Equilibrium Problem; Senior High School Level

[General_Sax]

Homework Statement

The reaction SO₂CL_2(g) == SO_2(g)+ Cl_2(g)
was studied in a 5.00 L container at 100C. Initially, 2.65 mol of Cl_2(g) and 4.85 mol of SO₂CL_2(g) were present in the container. The equilibrium constant is 2.60. Calculate the equilibrium concentrations of the reactant and products.

[CL]_initial = 2.65 mol / 5.00 L = 0.530 mol/L
[SOCL]_initial = 0.970 mol/L

Homework Equations

aA + bB == cC + dD

k_c = [A]^a * ^b / [C]^c * [D]^d

Initial [ ] + Change_in [ ] = Equilibrium [ ]

[ ] = concentration (mol/L)

The Attempt at a Solution

I was taught a method to solve these problems that utilizes a "I.C.E. table". To me it resembles a matrix (at least I think it does).

[SOCL] ||| [SO] ||| [CL]

Initial: 0.970 ||| 0 ||| 0.530


Equilibrium: 0.970 - y ||| y ||| 0.530 + y



K_c = 2.60


Because the constant terms aren't 1000 times greater than the equilibrium constant, I can't simplify the equation by substituting 0.970 for the equilibrium concentration for SOCL.
So I have this to work with:

K_c = y * (0.530 +y) / ( 0.970 - y )

So I do this:

2.6 * ( 0.970 - y ) = 0.530y + y²

All I can see is a quadratic equation, so after a lil' bit of tinkering I set up a quadratic equation.

y = -2.6 +- (sqrt)[14.728] / 2

y = 0.619 mol/L

However, if that was true then I should be able to check that value against the equilibrium constant of 2.60. I don't want to rewrite another equation, but if you substitute in the new values for the equilibrium concentrations into the original formula you don't end up with 2.60, but instead you arrive at value of approximately 2.02.

Can someone please help me?

 

[General_Sax]

Great after all that work typing my problem up, I've solved my problem!

If anyone is searching threads, for aid with one of their own problems, remember to be careful with your algebra.

 

[Borek]

Great after all that work typing my problem up, I've solved my problem!

That's one of the reasons why we want you to show you did. And that's no joke, you will be surprised how often people realize what they did wrong when they try to present their work to others.

Glad it worked for you.