At a certain temperature, the reaction
CO(g) + 2H2(g) <===> CH3OH(g) has Kc = 0.500. If a reaction mixture at equilibrium contains 0.00436 M CH3OH and 0.220 M H2, what is the equilibrium concentration of CO?
The answer is 0.280 M. I don't know how to get it.
Thanks a lot! =) Very helpful.
sorry 0.180
Thanks for posting the correct answer. I was posting that the book had an error. Here is how you do it.
Kc = (CH3OH)/(H2)^2(CO)
Solve for (CO) = (CH3OH)/Kc(H2)^2
(CO) = (0.00436)/0.500*(0.22)^2
(CO) = 0.18017 which rounds to 0.180 to 3 s.f.
To find the equilibrium concentration of CO, we can use the concept of the equilibrium constant (Kc) and the stoichiometry of the balanced chemical equation. Here's how you can solve it step by step:
1. Write the balanced chemical equation for the given reaction:
CO(g) + 2H2(g) <===> CH3OH(g)
2. Determine the stoichiometric ratio of the reactants and the product:
From the balanced equation, we can see that for every one mole of CO, two moles of H2 are required to produce one mole of CH3OH.
3. Set up an ICE (initial, change, equilibrium) table:
We start by filling in the initial concentrations of the reactants and product. In this case, the initial concentration of CH3OH is given as 0.00436 M, and the initial concentration of H2 is given as 0.220 M. Since we don't have any CO initially, its initial concentration is 0 M.
Initial concentrations:
CO: 0 M
H2: 0.220 M
CH3OH: 0.00436 M
4. Define the change and equilibrium concentrations:
Let's assume x moles of CO react to produce x moles of CH3OH. Since two moles of H2 are required per mole of CO that reacts, 2x moles of H2 will be consumed. Thus, the change in concentration for CO will be -x, and for H2, it will be -2x. The change in concentration for CH3OH will be +x.
Therefore, the equilibrium concentrations will be:
CO: 0 - x = -x M
H2: 0.220 - 2x M
CH3OH: 0.00436 + x M
5. Write the expression for the equilibrium constant:
Kc = [CH3OH] / ([CO] * [H2]^2)
Plug in the given Kc value: 0.500.
6. Substitute the equilibrium concentrations into the Kc expression:
0.500 = (0.00436 + x) / (-x * (0.220 - 2x)^2)
7. Solve the equation for x:
Rearrange the equation and solve for x:
0.500 * (-x * (0.220 - 2x)^2) = 0.00436 + x
-0.440x^3 + 1.1444x^2 - 0.22209x + 0.00436 = 0
This equation is a cubic equation, and solving it can be complex. To simplify the calculation, you can use online cubic equation solvers or graphing calculators to find the value of x.
8. Once you have found the value of x, substitute it back into the equilibrium concentrations for CO to find the equilibrium concentration:
CO = -x
For example, if x = 0.280 M, then CO = -0.280 M.
Therefore, the equilibrium concentration of CO is 0.280 M.