[o1ocups]

Problem
Reaction: aA(g) + bB(g) <-> cC(g)
Equilibrium Constant (Kc) = 4.0
Find the equilibrium concentrations of A, B, and C for a=1, b=1, and c=2. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction.

What I did

	A	B	C
Initial Concentration	1.0M	1.0M	0.0M
Change in Concentration	-x	-x	+x
Equilibrium Concentration	1-x	1-x	x

4.0=x^2/[(1-x)^2]
4(1-x)^2=x^2
4-4x^2=x^2
5x^2=4
x^2=4/5
x=0.894

Equilibrium Concentrations
A: 1-x=1-0.894=0.106 M
B: 1-x=0.106 M
C: x=0.894 M

But it's wrong...    Please tell me where I did wrong. Thanks!!

[plat_num]

I think it has to do with the fact that 2 moles of C are produced in the balanced equation.  However you have only single "x" values for all of A, B and C.  Either change the C one to 2x, or change the A and B ones to .5

caution: I'm also learning this stuff so I might not be correct.

[o1ocups]

That's it! I can't believe that I didn't even think about it. Let me try and see if I can get the correct answer. Thank you for the hint!!

MODIFY: I still can't get it 

[Borek]

Hard to tell without looking at equations and numbrs. Please show your work now.

[o1ocups]

Hi Borek!

Hi Borek!

OK. Here is my new work:

	A	B	C
Initial Concentration	1.0M	1.0M	0.0M
Change in Concentration	-x	-x	+2x
Equilibrium Concentration	1-x	1-x	2x

4.0 = C^2/(A)(B)
C=2x, A=B=1-x
4.0=[(2x)^2]/[(1-x)^2]
4(1-x)^2=4x^2
4-4x^2=4x^2
8x^2=4
x^2=4/8=1/2
x=0.707

Equilibrium Concentrations
A: 1-x=1-0.707=0.293 M
B: 1-x=0.293 M
C: x=1.414 M

Thanks!

[o1ocups]

Would my original answers be correct if a, b, and c all equal 1?

[Borek]

4(1-x)² is not 4-4x²

[o1ocups]

4(1-x)² is not 4-4x²

You are right 

4.0 = C^2/(A)(B)
C=2x, A=B=1-x
4.0=[(2x)^2]/[(1-x)^2]
4=[(2x)^2]/[x^2-2x+1]
4(x^2-2x+1)=4x^2
4x^2-8x+4=4x^2
4=8x
x=2??

Am I missing something again? Sorry, my math is not very good.

[Borek]

4=8x
x=2??

No, but you are verrrry close.

If x is 2, 8x is 16, not 4.

How do you get rid of the 8 on the right?

[o1ocups]

4=8x
x=2??

No, but you are verrrry close.

If x is 2, 8x is 16, not 4.

How do you get rid of the 8 on the right?

OMG! x=1/2
THANKS.