Answer:
PCl₅: 0.1192M
PCl₃: 0.0734M
Cl₂: 0.0734M
Explanation:
Based on the reaction:
PCl₅ ⇄ PCl₃ + Cl₂
K of reaction is defined as:
K = [PCl₃] [Cl₂] / [PCl₅]
Replacing with concentrations of gases in equilibrium:
K = [0.119] [0.119] / [0.313]
K = 0.0452
Moles of each gas is:
PCl₅: 7.40L × (0.313mol / L) = 2.3162 moles
PCl₃: 7.40L × (0.119mol / L) = 0.8806 moles
Cl₂: 7.40L × (0.119mol / L) = 0.8806 moles
When the volume of the container is increased the system will produce more moles, (That is, produce more products) in order to keep constant the pressure of the container -Le Chatelier's principle-. In equilibrium, molarity of each gas is:
PCl₅: 2.3162 moles - x / 16.6L
PCl₃: 0.8806 moles + x / 16.6L
Cl₂: 0.8806 moles + x / 16.6L
Where X is reaction coordinate.
Replacing in K formula:
0.0452 = [0.05305 + X/16.6] [0.05305 + X/16.6] / [0.13953 - X/16.6]
6.3068x10⁻³ - 2.723x10⁻³ X = 0.0028143 + 0.00639157 X + 0.00362897 X²
0 = -0.0034925 + 0.00911457X + 0.00362897 X²
Solving for X:
X = -2.8 → False answer. There is no negative concentrations
X = 0.3378 moles
Replacing:
PCl₅: 2.3162 moles - 0.3378 / 16.6L = 0.1192M
PCl₃: 0.8806 moles + 0.3378 / 16.6L = 0.0734M
Cl₂: 0.8806 moles + 0.3378 / 16.6L = 0.0734M
Beeing these concentrations the concentrations in equilibrium of the three gases
