Understanding the Problem

You're given:

* Equilibrium constant (K) = 0.625 This tells us the relative amounts of reactants and products at equilibrium.

* [O₂] = 0.40 M The concentration of oxygen at equilibrium.

* [H₂O] = 0.20 M The concentration of water at equilibrium.

* We need to find [H₂O₂] The concentration of hydrogen peroxide at equilibrium.

The Reaction

The reaction you're describing is the decomposition of hydrogen peroxide:

2 H₂O₂ (l) ⇌ 2 H₂O (l) + O₂ (g)

Setting Up the Equilibrium Expression

The equilibrium constant expression for this reaction is:

K = ([H₂O]²[O₂]) / [H₂O₂]²

Solving for [H₂O₂]

1. Plug in the known values:

0.625 = (0.20² * 0.40) / [H₂O₂]²

2. Solve for [H₂O₂]²:

[H₂O₂]² = (0.20² * 0.40) / 0.625 = 0.0256

3. Take the square root of both sides:

[H₂O₂] = √0.0256 = 0.16 M

Answer

The concentration of H₂O₂ at equilibrium is 0.16 M.