Consider the reaction: CO2(g) + H2(g) ↔ CO(g) + H2O(g), for which Kc = 0.64 at 900 K. If the initial CO2 and of H2 are each 0.100 M, what will be the equilibrium concentrations of each species after the reaction reaches equilibrium?
................CO2(g) + H2(g) ↔ CO(g) + H2O(g)
initial.........0.1.............0.1..........0.............0
Change.......-x...............-x...........x.............x
Equilibrium..0.1-x.......0.1-x..........x.............x
Kc = (CO)(H2O)/(CO2)(H2) = 0.64
Plug in the values for Kc, and from the Eline of the ICE table, solve for x, then evaluate of the four terms in the E line.
Post your work if you get stuck.
To find the equilibrium concentrations of each species, we need to make an ICE (Initial, Change, Equilibrium) table and use the given equilibrium constant (Kc) value.
The balanced chemical equation for the reaction is: CO2(g) + H2(g) ↔ CO(g) + H2O(g)
Initial concentrations:
CO2 = 0.100 M
H2 = 0.100 M
CO = 0 M (since it's not present initially)
H2O = 0 M (since it's not present initially)
Let's assume x mol/L of CO2 and H2 react to produce x mol/L of CO and H2O.
Change:
CO2(g) + H2(g) ↔ CO(g) + H2O(g)
- x - x + x + x
Equilibrium concentrations:
CO2 = 0.100 - x M
H2 = 0.100 - x M
CO = x M
H2O = x M
The equilibrium constant expression for this reaction is:
Kc = [CO][H2O] / [CO2][H2]
Given Kc = 0.64, we can substitute the equilibrium concentrations into the expression:
0.64 = (x * x) / ((0.100 - x) * (0.100 - x))
Solving this equation is a quadratic equation. By rearranging and solving for x, we find x ≈ 0.037 M.
Now we can substitute this value of x into the equilibrium concentrations:
CO2 = 0.100 - 0.037 ≈ 0.063 M
H2 = 0.100 - 0.037 ≈ 0.063 M
CO = 0.037 M
H2O = 0.037 M
Therefore, at equilibrium, the concentrations of each species will be approximately:
CO2 ≈ 0.063 M
H2 ≈ 0.063 M
CO ≈ 0.037 M
H2O ≈ 0.037 M
To determine the equilibrium concentrations of each species after the reaction reaches equilibrium, we can use the expressions for the equilibrium concentrations derived from the reaction stoichiometry and the given equilibrium constant (Kc).
Let's denote the equilibrium concentrations of CO2, H2, CO, and H2O as [CO2], [H2], [CO], and [H2O] respectively.
From the balanced equation, we can see that the stoichiometric coefficient of CO2 is 1, H2 is 1, CO is 1, and H2O is also 1.
At equilibrium, according to the law of chemical equilibrium, the ratio of the product concentrations to the reactant concentrations raised to their stoichiometric coefficients will be equal to the equilibrium constant (Kc).
Therefore, we can write the equation based on the given equilibrium constant and the concentrations at equilibrium as:
Kc = ([CO] * [H2O]) / ([CO2] * [H2])
Now let's substitute the given values into the equation:
Kc = 0.64
[CO] = x (unknown equilibrium concentration)
[H2O] = x (unknown equilibrium concentration)
[CO2] = 0.100 M (initial concentration)
[H2] = 0.100 M (initial concentration)
0.64 = (x * x) / (0.100 * 0.100)
Solving this equation will give us the value of x, which represents the equilibrium concentration of both CO and H2O.
0.64 = x^2 / 0.010
x^2 = 0.064
x = √(0.064)
x ≈ 0.253 M
So, the equilibrium concentrations of CO and H2O are approximately 0.253 M.
Since the stoichiometric ratio is 1:1, the equilibrium concentrations of CO2 and H2 will be the same as their initial concentrations, which is 0.100 M.
Therefore, the equilibrium concentrations of each species after the reaction reaches equilibrium are approximately:
[CO2] ≈ 0.100 M
[H2] ≈ 0.100 M
[CO] ≈ 0.253 M
[H2O] ≈ 0.253 M