Find the amount of NO2 that must be added to 2.3 mol of SO2 (10 points)?

Let y mol be the amount of NO₂ added.

Balanced equation :
SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g)

Initial concentrations :
nₒ(SO₂) = 2.3 mol, nₒ(NO₂) = y mol
nₒ(SO₃) = nₒ(NO) = 0 mol

1.1 mol of SO₃ is formed. Equilibrium concentrations :
n(SO₂) = 2.3 - 1.1 = 1.2 mol, n(NO₂) = (y - 1.1) mol
n(SO₃) = n(NO) = 1.1 mol

Let V L be the volume of the system.

Kc = [SO₃] [NO] / ([SO₂] [NO₂])
(1.1/V) × (1.1/V) / {(1.2/V) × [(y - 1.1)/V]} = 3.0
1.1 × 1.1 / [(1.2 × (y - 1.1)] = 3.0
1.21 / [1.2 × (y - 1.1)] = 3.0
3.0 × 1.2 × (y - 1.1) = 1.21
y - 1.1 = 1.21 / (3.0 × 1.2)
y - 1.1 = 0.336
y = 1.436

Amount of NO₂ must be added = 1.436 mol

SO2 + NO2 = SO3 + NO
Kc = [SO3][NO]/[SO2][NO2] = 3
3 = (1.10)(NO)/(2.30)(NO2)
We need to be given the value of [NO]