[Jutlander]

Hey all 

I have a question for you guys, right now Iam sitting here with some problems, and I got an problem that i can't figure out.

Explain why is the pKa of H3O+ = -1.74 and not =0???

First of all i found out that kw=[H3O+][OH-]/[H2O] is
                                    kw=[10^-7][10^-7]/[55.5]=1.8*10^-16=pKa=-1.74

I dont know how I get it to = 0, because of that i got problems to explain why 
And what does the value 55.5M come from.
can someone give me an good explanation of this question?

thanx in advance ^^

[borodin]

I think it's because you are using liquid watter in equillibrium!

Kw = [H⁺] [OH^-]

[agrobert]

55.5 M is the concentration of water ~55.5 moles of water/liter

[RBF]

Well the 55.5 is the molar concentration of pure water.  (1 liter = 1000g.  18g/mole ==> 55.5mole/liter.  The rest of the question may be more complicated than it appears.  How do you measure the Ka for the equation  H₃O⁺ + H₂O==>H₂O + H₃O⁺ with each substance in the standard state?  The following article discusses the issues here:  J. Chem Ed. 1990 67, 386

[AWK]

kw=[10^-7][10^-7]/[55.5]=1.8*10^-16=pKa=-1.74

Check your calculations

[RBF]

That calculation will give the pK_a of water, not the hydronium ion.

[Jutlander]

ops must have been tired  kw=[10^-7][10^-7]/[55.5]=1.8*10^-16=pKa= 15.74429!
not -1.74

-log 55,5 =-1.74 any connections....? what does it mean  has the concentration of water anything to do with pka of H3O+..

[RBF]

In a way, yes.  The calculations are explained in the J.Chem.Ed article I referenced in a previous post.  It can be accessed here, but a subscription is probably necessary.

http://jchemed.chem.wisc.edu/Journal/Issues/1990/May/jceSubscriber/JCE1990p0386.pdf

The calculations are complicated by the fact that they involve 'activities' of each of the components involved at infinite dilution (the acidity of pure substances is not the same as diluted components).  When the equilibrium equation is defined for K_a of H₃O⁺ in terms of activities and standard states, the result is 55.3 which happens to be the concentration of pure water at its standard state.
(It's not 55.5, which is the concentration of water at 4C;  the density of water at 25C is 0.997g/mL, which leads to the somewhat smaller 55.3moles/liter).  The log  of each value, however gives the same number to 3 sig figs.

[Hand15]

kw=[H3O+][OH-]/[H2O]

Why are you using this formula kw=[H3O+][OH-]/[H2O] ?

It is certainly not correct to have [H2O]=55.5M because actually this 'approachment' would ommit liquid and solid and regarded them as equivalent of 1, so the formula will be: Kw=[H3O+][OH-]

Unless you want to be precise: Kw={H3O+}{OH-}/{H2O}
Here it is the activity, not the concentration, that actually influence value of Kw

[Jutlander]

ty ill try and read the article mabey I can read it via my libary
I think the answer is somewhat an connection with waters autoprotolysis that the H30+ is not =0 and is -1.74

[Borek]

For pKw being either 14 or 15.7 - see http://www.chembuddy.com/?left=pH-calculation&right=water-ion-product