What is the equillibrium

Question

An empty steel container is filled with 0.0400 atm of HF. The system is allowed to reach equilibrium. If Kp = 2.76 for the reaction below, what is the equilibrium partial pressure of H₂? 2 HF (g) ⇌ H₂ (g) + F₂ (g)

Answer 1

We can construct and ICE table (I = initial, C = change, E = equilibrium)

         HF                 H2             F2

I         0.04atm        0               0

C        -2X                 +X            +X

E       0.04 – 2X         X              X

Kp = X^2 / (0.04 – 2X)^2

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Substituting for Kp = 2.76 and solving for X (partial pressures of H2 and F2 at equilibrium),

you get a quadratic equation of the form

10.0X^2 – 0.442X + 0.00442 = 0

Using the quadratic formula, we get X = 0.0289 atm and 0.0153 atm for the two solutions.

Only 0.0153 atm makes sense since using 0.0289 gives a negative equilibrium pressure for HF

(0.04 – 2X) = -0.0178 when X = 0.0289.

Check all math.