/(RT)
n(Cl2) = (P(Cl2)) * (1.5 L) / (0.0821 L·atm/(mol·K) * 800 K)
Since the stoichiometry of the reaction states that the ratio of CO:Cl2:COCl2 is 1:1:1, we can conclude that the number of moles of Cl2(g) is equal to the number of moles of CO(g) and COCl2(g) at equilibrium, which is 0.00925 moles.
Now, we can calculate P(Cl2):
n(Cl2) = (P(Cl2)) * 1.5 L / (0.0821 L·atm/(mol·K) * 800 K)
0.00925 moles = (P(Cl2)) * 1.5 L / (0.0821 L·atm/(mol·K) * 800 K)
Solving for P(Cl2):
P(Cl2) = (0.00925 moles * 0.0821 L·atm/(mol·K) * 800 K) / 1.5 L
P(Cl2) ≈ 0.405 atm
Now we have all the values to calculate Kp:
Kp = (0.497 atm)^1 / (0.497 atm)^1 * (0.405 atm)^1
Kp ≈ 1.205
Therefore, the equilibrium constant Kp for the reaction CO(g) + Cl2(g) = COCl2(g) is approximately 1.205.