4) The equilibrium constant, Kc, is 3.2 x 10-34 at 25 °C for the reaction represented below.
2 HCl(g) = H2(g) + Cl2(g)
a. Write the equilibrium expression, Kc, for the reaction.
b. Suppose you start out with only reactants in a rigid container at 25°C. The
initial concentration of HCl(g) is measured to be 0.375 M. What are the
concentrations of each gas when the system reaches equilibrium?

a. Kc = [H2] [Cl2] / [HCl]²

b. [H2] = 6.7x10⁻¹⁸M

[Cl2] = 6.7x10⁻¹⁸M

HCl ≈ 0.375M

Explanation:

a. The expression, Kc, is defined as the ratio of the concentrations of the products over reactants powered to its coefficients. For the reaction, Kc is:

b. If you start with a concentration of HCl of 0.375M, the concentrations in equilibrium are:

[H2] = X

[Cl2] = X

[HCl] = 0.375M - 2X

Where X is reaction coordinate

Replacing:

3.2x10⁻³⁴ =  [X] [X] / [0.375M - 2X]²

3.2x10⁻³⁴ =  X² / 0.140625 - 1.5 x + 4 X²

4.5x10⁻³⁵ - 4.8x10⁻³⁴X + 1.28x10⁻³³X² = X²

4.5x10⁻³⁵ - 4.8x10⁻³⁴X - X² = 0

Solving for X:

X = -6.7x10⁻¹⁸. False solution, there is no negative concentrations

X = 6.7x10⁻¹⁸M

Thus:

[H2] = 6.7x10⁻¹⁸M

[Cl2] = 6.7x10⁻¹⁸M

HCl ≈ 0.375M

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