# Advanced ICE Table (chemical equilibria)

## Homework Statement

Derive an expression for equilibrium concentrations in terms of formality f (and Keq) for the compounds in the the equilibrium reactions shown bellow.

## Homework Equations

A2 + 2S <---> 2SA
SA <---> S + A

Where S is a substrate (THF) and A is an adduct (BH3). Delta G and thus Keq have been calculated previously. We are supposed to use an ICE-table.
Keq can be expressed in terms of mole fractions, which can be expressed in terms of a,b,f and m (obtained from eq in the ICE table), and then using the Keq for each reaction I need to solve for a and b (to plug into the equilibrium equations obtained from the ICE table, and thus find equilibrium concentrations in terms of formality f).

## The Attempt at a Solution

f = formality, m = coefficient allowing use to write formality of S in terms of f
a and b are simply coefficients to express change. Periods are used instead of spaces because extra spaces are deleted when saved.

...........A2.....+........2S <--->....2SA.............SA <--->.....S....+.....A
I..........f.................mf.............0..................0...............0...........0
C1......-af..............-2af...........+2af............+2af.........................-2af
C2........................+2bf...........-2bf.............-2bf...........+2bf.......+2bf
eq......f(1-a)......2f(2b-2a+m)....2f(a-b)........2f(a-b)..........2bf......f(2b-2a+m)

there are several approximations I can make: m>>b>a. I can always end up with the demoninator of the approximated mole fraction to be 2fm, but I can't seem to make any approximations to solve for a and b. If you are unfamiliar with such procedures I can explain in more detail, for some reason when I post the formating of the ICE-table is changed and makes it very difficult to read. SOMEBODY PLEASE HELP ME!

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Borek
Mentor
Keq of what reaction do you know?

The compounds A and S represent are shown above: BH3 and THF (tetrahydrofuran) respectively.

Borek
Mentor
That's not what I asked, sorry if I wasn't clear.

You listed two consecutive reactions, but only one Keq. How are these reactions related to the Keq?

Keq for each reaction (there is one Keq for each reaction) are equal the the mole fractions of products over reactants (raised to the coefficient for that molecule). The mole fractions are obtained by dividing the equilibirum concentration by the sum of all the equilibrium concentrations. The Keq are known, formality f is a variable, while a and b need to be solved for to generate equations for the equilibrium concentrations. Using some approximations a and b should be able to be solved for, but I can not seem to do it with the approximations seem reasonable.

My ICE-table gets automatically formatted when I post it, I could try using periods instead of spaces.

Borek
Mentor
OK, so you have TWO KEq values, one for each reaction, from the way you worded the problem initially I got the impression you have only one value.

I have never seen ICE table used this way, and I don't think what you wrote is right. In the line C1 you wrote that concentration of A changed by -2af. Did it? If so, how come concentration of A changes but concentration of S doesn't at the same time in the same way? ICE table simply helps you keep track of the reaction stoichiometry, as S & A are products of the same reaction their concentration must go up at the same time and at the same rate; they are not consumed in the same way, but that will be accounted for in C2 line.

Show what equations you got from the ICE table (use LaTeX for that). And please list what are Keq values - not knowing them it is impossible to decide what approximations will hold.

That LateX is kinda of tricky for this stuff, but I did figure out the problem. If you're interested maybe I could scan my paper or something; it's a lot of algebra. Thanks for helping though!