Given that Kp at 900 K is K = 16, calculate the equilibrium pressure of HCl

Question

In the reaction below, 5 atm of H₂ and 6 atm of Cl₂ were placed into a 1.00 L flask and allowed to react: 

H₂(g) + Cl₂(g) <=> 2 HCl(g) 

Given that Kp at 900 K is K = 16, calculate the equilibrium pressure of HCl and give to 2 decimal places.

answer is 7.24

Answer 1

Write the equilibrium expression:

Kp = (P_HCl)²/(P_H2)(P_Cl2)

Set up an ICE table:

H2(g) + Cl2(g) <====> 2HCl(g)

5atm..........6atm..................0atm.....Initial

-x............-x.........................+2x.......Change

5-x.........6-x........................2x........Equilibrium

Substitute values in the equilibrium expression:

16 = (2x)² / (5-x)(6-x)

16 = 4x²/(x² -11x + 30)

12x² -176x + 480 = 0

Using quadratic to solve, we obtain

x = 3.62 and substituting this back into the ICE table the concentration of HCl at equilibrium is...

2x = 2 * 3.62 = 7.24 atm