Answer:
1.9
Explanation:
The reaction that occurs is:
CH₄(g) + 2H₂O(g) ⇄ CO₂(g) + 4H₂(g)
The equilibrium is achieved when the velocity of the formation of the reactants is equal to the velocity of the formation of the reactants, thus the concentrations remain equal. It can be characterized by the concentration equilibrium constant (Kc), or by the pressure equilibrium constant (Kp).
Both of them depend on the activity of the substances, but for Kc, it is substituted by the concentration, and at Kp, by the partial pressure. The activity of solids and pure liquids (as water) is equal to 1, so they are not used in the calculus. Kp is calculated only the gas substances.
So, to know the Kc, we need to now the equilibrium concentrations, so let's make an equilibrium chart:
CH₄(g) + 2H₂O(g) ⇄ CO₂(g) + 4H₂(g)
20 mol 10 mol 0 0 Initial
-x -2x +x +4x Reacts (stoichiometry is 1:2:1:4)
20-x 10-2x x 4x Equilibrium
4x = 18
x = 4.5 mol
So, the amount of the gases are:
nCH₄ = 20 - 4.5 = 15.5 mol
nH₂O = 10 - 2*4.5 = 1 mol
nCO₂ = 4.5 mol
nH₂ = 18 mol
The concentration is the number of moles divided by the volume (125 L), so:
[CH₄] = 15.5/125 = 0.124 M
[H₂O] = 1/125 = 0.008 M
[CO₂] = 4.5/125 = 0.036 M
[H₂] = 18/125 = 0.144 M
Kc is the ratio of the multiplication of the concentration of the products by the multiplication of the concentration of the reactants, each concentration elevated by the substance coefficient, so:
Kc = 1.9