Kp is the equilibrium constant of the equilibrium reaction in terms of partial pressure. It is the pressure ratio of the products to the reactants raised to the power of their stoichiometric coefficients.
So, we let x be the partial pressure of H₂S initially. Let y be the partial pressure that reacted to produce the products. The ICE(Initial-Change-Equilibrium) analysis is as follows:
2 H₂S → 2 H₂ + S₂
Initial x 0 0
Change -2y +2y y
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Equilibrium x-2y 2y y
Thus, the equilibrium pressure of H₂S is: x-2y = 0.25. Then, using the definition of Kp,
0.012 = (2y)²(y)/(x-2y)²
Substitute 0.25 to (x-2y)
0.012= (2y)²(y)/(0.25)²
y = 0.0572
So, we use the value of y to the first equation to determine x:
x-2(0.0572)= 0.25
x=0.364 atm