Question

Phosphorus pentachloride is formed when phosphorus trichloride and chlorine react.

PCl_3(g) + Cl_2(g) ⇌ PCl_5(g)

The equilibrium constant for the reaction is K_C = 37.8 at 110 °C. If 0.887 mol of phosphorus trichloride is added to 0.550 mol of chlorine in a 1.02-L reaction vessel at this temperature, what is the equilibrium concentration (in mol/L) of phosphorus pentachloride?

Report your answer to THREE significant figures.

Answer 1

Ans :-

Initial molar concentration of PCl₃ = Moles/Volume in L

= 0.887 mol / 1.02 L

= 0.8696 M

Initial molar concentration of Cl₂ = Moles/Volume in L

= 0.550 mol / 1.02 L

= 0.5392 M

ICE table is :

........................PCl_3(g)....................... +............................ Cl_2(g) <-----------------------------> PCl_5(g)

Initial................0.8696 M..................................................0.5392 M ..........................................0.0 M

Change...............-y................................................................-y......................................................+y

Equilibrium.......(0.8696-y) M...........................................(0.5392-y) M.........................................y

Where, y = Amount dissociated per mole

Expression of Equilibrium constant i.e. K_c(which is equal to the product of the molar concentration of products divided by product of the molar concentration of reactants raise to power their stoichiometric coefficient when reaction is at equilibrium stage).

K_c = [PCl₅]/[PCl₃].[Cl₂]

37.8 = y/(0.8696-y)(0.5392-y)

37.8 = y/(y² - 1.4088 y + 0.469)

y² - 1.4088 y + 0.469 - 0.02646 y = 0

y² - 1.43526 y + 0.469 = 0

On solving

y = 0.50317

Therefore,

Equilibrium concentration (in mol/L) of phosphorus pentachloride (PCl5) = y = 0.503 M