At a particular temperature, K=3.75 for the following reaction. SO2(g) + NO2(g) (reversible arrows) SO3(g) + NO(g) If all four gases had initial concentrations of 0.500 M, calculate the equilibrium concentrations of the gases.

K=(.5+x)^2/(.5-x^2)

solve for x

I will be happy to critique your thinking

I might have done something wrong. I get that SO2 and NO2 have concentrations of 0 and SO3 and NO have concentrations of 1. That doesn't seem correct, but I did the work several times.

Post your work and we will find your error.

Thanks! (.5+x)2/(.5-x)2=3.75 When I solved for x, I got x=.5. When plugging into the original concentrations, you get that at equilibrium, since SO2 and NO2 are both initially .500 M, that they are 0 M. SO3 and NO are initially .500 M so at equilibrium they are 1 M. Correct?

No. Show your work. You should have
(0.5+x)(0.5-x) = sqrt (3.75)
and solving that equation doesn't give 0.

Let's go through the process step by step to find the correct equilibrium concentrations.

Given the equilibrium constant K = 3.75 for the reaction:
SO2(g) + NO2(g) ⇌ SO3(g) + NO(g)

We start with all four gases having initial concentrations of 0.500 M. Let's assume the change in concentration of each gas is represented by 'x' at equilibrium.

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

From this equation, we can write the expression for K in terms of concentrations:
K = ([SO3] * [NO]) / ([SO2] * [NO2])

Substituting the initial concentrations into the expression for K:
3.75 = ([SO3] * [NO]) / (0.500 * 0.500)

Now, let's create an ICE table to help us organize the changes in concentrations:

SO2 + NO2 ⇌ SO3 + NO
Initial (M) 0.500 + 0.500 0 0
Change (M) -x -x +x +x
Equilibrium (M) 0.500-x + 0.500-x +x +x

Since both NO2 and SO2 have initial concentrations of 0.500 M and will react to form NO and SO3, the change in their concentrations will be -x. Similarly, the concentrations of NO and SO3 at equilibrium will be +x.

Now let's substitute these equilibrium concentrations into the expression for K:

3.75 = ([SO3] * [NO]) / (0.500 - x)^2

To solve for x, we'll rearrange the equation:

(0.500 - x)^2 = ([SO3] * [NO]) / 3.75

Now we need additional information to solve for x. If we are given the equilibrium concentrations of either SO3 or NO, we can substitute that value into the equation and solve for x. Without that information, we cannot find the exact equilibrium concentrations.

So, in order to determine the equilibrium concentrations of the gases from the given information, we need additional data.