Is There an Error in My Equilibrium Calculations?

[nuomi]

1.The equilibrium constant is Kc = 85.0 at 460°C for the reaction
SO₂(g) + NO₂(g)\UpdownarrowNO(g) + SO₃(g)
If 2.24L SO₂, 4.48 L NO₂, 2.24 L NO and 3.36 L SO₃ (ALL AT STP) are transferred to a 5.00 L reaction vessel and heated to 460°C, what will be the equilibrium molar concentrations?
2. because it is at STP it's safe to assume that 1 mole will equal 22.4 L, therefore I could divide all the initial volumes by 22.4L to get mol then divide by 5.00L to get mol L^-1.
3. I made an initial, change, equilibrium chart.
SO₂ NO₂ NO SO₃
I: .02, .04, .02, .03
C: -x, -x, +x, +X
E: .02-x, .04-X, .02+x, .03+x

K_c= C_NOC_SO3/C_SO2C_NO2
85= (.02+x) (.03+x)/(.02-x)(.04-X) -> 85= .0006+.05X+x²/.0008-.06x-x² -> 85(.0008-.06x-x²)=.0006+.05X+x²-> .068-5.1x-85x²=.0006+.05X+x²-> 84x²-5.15x+.00674=0
-(-5.15) +-\sqrt{(-5.15)^2-4(84*.0674)} divided by 2(84)
x=.0424, x=.0189

now when equated back into the calculations for equilib. concentrations
E: .0011, .0211,.0389,.0489
those numbers can't be correct because in order to be a valid assumption doesn't the number i got for x/by the initial given*100 have to be less than 5%...mine are not therefore there must be something mistaken in my calculations. can someone please explain this to me.

 

[Borek]

85= (.02+x) (.03+x)/(.02-x)(.04-X) -> 85= .0006+.05X+x²/.0008-.06x-x² -> 85(.0008-.06x-x²)=.0006+.05X+x²-> .068-5.1x-85x²=.0006+.05X+x²-> 84x²-5.15x+.00674=0

Check your math.

those numbers can't be correct because in order to be a valid assumption doesn't the number i got for x/by the initial given*100 have to be less than 5%...

Where have you used assumptions that work if 5% rule is obeyed?

 

[nuomi]

this is the other eq. that i got

-86x²-5.15x+.0674

-(-5.15) +- \sqrt{(-5.15)^2*4(-86*.0674)} divided by 2(-86)


is there a rule of mathematics that i might not be following...i am a little rusty on algebra etc.
the 5% rule was out of my textbook but it doesn't seem to work on any of my other problems so i think there is something I'm not factoring into it.

 

[Borek]

85= (.02+x) (.03+x)/(.02-x)(.04-X) is OK, you make some error later.

State 5% rule.