Consider the reaction:

SO2 (g) + NO2 (g) ==> SO3 (g) + NO (g)
At T = 1000 K, where the reaction is exothermic with an equilibrium constant K = 9.00

The reaction vessel is charged initially with all four gases, each at a pressure of 0.5 atm. After equilibrium is achieved, the partial pressure of SO3 will be:
a) 0.250 atm
b) 0.500 atm
c) 0.750 atm
d) 0.900 atm
e) none of these

First you must determine which way the reaction will shift to reach equilibrium.

Q = (SO3)(NO)/(NO2)(SO2) = (0.5*0.5/0.5*0.5) = 1. With K = 9 that means products are too small and reactants too large so the rxn must shift to the right to reach equilibrium.
.....SO2(g) + NO2(g) ==> SO3(g) + NO(g)
I...0.5.......0.5.........0.5.....0.5
C.....-x......-x..........x.......x
E...0.5-x...0.5-x........0.5+x...0.5+x

Substitute into Keq an solve for x, then evaluate each constituent.

To find the partial pressure of SO3 at equilibrium, we need to use the equilibrium constant expression for this reaction:

K = (P_SO3 * P_NO) / (P_SO2 * P_NO2)

Since the initial pressure of all gases is 0.5 atm, we can substitute this value into the equation:

9.00 = (P_SO3 * P_NO) / (0.5 * 0.5)

Rearranging the equation, we get:

P_SO3 * P_NO = 9 * 0.25

P_SO3 * P_NO = 2.25

Since we are looking for the partial pressure of SO3, we can set P_NO to its initial value of 0.5 atm:

P_SO3 * 0.5 = 2.25

Solving for P_SO3, we get:

P_SO3 = 2.25 / 0.5

P_SO3 = 4.50 atm

Therefore, the partial pressure of SO3 at equilibrium is 4.50 atm. However, none of the available options match this value, so the correct answer is e) none of these.

To determine the partial pressure of SO3 at equilibrium, we need to use the equilibrium constant expression and the initial pressures of the gases.

The given equation for the reaction is:
SO2 (g) + NO2 (g) ⇌ SO3 (g) + NO (g)

The equilibrium constant expression for this reaction at temperature T can be written as follows:
K = ([SO3] * [NO]) / ([SO2] * [NO2])

Since the reaction is exothermic, it means that the formation of products is favored at low temperatures. Therefore, to determine the equilibrium concentrations, we need to know the initial concentrations and the stoichiometry of the reaction.

The initial pressures of all four gases are given as 0.5 atm. Since pressure is directly proportional to concentration for gases, we can consider these pressures as initial concentrations.

Let's assume that x is the change in the concentration of SO2, NO2, SO3, and NO at equilibrium.

According to the stoichiometry of the reaction, the concentration of SO3 at equilibrium will be [SO3] = x, and the concentration of NO at equilibrium will also be [NO] = x.

Since both SO2 and NO2 have the same initial concentration of 0.5 atm, their concentrations at equilibrium will be [SO2] = 0.5 - x and [NO2] = 0.5 - x, respectively.

By substituting the concentrations into the equilibrium constant expression, we get:

K = (x * x) / [(0.5 - x) * (0.5 - x)]

Now, we can solve for x.

9 = (x^2) / [(0.5 - x)^2]

Rearranging the equation:

9 * (0.5 - x)^2 = x^2

Expanding and rearranging:

18 * (0.5 - x)^2 = 2x^2

9 * (0.5 - x)^2 = x^2

Simplifying:

9 * (0.25 - x + x^2) = x^2

9 * 0.25 - 9x + 9x^2 = x^2

2.25 - 9x + 9x^2 = x^2

8x^2 + 9x - 2.25 = 0

By solving this quadratic equation, we find two solutions for x: x = 0.25 and x = -1.

Since x represents the change in concentration at equilibrium, we discard the negative solution, x = -1. Therefore, the concentration of SO3 at equilibrium is x = 0.25 atm.

So, the partial pressure of SO3 at equilibrium is 0.25 atm.

Hence, the correct answer is option a) 0.250 atm.