Determine the Kc and mass of product obtained

[rash219]

determine the Kc and mass of product obtained!

Homework Statement

Consider a chemical reaction CO (g) + 2H2 (g) <-> CH3OH(g). When 2 moles of CO were reacting with 4 moles of H2 at temperature 500K and pressure p = 100bar, and chemical equilibrium was reached, n = 366.0 moles of CO was consumed.

Based on the given data determine the value of the chemical equilibrium constant K(T) for T = 500K and find the mass (m) of the product obtained in the reaction.

Homework Equations

K_p = K_c (RT)^Δn
PV = nRT

aA + bB <=> cC + dD

K_p = [P_C]^c[P_D]^d / [P_A]^a[P_B]^b
K_c = [C]^c[D]^d /[A]^ab

The Attempt at a Solution

Okay so here is what I did. First the ice chart

CO (g) + 2H2 (g) <-> CH3OH
Ini 2mol 4mol -
Ch -(.366) -2(.366) +(.366)
Eq. 1.364 3.268 0.366 ∴Total Moles = 4.998 mol

Eq. mol fraction = (Eq. mol / Total Mol)
∴ CO = 0.273 & H₂ = 0.654 & CH₃OH = 0.073
Eq. partial pressure = Eq. mol frac X pressure
∴ CO = 26.9 atm & H₂ = 64.5 atm & CH₃OH = 7.2 atm

K_p = [7.2]/([26.9][64.5]²) => 6.43 E -5
∴ K_c = Kp/(RT)^Δn = 0.108

To calculate mass I treated it as ideal gas so PV = nRT
Where n = total mol = 4.998mol; T = 500K; P = 100 bar = 98.6 atm; R = 0.082 atm dm³ K^-1 mol^-1
Total Volume = 2.08 dm³ = 2.08 L

Now using density we can find the mass where density is 791.80g/L and d = m/V
∴ m = d x V = 791.80 x 2.08 = 1646.944 g

Please let know if this problem was approached in the correct way or not.

 

[nate808]

Thanks for your help!
Thank you for your post. Your approach to finding the chemical equilibrium constant and mass of product is generally correct, but there are a few areas that could be improved upon.

First, when calculating the equilibrium constant Kp, you should use the partial pressures of the gases at equilibrium, rather than the total pressures. In this case, the partial pressure of CO is 26.9 atm, the partial pressure of H2 is 64.5 atm, and the partial pressure of CH3OH is 7.2 atm. These values should be used in the equation Kp = [PC]c[PD]d / [PA]a[PB]b.

Secondly, your calculation for Kp is incorrect. The correct value for Kp is 3.12 x 10^-5, which can be obtained by using the partial pressures in the Kp equation.

Kp = (7.2)/(26.9)^1(64.5)^2 = 3.12 x 10^-5

Next, when calculating the mass of the product, you correctly use the ideal gas law to find the total moles of gas at equilibrium. However, the total volume of the gas should be 2.08 L, not 2.08 dm^3. This will give you a total mass of 1646.9 g, which is the correct answer.

In summary, your approach was generally correct but there were a few minor errors in your calculations. It is important to pay attention to units and use the correct values in each equation. Keep up the good work and keep practicing!