[mechareaper]

I'm having difficulty solving part of a problem, and it's driving me nuts! I know it should be easy, but I've tried for hours, and its still not coming out right. Here's the problem I'm having...

Consider a saturated solution of LiF in which ONLY the following reactions take place.

LiF(s) ⇌ Li+(aq) + F−(aq)   Ksp = 1.7 × 10−3
HF(aq) ⇌ H+(aq) + F−(aq)   Ka = 6.8 × 10−4
H2O(l) ⇌ H+(aq) + OH−(aq)   Kw = 1.01 × 10−14

   Neglecting activities, use the systematic treatment of equilibrium to derive an expression for Ksp that depends only on the equilibrium constants and [H]+.

First I set the charge balance equation: [Li+]+[H+]=[F-]+[OH-]
Then mass balance, though I'm not sure if it's correct, my suspicion is that it isn't, since after a lot of algebra, an impossible equation pops out...:[Li+]=[HF]+[F-]

so, obviously, I solve for [HF] in terms of Ka ( so its [HF]=[H+][F-]/ka) and [OH-] in terms of Kw and [H+], so [OH-]=kw/[H+]

after that, I've tried the algebra multiple times, and I can't get the needed equation (in a form that isn't impossible to solve)

I don't know why I can't see it, could someone please assist!

[Borek]

Your approach so far is correct. I am not sure what it means to solve for Ksp if Ksp is given.

I can't get the needed equation (in a form that isn't impossible to solve)

Do you know how the answer looks like? Why do you think what you get is impossible to solve?

[mechareaper]

Did you even read it? It doesn't say to solve for Ksp, it says DERIVE AN EXPRESSION IN TERMS OF [H+] only and the other EQUILIBRIUM CONSTANTS. I thought I would get help, not a smart ass answer...

[mechareaper]

No offense, but the first and most important step is to actually read the problem...
Anyway, what I mean by, it's impossible, is I get [H+] to the third, second, and first power. Maybe it IS possible and I just discouraged myself, as long as the mass balance equation is correct, but I don't feel it is. Could you just look?

Also, the cross posting was just a mistake, I just saw "Undergraduate" and "Chemistry"