Phosphorus pentachloride decomposes according to the chemical equation PCI; (g) =PC12(g) + Cl2(8)
Kc = 1.80 at 250 °C
A 0.4192 mol sample of PCI (g) is injected into an empty 4.45 L reaction vessel held at 250 °C.
Calculate the concentrations of PCI (g) and PC12(g) at equilibrium.
[PCI5)=

[PC13] =

[PCl₅]  → 4.47×10⁻³ M

[PCl₃]  → 0.0897M

Explanation:

We state the equilibrium: PCl₅ (g) ⇄  PCl₃(g) + Cl₂(g)

Initially we have 0.4192 moles of  PCl₅ so during the reaction, x moles of it have been reacted. In conclussion after the equilibrium we may have x moles of PCl₃ and Cl₂. In order to find the final concentration, we use the Kc, but we need molar concentrations. That's why we divide all the values with the 4.5L, volume for the vessel. The expression for Kc is:

Kc = [PCl₃] . [Cl₂] / [PCl₅]

1.80 = (x/ 4.45) . (x/ 4.45) / ((0.4192-x) /4.45)

1.80 = (x² / 4.45²) / ((0.4192-x) /4.45)

1.80 = x² / 4.45 / (0.4192-x)

1.80 (0.4192-x) = x² / 4.45

1.80 (0.4192-x) . 4.45 - x² = 0

3.36 - 8.01x - x² = 0 → Quadractic

a = -1  b = -8.01  c = 3.36

(-b + √(b² - 4ac)) / (2a)

(-(-8.01) + √((-8.01)² - 4(-1)3.36)) / (2(-1) = 0.3995

[PCl₅] = (0.4192 - 0.3995) / 4.45L → 4.47×10⁻³ M

[PCl₃] = 0.3995 /4.45L → 0.0897M