At 930 K, Kp = 0.30 for the following reaction.
2 SO2(g) + O2(g)=>2 SO3(g)
Calculate the equilibrium partial pressures of SO2, O2, and SO3 produced from an initial mixture in which the partial pressures of SO2 and O2 = 0.51 atm and the partial pressure of SO3 = 0 (exactly).
partial pressure of SO2
partial pressure of O2
partial pressure of SO3
.........2SO2(g) + O2(g)=> 2SO3(g)
I.........0.51.....0.51......0
C..........-2x......-x......2x
E.......0.51-2x...0.51-x....2x
Substitute the E line into Kp expression and solve for x, then evaluate the other numbers.
To calculate the equilibrium partial pressures of SO2, O2, and SO3, we can use the given value of Kp and the initial partial pressures of the gases.
First, let's assign variables to the equilibrium partial pressures:
- The equilibrium partial pressure of SO2 will be represented as P(SO2)
- The equilibrium partial pressure of O2 will be represented as P(O2)
- The equilibrium partial pressure of SO3 will be represented as P(SO3)
We are given the initial partial pressures of SO2 and O2 as 0.51 atm, and the initial partial pressure of SO3 as 0 atm.
Using the reaction equation and stoichiometry, we can determine the change in partial pressures from the initial state to the equilibrium state:
2 SO2(g) + O2(g) ⟶ 2 SO3(g)
Since two moles of SO2 react to form two moles of SO3, the change in partial pressure for SO2 and SO3 will be equal but opposite. Similarly, the change in partial pressure for O2 will be half of the change in partial pressure for SO2 and SO3 gases.
Let's assume the change in partial pressures for SO2 and SO3 is x atm. Therefore, the change in partial pressure for O2 will be x/2 atm.
Now we can write the expressions for the equilibrium partial pressures:
P(SO2) = 0.51 - x
P(O2) = 0.51 - x/2
P(SO3) = 0 + x
Using the given value for Kp and the equilibrium concentrations, we can set up an equation:
Kp = (P(SO3))^2 / ((P(SO2))^2 * P(O2))
0.30 = (x^2) / ((0.51 - x)^2 * (0.51 - x/2))
To solve this equation, we need to rearrange it and use the quadratic formula:
0.30 = x^2 / ((0.51 - x)^2 * (0.51 - x/2))
0.30 * ((0.51 - x)^2 * (0.51 - x/2)) = x^2
(0.30 * (0.51 - x))^2 = x^2
(0.153 - 0.30x)^2 = x^2
0.023409 - 0.0918x + 0.09x^2 = x^2
0.09x^2 + 0.0918x - x^2 + 0.023409 = 0
0.08x^2 + 0.0918x + 0.023409 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
= (-0.0918 ± √(0.0918^2 - 4*0.08*0.023409)) / (2*0.08)
Solving this equation will give us two possible values for x. We can substitute these values back into the expressions for the equilibrium partial pressures to find the exact values.