Equilibrium Constant Kp

Question

A 79.2 g chunk of dry ice (solid CO2) and 30.0 g of graphite (carbon) were placed in an empty 5.00 L container, and the mixture was heated to achieve equilibrium. The reaction is

CO2(g)+C(s)⇌2CO(g). What is the value of Kp at 1100 K if the gas density at 1100 K is 16.9 g/L?

This question is confusing me, because it's a part of a two part problem and I got the first part correct. The first part asked for the value of Kp at 1000 K and a gas density of 16.3 g/L, so slightly different values, and what I did was convert the masses into moles and set up an ICE table. The resulting values from the table were 1.8-x for CO2, 2.5-x for C (which we can disregard after this since it's solid) and 2x for 2CO, leading to an equation where I set up these mole equations equal to the total amount of gas which was found by multiplying density by the volume. It looked like this: 81.5=(1.8-x)(44)+(2x)(28). Then, I found x, subtracted it and multiplied it respectively to find the amount of equilibrium moles for each gaseous substance, and plugged those both into P=nrt/v to find their partial pressures. Finally, I put them in the Kp form where PCO^2/PCO2 and I got Kp = 1.5, which was correct.

HOWEVER, when I did the same thing but switching out the density and the temperature I got 10.37, which is apparently wrong. Where did I mess up, given I solved the very similar problem correctly? How do you do this? Thanks a million in advance.

Answer 1

I basically followed the procedure you used but got a different result. Here are my steps.

Moles of CO2 at equilibrium = 1.8 – X where X is moles CO2 reacted.

Moles of CO at equilibrium = 2X

Grams of CO2 at equil. = (1.8 – X) x 44

Grams of CO at equil. = 2X(28)

Total grams of gases at equil. = 16.9 g/L x 5 = 84.5 g

Solve (1.8 – X) x 44 + 2X (28) = 84.5 for X

X= 0.44 moles CO2 reacted

Moles of CO2 at equil. = (1.8 – 0.44) = 1.79 moles

Moles of CO at equil = 2 x X = 0.88 moles

Pco2 = 1.79 moles x 0.082 Latm/mol° x 1100K / 5L = 32.3 atm

Pco = 0.88 x 0.082 x 1100 / 5 = 15.9

Kp = 15.9^2 / 32.3 = 7.8

Check my math and let me know if this answer is correct. Thanks.