At a certain temperature, the Kp for the decomposition of H2S is 0.774.
H2S(g) <---> H2(g)+S(g)
Initially, only H2S is present at a pressure of 0.120 atm in a closed container. What is the total pressure in the container at equilibrium?
.........H2S ==> H2(g) + S(g)
I......0.120......0......0
C........-x.......x......x
E......0.120-x....x......x
Kp = pH2*pS/pH2S
0.774 = (x)(x)/(0.120-x)
Solve for x and 0.120-x, then
Ptotal = pH2 + pS + pH2S
To find the total pressure in the container at equilibrium, we need to use the equilibrium expression and the information given about the value of Kp for the reaction.
The equilibrium expression is given by:
Kp = (P_H2 * P_S) / P_H2S
Where:
Kp is the equilibrium constant,
P_H2 is the partial pressure of H2,
P_S is the partial pressure of S, and
P_H2S is the partial pressure of H2S.
In this case, the balanced equation is:
H2S(g) ↔ H2(g) + S(g)
The initial pressure of H2S is given as 0.120 atm, and initially, no H2 or S is present. Therefore, the initial partial pressure of H2 and S is 0 atm.
To find the equilibrium partial pressures, we can assume that x is the change in pressure for H2 and S. Since the stoichiometry of the balanced equation is 1:1:1, the equilibrium partial pressures for H2 and S will be x.
Substituting the values into the equilibrium expression, we have:
0.774 = (x * x) / (0.120 - x)
Simplifying the equation, we get:
0.774(0.120 - x) = x^2
Rearranging and solving the quadratic equation, we find:
x^2 + 0.774x - 0.093 = 0
Using the quadratic formula, we can solve for x:
x = (-0.774 ± √(0.774^2 - 4(1)(-0.093))) / (2(1))
Calculating x, we find two possible solutions:
x ≈ -0.450 (positive value is not physically meaningful)
x ≈ 0.033
Since x represents a change in pressure, we disregard the negative value and use the positive value as the change in pressure for H2 and S at equilibrium.
Now, we can find the equilibrium partial pressures:
P_H2 = P_S ≈ x = 0.033 atm
To find the total pressure at equilibrium, we add the partial pressures together:
P_total = P_H2S + P_H2 + P_S
= 0.120 + 0.033 + 0.033
= 0.186 atm
Therefore, the total pressure in the container at equilibrium is approximately 0.186 atm.