The dissociation of molecular iodine into iodine atoms is represented as i2(g) ⇌ 2i(g) at 1000 k, the equilibrium constant kc for the reaction is 3.80 × 10−5. suppose you start with 0.0456 mol of i2 in a 2.28−l flask at 1000 k. what are the concentrations of the gases at equilibrium? what is the equilibrium concentration of i2

First, we must write the balanced chemical equation for the process:

I₂ (g) ⇌ 2I (g)

The chemical reactions that occur in a closed container can reach a state of chemical equilibrium that is characterized because the concentrations of the reactants and products remain constant over time. The equilibrium constant of a chemical reaction is the value of its reaction quotient in chemical equilibrium.

The equilibrium constant (Kc) is expressed as the ratio between the molar concentrations (mol/L) of reactants and products. Its value in a chemical reaction depends on the temperature, so it must always be specified.

So, the equilibrium constant for the above reaction is,

Kc =

The initial concentration of I₂ is:

[I₂]₀ = → [I₂]₀ = 0.0200 M

To facilitate the visualization of the reaction, we can write it in the following way,

        I₂        ⇌         2I

0.0200 M                -                   initial

0.0200 M - x          2x                 equilibrium

As the reaction doesn't go to completion, at equilibrium an amount x dissociates of the initial concentration of I₂ to produce 2x of I  (because of the stequiometric coefficients).

At equilibrium [I₂] = 0.0200 M - x and [I] = 2x. By substituting this in the above equation for kc we will be able to find the value of x and then calculate the concentrations of both gases in equilibrium.

If kc = 3.80ₓ10⁻⁵ we have,

Kc =

Since the dissociation constant has such a low value, we can assume that the degree of dissociation of I₂ is very low, therefore x ≈ 0 and,

→ x = 4.36ₓ10⁻⁴ M

Then, the concentrations of the gases I₂ and I at equilibrium are,

[I₂] = 0.0200 M - x = 0.0200 M - 4.36ₓ10⁻⁴ M →  [I₂] = 0.0196 M

[I] = 2x = 2 x 4.36ₓ10⁻⁴ M →  [I] = 8.72ₓ10⁻⁴ M