Question

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride according to the following equilibrium: PCl3(g)+Cl2(g)⇌PCl5(g) A 7.5-L gas vessel is charged with a mixture of PCl3(g) and Cl2(g), which is allowed to equilibrate at 450 K . At equilibrium, the partial pressures of the three gases are PPCl3 = 0.129 atm , PCl2 = 0.159 atm , and PPCl5 = 1.20 atm .

1. What is the value of Kp at this temperature?

Express the equilibrium constant to three significant figures.

2. Calculate Kc for this reaction at 450 K.

Express the equilibrium constant to two significant figures.

Answer 1

1.

The given equilibrium reaction is

For a generic reaction, , the equilibrium constant Kp is expressed as

Where the pressures are equilibrium partial pressures.

Hence, for the given value of equilibrium partial pressures of our reaction, we can calculate the value of K_p as follows:

Hence, Kp of the reaction at the given temperature is about 58.5. (Rounded to three significant figures).

2.

Now, the equilibrium constants K_p and K_c are related as follows:

Where

R = gas constant = 0.08206 L atm K^-1 mol^-1.

T = temperature = 450 K

total moles of gas on product side - total moles of gas on reactant side.

In our case, there is one mole of gas on product side (PCl₅) and two moles of gas on reactant side.

Hence,

Hence, we can write

Hence, the value of K_c is approximately . ( rounded to two significant figures).