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**1. Homework Statement**

The reaction SO

_{2}CL

_{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 SO

_{2}CL

_{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

**2. Homework Equations**

aA + bB == cC + dD

k

_{c}= [A]

^{a}*

Initial [ ] + Change_in [ ] = Equilibrium [ ]

[ ] = concentration (mol/L)

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

Because the constant terms aren't 1000 times greater than the equilibrium constant, I cant simplify the equation by substituting 0.970 for the equilibrium concentration for SOCL.

So I have this to work with:

K

So I do this:

2.6 * ( 0.970 - y ) = 0.530y + y

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?

^{b}/ [C]^{c}* [D]^{d}Initial [ ] + Change_in [ ] = Equilibrium [ ]

[ ] = concentration (mol/L)

**3. 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}= 2.60Because the constant terms aren't 1000 times greater than the equilibrium constant, I cant 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 + y

^{2}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?