Answer:
See explanation below
Step-by-step explanation:
Let's write the equation again:
CO(g) + Cl2(g) <--------> COCl2(g) Kp = 1.57
And we have the innitial partial pressure of the reactants, which means that we do not have COCl2 yet.
In order to calculate the partial pressure of all species in equilibrium, we need to do an ICE chart, and then, write the expression for the equilibrium constant and solve for the partial pressures.
The ICE chart:
CO(g) + Cl2(g) <--------> COCl2(g) Kp = 1.57
I: 1.65 1.65 0
C: -x -x +x
E: 1.65-x 1.65-x x
The expression for Kp:
Kp = PpCOCl2 / PpCl2 * PpCO
Replacing the values:
1.57 = x / (1.65-x)² ---> Now we have to solve for x here:
1.57(2.7225 - 3.3x + x²) = x
4.2743 - 5.181x + 1.57x² = x
1.57x² - 6.181x + 4.2743 = 0
Now, at this point, we use the general formula to calculate x from a quadratic equation:
x = -b ±√b² - 4ac / 2a
From the equation, we have: a = 1.57; b = -6.181; c = 4.2743
x = 6.181 ±√(6.181²) - 4*1.57*4.2743 / 2*1.57
x = 6.181 ±√38.2048 - 26.8426 / 3.14
x = 6.181 ±√11.3622 / 3.14
x = 6.181 ± 3.371 / 3.14
x1 = 6.181 - 3.371 / 3.14 = 0.89
x2 = 6.181 + 3.371 / 3.14 = 3.04
Now, looking at the values of the innitial pressure, these values are <2, so X2 cannot be the value we are looking, instead, it has to be x1, cause is <1 and the calculations make sense. Therefore the partial pressure at equilibrium for each species are:
PpCO = PpCl2 = 1.65 - 0.89 = 0.76 atm
PpCOCl2 = 0.89 atm