Steam reforming of methane ( CH4 ) produces "synthesis gas," a mixture of carbon monoxide gas and hydrogen gas, which is the starting point for many important industrial chemical syntheses. An industrial chemist studying this reaction fills a 125L tank with 20 mol of methane gas and 10 mol of water vapor at 38 degrees celsius. He then raises the temperature, and when the mixture has come to equilibrium measures the amount of hydrogen gas to be 18 mol . Calculate the concentration equilibrium constant for the steam reforming of methane at the final temperature of the mixture. Round your answer to significant digits.

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:

[tex]Kc = \frac{[H_2]^4*[CO_2]}{[H_2O]^2*[CH_4]}[/tex]

[tex]Kc = \frac{(0.144)^4*0.036}{(0.008)^2*0.124}[/tex]

Kc = 1.9