The reaction CO(g) + H2O(g)--> CO2(g) + H2(g) has Kc = 102 at 500 K. If a reaction mixture initially contains 0.154 M CO and 0.154 M H2O, what will be the equilibrium concentration of H2?
To find the equilibrium concentration of H2, we first need to set up an ICE (Initial, Change, Equilibrium) table and use the given values and stoichiometry of the reaction.
The balanced equation for the reaction is:
CO(g) + H2O(g) -> CO2(g) + H2(g)
Using the ICE table, we can set up the equation:
Initial concentrations: CO + H2O -> CO2 + H2
0.154 M 0.154 M 0 M 0 M
Change in concentrations: -x -x +x +x
Equilibrium concentrations: CO - x H2O - x CO2 + x H2 + x
By using the stoichiometry of the reaction, we know that the change in concentration of H2 is equal to the change in concentration of CO because the coefficients are the same. Therefore, we can write:
x = [H2] = [CO]
Substitute the known values into the Kc expression:
Kc = [CO2][H2]/[CO][H2O]
102 = (x)(x)/(0.154 - x)(0.154)
At equilibrium, we can assume that x is very small compared to 0.154, so we can approximate:
102 = (x)(x)/(0.154)(0.154)
102 = (x^2)/(0.023716)
Rearranging the equation to solve for x:
x^2 = 102 * 0.023716
x^2 = 2.419432
x = 1.555
Since the value of [H2] is equal to x, the equilibrium concentration of H2 is 1.555 M.
To determine the equilibrium concentration of H2 in the reaction mixture, we will use the equation and the equilibrium constant.
The reaction is given by the equation: CO(g) + H2O(g) --> CO2(g) + H2(g)
The equilibrium constant, Kc, is 102 at 500 K. The equilibrium expression is written as follows:
Kc = [CO2] * [H2] / [CO] * [H2O]
Given that the initial concentrations of CO and H2O are both 0.154 M, we can assume that they will react to reach the equilibrium state.
Let's assume that at equilibrium, the concentration of H2 is x M.
Using the equilibrium expression, we can express the concentrations of CO2, CO, and H2O in terms of x:
[CO2] = 0 M (because CO and H2O are the reactants and there is no CO2 initially)
[H2] = x M (the concentration we need to find)
[CO] = 0.154 M - x M (initial concentration minus the amount that reacts)
[H2O] = 0.154 M - x M (initial concentration minus the amount that reacts)
Now, plug these values into the equilibrium expression:
Kc = [CO2] * [H2] / [CO] * [H2O]
102 = (0 M) * (x M) / (0.154 M - x M) * (0.154 M - x M)
Since [CO2] and [H2] are both zero and anything multiplied by zero is zero, we can simplify the equation to:
102 = 0 / (0.154 - x) * (0.154 - x)
To solve for x, we can cross-multiply and rearrange the equation:
0 = 102 * (0.154 - x)^2
Solving for x gives:
(0.154 - x)^2 = 0
Taking the square root of both sides, we get:
0.154 - x = 0
Rearranging the equation to isolate x yields:
x = 0.154
Therefore, at equilibrium, the concentration of H2 will be 0.154 M.