Solving for fF in K = fF/(1-fF)

[Monique]

$$K = \frac{f_F}{1-f_F}$$

OK, I feel like the stupidest person ever, but if I know K, how do I find f_F?

I even know the answer.. if K = 0.504.. f_F will be 0.335.. which is 33.5%, the other fraction is 66.5%, which is 0.504..

Still can't figure how to solve the formula :(

 

[master_coda]

$$\begin{align*}<br /> K&=\frac{f_F}{1-f_F} \\<br /> K-Kf_F&=f_F \\<br /> K&=f_F(1+K) \\<br /> \frac{K}{1+K}&=f_F<br /> \end{align*}$$

 

[Monique]

see, I knew it was stupid

Thanks!

 

[PrudensOptimus]

k = f/1-f

k - kf = f.

k = fk + f = f(1 + k)

f = k/(1+k)

 

[PrudensOptimus]

oh already solved


such easy equations... sigh, noob chemists

 

[Monique]

I know, I got to the second part, realized that instead of having 1k and 2f, I had 2k and 2f, after which I panicked and gave up :P

maybe some sleep would be good, it is already 5.40 am after all, but the nernst equation is making absolutely NO sense! [b(]

 

[Monique]

gonna make some coffee..

 

[uart]

Originally posted by Monique
gonna make some coffee..

LOL, it's funny how every now and then that one can get stuck on a really simple problem, like a mental block or something.

A few weeks ago I was trying to re-arrange an equation, and I knew it had a fairly simple final form (I even knew how it should end), but I just kept getting stuck at one point and couldn't get any further.

It was quite frustrating and several times I thought about posting it here but each time refrained as I knew the answer must be very simple and was afraid of looking too dumb. Eventually I figured it out, and as expected, it was actually very easy, even though it stumped me for two days!. :)