Method for getting correct answer for this? Thank you! A mixture containing an initial concentration of 0.1877 M for H2 and 0.1432 M for Cl2 is allowed to come to equilibrium (see reaction below). What must be the equilibrium concentration of HCl?
H2(g) + Cl2(g) ↔ 2HCl(g) Kc = 5.00e16
a. 0.1432 M
b. 0.0716 M
c. 0.2864 M
d. 0.0865 M
........H2 + Cl2 ==> 2HCl
I...0.1877.0.1432......0
C.......-x....-x.......2x
E...0.1877-x.0.1432-x..2x
Substitute the E line into Kc expression and solve for x, then evaluate each individual term.
To find the equilibrium concentration of HCl, we can use the balanced equation and the equilibrium constant, Kc.
The balanced equation is:
H2(g) + Cl2(g) ↔ 2HCl(g)
The equilibrium constant expression is:
Kc = [HCl]^2 / ([H2] * [Cl2])
Given initial concentrations:
[H2] = 0.1877 M
[Cl2] = 0.1432 M
Let's substitute these values into the equation:
Kc = [HCl]^2 / (0.1877 * 0.1432)
Now, let's solve for [HCl]:
[HCl]^2 = Kc * (0.1877 * 0.1432)
[HCl]^2 = (5.00e16) * (0.1877 * 0.1432)
[HCl]^2 = (5.00e16) * (0.02684824)
[HCl]^2 = 1.342e15
Taking the square root of both sides, we get:
[HCl] = √(1.342e15)
[HCl] ≈ 1.159e8
Therefore, the equilibrium concentration of HCl is approximately 1.159 x 10^8 M.
None of the given answer choices match this value.
To find the equilibrium concentration of HCl, we need to use the equilibrium expression and the stoichiometry of the balanced chemical equation.
The equilibrium expression for the given reaction is:
Kc = [HCl]^2 / ([H2] * [Cl2])
where [HCl], [H2], and [Cl2] represent the equilibrium concentrations of HCl, H2, and Cl2, respectively.
The initial concentration of H2 is given as 0.1877 M and the initial concentration of Cl2 is given as 0.1432 M.
Let's assume the equilibrium concentration of HCl as x M. Since the stoichiometry of the balanced chemical equation is 1:1:2 for H2, Cl2, and HCl respectively, the equilibrium concentration of H2 and Cl2 will also be x M.
Substituting these values into the equilibrium expression:
Kc = (x)^2 / (x * x) = x^2/x^2 = 1
Since the value of Kc is given as 5.00e16, which is very large compared to 1, it means that the forward reaction is favored. This implies that the reactants, H2 and Cl2, are mostly converted to products, and the equilibrium concentration of HCl must be greater than the initial concentrations of H2 and Cl2.
Looking at the answer choices:
a. 0.1432 M (the initial concentration of Cl2) is less than the equilibrium concentration of HCl, so it can be eliminated.
b. 0.0716 M is half of the initial concentration of Cl2, so it can also be eliminated.
d. 0.0865 M is less than the initial concentration of H2, so it can be eliminated.
The correct answer is:
c. 0.2864 M, which is twice the initial concentration of Cl2 and equal to the equilibrium concentration of HCl.
Therefore, the equilibrium concentration of HCl must be 0.2864 M.