Phosphorus pentachloride decomposes according to the chemical equation PCl5(g)↽−−⇀PCl3(g)+Cl2(g)Kc=1.80 at 250° C PCl 5 ( g ) ↽ − − ⇀ PCl 3 ( g ) + Cl 2 ( g ) K c = 1.80 a t 250 ° C A 0.285 0.285 mol sample of PCl5(g) PCl 5 ( g ) is injected into an empty 3.45 3.45 L reaction vessel held at 250° C. Calculate the concentrations of PCl5(g) PCl 5 ( g ) and PCl3(g) PCl 3 ( g ) at equilibrium using quadratic formula.

[PCl₅] =  0.00348 M

[PCl₃] = 0.07912 M

Explanation:

Step 1: Data given

Kc = 1.80 at 250 °C

Number of moles PCl5 = 0.285 moles

Volume = 3.45 L

Temperature = 250 °C

Step 2: The balanced equation

PCl5(g)⇔PCl3(g)+Cl2(g)

Step 3: Calculate molarity of PCl5

Molarity PCl5 = moles PCl 5 / volume

Molarity PCl5 = 0.285 moles / 3.45 L

Molarity PCl5 = 0.0826 M

Step 4: The initial concentration

[PCl5] = 0.0826 M

[PCl3]= 0M

[Cl2] = 0M

Step 5: The concentration at the equilibrium

[PCl5] = (0.0826 - x)M

[PCl3] = xM

[Cl2] = xM

Step 6: Calculate [PCl5] and [PCl3]

Kc =  [ (PCl₃) ] [ Cl₂ ] / [PCl₅]

1.80 = x² / (0.0826 - x)

x = 0.07912 M

[PCl₅] =  (0.0826 - 0.07912)M = 0.00348 M

[PCl₃] = 0.07912 M