[Jules18]

This is what my lecture notes say, printed directly from the prof's website.  I have a few problems understanding it that I bolded:

Keq = [H+][OH-]/[H20]     I thought we always omitted H2O in a Keq??

Molarity of H2O is 55.5M, I get that, but then they say that Keq*[55.5M] is this constant called Kw...

Keq*[55.5M] = Kw = 1.0E^-14

I thought Kw was the same thing as Keq of water?  So what is the purpose of Kw, and is it always 1.0*10^-14?

Kw = [H+][OH-] = [H+]²
     = (55.5M)(1.8E^-6)
     = 1.0E^-14

^ This I don't get because where did the 55.5M (molarity of water) come from all of a sudden, and the 1.8E^-6?

[MrTeo]

I think that this:

Kw = [H+][OH-] = [H+]²

should be rewritten as:

K_w[H₂O]=[H+][OH-]=[H+]²

and the K_eq value should be 1.8e-16

Then, K_w is 1.0e-14 at 25ºC (actually at 24ºC if i remember right, but 25ºC it's the standard temperature, so as it's almost equal with a change of only 1º we use the same value) and increases with temperature as the autoprotolysis of water is an endergonic reaction so it's favored by the rise of temperature.

Moreover we omit water only when we work with reactions in which this value is big enough that we can forget it, but removing water here makes the whole expression senseless (we have ions produced from what?) so we need  to find out what's the concentration of the acid and basic ions in standard conditions in a neutral solution (1.0e-7) and that's just what K_w tells us if [H⁺]=[OH^-]

K_w=[OH^-][H⁺]
K_w=[H⁺]²
[H⁺]=1.0e-7

pH=-log[H⁺]=7

if [OH^-]<[H⁺] the solution is acidic, while if [OH^-]>[H⁺] it's basic, but the value of K_w is always the same.

Just another note... being more precise (nay correct) H⁺ should be written as H₃O⁺ as you won't find protons alone in a watery solution but only in this form 

[Borek]

Compare:

http://www.chembuddy.com/?left=pH-calculation&right=water-ion-product

[Jules18]

Thanks Mr. Teo! 

I just have one more q'n:  Is there any information that can be derived from Kw that can't be derived from the Keq of water?  I mean, if a question asks us to use Kw to figure something out, can we substitute Keq of water and instead use 1E^-7?

[Jules18]

Thanks Borek

[Borek]

Kw (1e-14) is sometimes not precise enough. Rarely, but it happens, especially when concentration of water is lower that usuall for whatever reason. In such cases usually activity coefficients are far from 1, which makes calculations much more difficult.

1e-7, not 1e^-7, after all e notation is there to get rid of superscripts.

if a question asks us to use Kw to figure something out, can we substitute Keq of water and instead use 1E^-7?

No idea what you mean.