At elevated temperatures, solid silicon reacts with chlorine gas to form gaseous SiCl4. At some temperature, the equilibrium constant for this reaction is 0.30. If the reaction is started with 0.10 mol of SiCl4 in a one-liter flask, how much Cl2 will be present when equilibrium is established?

[Cl₂] = 0.1804M

Explanation:

The reaction of Si with Cl₂ is:

Si (s) + 2Cl₂ (g) ⇄ SiCl₄ (g)

Where equilibrium constant, k, is:

k = 0.30 = [SiCl₄] / [Cl₂]²

Si (s) is not in the equilibrium reaction because pure solids don't take part in the equilibrium.

As initial concentration of SiCl₄ is 0.10mol / 1L = 0.10M, when the equilibrium is established, concentrations are:

[SiCl₄] = 0.10M - X

[Cl₂] = 2X

Where X is the reaction coordinate.

Replacing in k equation:

0.30 = [0.10-X] / [2X]²

0.30 = [0.10-X] / 4X²

1.2X² = 0.10 - X

1.2X² + X - 0.10 = 0

Solving for X:

X = - 0.92M → False solution. There is no negative concentrations.

X = 0.0902M → Right solution.

[Cl₂] = 2*0.0902M = 0.1804M

[Cl₂] = 0.1804M