At a particular temperature, K = 3.75 for the following reaction.
SO2(g) + NO2(g) <==> SO3(g) + NO(g)\
If all four gases had initial concentrations of 0.550 M, calculate the equilibrium concentrations of the gases.
Since you gave concns in M, I assume the K given is Kc. First, calculate Qrxn.
Q = (SO3)(NO)/(SO2)(NO2) = 1 (you can plug in the numbers to see Q = 1. So Kc = 3.75 which means the reaction must move to the right to attain equilibrium.
..............SO2 + NO2 ==> SO3 + NO
initial.....0.550..0.550..0.550...0.550
change........-x.....-x........x....+x
final0.550-x..0.550-x..0.550+x 0.550+x
Substitute the final (equilibrium but I didn't have enough space to write that) into the Kc expression and solve for x, then evaluate 0.550+x and 0.550-x.
To calculate the equilibrium concentrations of the gases, we can use the equilibrium expression and the given value of the equilibrium constant (K).
The equilibrium expression for the reaction is:
K = [SO3] * [NO] / [SO2] * [NO2]
Let's assume that at equilibrium, the concentrations of SO3 and NO are x M, and the concentrations of SO2 and NO2 are (0.550 - x) M.
Substituting the concentrations into the equilibrium expression, we have:
K = (x) * (x) / (0.550 - x) * (0.550 - x)
Simplifying the equation, we have:
3.75 = x^2 / (0.550 - x)^2
Multiplying both sides by (0.550 - x)^2, we have:
3.75 * (0.550 - x)^2 = x^2
Expanding and rearranging the equation, we obtain:
2.0625 - 4.59375x + 2.53125x^2 = x^2
Rearranging the terms, we get:
x^2 - 2.53125x^2 + 4.59375x - 2.0625 = 0
This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula.
By factoring or using the quadratic formula, we find that x = 0.419 M.
Therefore, at equilibrium, the concentrations of SO3 and NO are both 0.419 M, and the concentrations of SO2 and NO2 are both (0.550 - 0.419) M = 0.131 M.