### Related Problems with Solution

##### Problem 2 : For the reaction:

N₂O₄(g) ⇌ 2NO₂(g) Kc = 0.040

Given:

- Initial concentration of N₂O₄ = 0.10 M

Calculate the equilibrium concentrations of N₂O₄ and NO₂.

##### Solution :

Let x be the change in concentration at equilibrium: [N₂O₄] = 0.10 - x [NO₂] = 2x

Using the equilibrium constant expression: Kc = ([NO₂]²) / [N₂O₄] 0.040 = (2x)² / (0.10 - x)

Now, we can solve for x. Since Kc is relatively small, we can make an approximation that x will be small compared to the initial concentration of N₂O₄:

0.040 ≈ (4x²) / 0.10

4x² ≈ 0.040 * 0.10

4x² ≈ 0.004

x² ≈ 0.004 / 4

x² ≈ 0.001

x ≈ √0.001 ≈ 0.0316

So, the equilibrium concentrations are: [N₂O₄] ≈ 0.10 - 0.0316 ≈ 0.0684 M [NO₂] ≈ 2(0.0316) ≈ 0.0632 M