[Bigweight]

Hello everyone, I have to calculate the concentration of Diethylammine (Kb 8.6 10^-4) only knowing the PH of the solution, which is 8.2

How do I do it? I tried to do

C= [OH]^2/Kb

But the result doesn't make much sense..

[mjc123]

That equation is an approximation that applies only when the degree of ionisation is small.
Suppose the degree of ionisation is x. Then the concentration of free base is C(1-x) and [BH⁺] = [OH^-] = Cx.
Can you work out what x and C are?

[Bigweight]

That equation is an approximation that applies only when the degree of ionisation is small.
Suppose the degree of ionisation is x. Then the concentration of free base is C(1-x) and [BH⁺] = [OH^-] = Cx.
Can you work out what x and C are?

I did the approximation for the reason that I can't work out X and C.

All I have is the PH of the solution and of course the Kb of Diethylammine

[AWK]

Please, show your equation with numbers.

[Bigweight]

Please, show your equation with numbers.

Ok then:

PH starts at 8.2 meaning POH is 5.8

This means that [OH] is 10^-5.8

So the concentration of Diethylammine is

[D] = (10^-5.8 )^2/8.6 10^-4

Which is 2.9 10^-17 and it makes no sense

[mjc123]

I did the approximation for the reason that I can't work out X and C.

All I have is the PH of the solution and of course the Kb of Diethylammine

You have (modifying your equation above)
C(1-x) = [OH^-]²/K_b
and
Cx = [OH^-]
So you have two equations and two unknowns

[AWK]

This result is wrong - calculation error.
Solve more exact equation K_b=[OH^-]²/(c-[OH^-])

[Borek]

C= [OH]^2/Kb

That's just an approximation. Each time you use an approximated equation you should check, if you are allowed to do so - that is, whether the approximation used when deriving holds.

Do you know how this equation is derived? What approximation is being used? Does it hold?