As an EPA scientist studying catalytic converters and urban smog, you want to find Kc for the following reaction: 2NO2 (g) ⇋ N2 (g) + 2 O2 (g) Kc = ?. Use the following data to find the unknown Kc (1) ½ N2 (g) + 1/2 O2 (g) ⇋ NO (g) Kc = 4.8x10-10 (2) 2NO2 (g) ⇋ 2NO (g) + O2 (g) Kc = 1.1x10-5

Kc = 4.774 * 10¹³

Explanation:

the desired reaction is

2 NO₂ (g) ⇋ N₂ (g) + 2 O₂ (g)

Kc = [N₂]*[O₂]² / [NO₂]²

Since

1/2 N₂ (g) + 1/2 O₂ (g) ⇋ NO (g)

Kc₁ = [NO] / (√[N₂]√[O₂]) → Kc₁² = [NO]² / ([N₂][O₂])

and

2 NO₂ (g) ⇋ 2 NO (g) + O₂ (g)

Kc₂ = [NO]²*[O₂]/[NO₂]² → 1/Kc₂ = [NO₂]² / ([NO]²[O₂])

then

Kc₁² * (1/Kc₂) = [NO]² / ([N₂]*[O₂]) * [NO₂]² / ([NO]²[O₂]) = [NO₂]² / ([N₂]*[O₂]²) = 1/Kc

Kc₁² / Kc₂ = 1/Kc

Kc = Kc₂/Kc₁² = 1.1*10⁻⁵ / (4.8*10⁻¹⁰) ² = 4.774 * 10¹³