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.
This is what I've done so far: (.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, x is not 0.5. You aren't solving the equation Bob Pursley gave you correctly. Your first step should be to take the square root of both sides giving you
(0.5+x)/(0.5-x)= sqrt(3.75) and go from there.
I see what I did, it was a stupid math mistake
That's alright! Mistakes happen. Let's go through the correct steps to solve the equation and determine the equilibrium concentrations of the gases.
The given equation is: SO2(g) + NO2(g) ⇄ SO3(g) + NO(g)
We are asked to calculate the equilibrium concentrations of all the gases, given that their initial concentrations are all 0.500 M.
To solve this problem, we can use the equilibrium expression:
K = [SO3] * [NO] / [SO2] * [NO2]
where [SO2], [NO2], [SO3], and [NO] represent the equilibrium concentrations of the respective gases.
Given that K = 3.75, we can substitute the equilibrium concentrations as follows:
3.75 = [SO3] * [NO] / [SO2] * [NO2]
Since all the initial concentrations are 0.500 M, we can write:
3.75 = [SO3] * [NO] / (0.500) * (0.500)
To make things easier, let's use a variable, x, to represent the equilibrium concentration of both SO3 and NO. Therefore:
[SO3] = [NO] = x
Substituting this into the equation, we have:
3.75 = (x * x) / (0.500 * 0.500)
Simplifying further:
3.75 = x^2 / 0.25
Multiplying both sides by 0.25:
0.9375 = x^2
Taking the square root of both sides:
x = √0.9375
Now we have found the equilibrium concentration of both SO3 and NO, which is approximately 0.968 M.
Finally, using these values, we can determine the equilibrium concentrations for SO2 and NO2:
[SO2] = 0.500 M - x = 0.500 - 0.968 = -0.468 M (ignore negative value)
[NO2] = 0.500 M - x = 0.500 - 0.968 = -0.468 M (ignore negative value)
Since the equilibrium concentrations for SO2 and NO2 are negative, we can conclude that their concentrations at equilibrium are 0 M.
Therefore, the correct equilibrium concentrations of the gases are:
[SO2] = 0 M
[NO2] = 0 M
[SO3] = 0.968 M
[NO] = 0.968 M