What is the value of the equilibrium constant at this temperate for the reaction of SO2 with N2O to form SO3 and N2?

Question

At a certain temperature, a 25.5 -L container holds four gases in equilibrium. Their masses are 3.5 g SO₃, 4.6 g SO_{2 ,} 14.3 g N₂, and 0.98 g N₂O.

What is the value of the equilibrium constant at this temperate for the reaction of SO₂ with N₂O to form SO₃ and N₂? Make sure you balance the reaction using the lowest whole-number coefficients.

K_c=?

Answer 1

SO₂(g) + N₂O(g) ==> SO₃(g) + N₂(g) .. balanced equation

The expression for Kc is Kc = [SO₃][N₂] / [SO₂][N₂O]

In order to solve this for Kc, we need to first find the concentrations of the 4 compounds involved. We do this by dividing the mass of each compound by the molar mass of that compound and then divide by the volume (25.5 L) to obtain moles/liter (M) concentrations.

[SO₃] = 3.5 g x 1 mol / 80.1 g = 0.0437 mols / 25.5 L = 1.71x10^-3 M

[SO₂] = 4.6 g x 1 mol / 64.1 g = 0.0718 mols / 25.5 L = 2.81x10^-3 M

[N₂] = 14.3 g x 1 mol / 28 g = 0.5107 mols / 25.5 L = 0.0200 M

[N₂O] = 0.98 g x 1 mol / 44 g = 0.0222 mols / 25.5 L = 8.73x10^-4 M

Plugging these values into the Kc expression, we have ...

Kc = (1.71x10^-3 )(0.0200) / ( 2.81x10^-3)(8.73x10^-4)

Kc = 13.9