Question

Consider the following reaction:

CO(g) + 2H2(g) ⇌ CH3OH(g)
The reaction between CO and H2 is carried out at a specific temperature with initial concentrations of CO = 0.27 M and H2H2 = 0.55 M. At equilibrium, the concentration of CH3OH is 0.10 M.
Find the equilibrium constant at this temperature.
a) 0.20
b) 0.40
c) 0.80
d) 1.60
e) none of these

Answer 1

The equilibrium constant (K) for the reaction CO(g) + 2H2(g) ⇌ CH3OH(g) given the concentrations at equilibrium is approximately 0.80. This is found by using the expression for K and substituting the equilibrium concentrations for CO, H2, and CH3OH into the formula.

Step-by-step explanation:

The student has asked about finding the equilibrium constant (K) for the reaction CO(g) + 2H2(g) ⇌ CH3OH(g) at a specific temperature, given the initial concentrations of reactants and the concentration of CH3OH at equilibrium. To find the equilibrium constant, we can use the expression K = [CH3OH] / ([CO][H2]^2), where the values are the concentrations at equilibrium. Substituting the given equilibrium concentration of CH3OH (0.10 M) and calculating the changes in concentrations of CO and H2 from the initial values, we can solve for K.

Since CH3OH is 0.10 M at equilibrium, the change in concentration of CH3OH is +0.10 M. This means that the changes in CO and H2 must be −0.10 M and −0.20 M, respectively, based on the stoichiometry of the reaction. Thus, the equilibrium concentrations of CO and H2 would be 0.17 M (0.27 − 0.10) and 0.35 M (0.55 − 2*0.10), respectively. The equilibrium constant K is then calculated as K = [CH3OH] / ([CO][H2]^2) = 0.10 / (0.17 * 0.35^2) which equals approximately 0.80, making option (c) the correct answer.