Determining final concentrations of a Reaction given an equilibrium K

[BrettJimison]

Homework Statement

Rxn: 2SO_{2 (g)} + O_{2 (g)} $\Leftrightarrow$ 2SO_{3 (g)}

If the initial concentration of SO₃ is .500 M (moles/liter) @1500K, what are the final concentrations of [SO₂], [O₂] and [SO₃]. K_c = .15

Stop when you get to the cubic equation

Homework Equations

RICE table

K_c= [SO3]²/ [O2][SO2]² This is equilibrium quotient for forward reaction. I will flip it to get reverse reaction Kc equation

The Attempt at a Solution

This is the K_c given for the forward reaction. If I flip the reaction around I invert the K_c and it becomes = 6.6667 (for the reverse reaction)

I then used a "rice" table with the initial concentration of SO3 and "x" variable for the SO2 and O2[

Plugging these values in I get the kc equation:

6.6667= [2x]²[x]/[.500-2x]

I'm not getting the correct cubic equation when expanding this quotient. I'm sure of my math, so I was wondering if I'm setting up the quotient wrong? - Thanks!

 

[Borek]

You don't need to reverse the reaction (you flipped and calculated the inverse of the Kc, which effectively cancels out).

What is the "correct" answer you are expecting to get? At first sight I don't see anything wrong with your work.

 

[epenguin]

Looks OK to me too. Maybe the problem is this is a fairly complete conversion so don't round down too much your x as this could introduce considerable error in your (0.5 - 2x) when you back calculate to check?

(I get x = 0.24566)

 

[BrettJimison]

Thanks for the input Borek and epenguin.
If turns out there was an error on the answer sheet I was given.
My cubic equation was correct after all.

 

[DeeNos]

Your approach is correct. The equilibrium constant, Kc, is indeed equal to 6.6667 when the reaction is flipped to the reverse direction. However, the cubic equation that you are getting may not be correct due to a mistake in setting up the RICE table or a miscalculation in solving the equation. I would suggest double-checking your RICE table and making sure that your calculations for the equilibrium concentrations are correct. You can also try using an online equilibrium calculator to check your results. If you are still having trouble, please provide your full calculations so I can assist you further.