Simple approach (...)
[tex]K_a = \frac {[H^+][SO_4^{2-}]}{[HSO_4^-]} = \frac {x(x+0.1)}{0.1-x} = 0.01[/tex]
I take it that we both agree, that we both did put up the same expression for calculating this problem, except you did use 0.01 instead of 10^-1.9 for the K-value (which is quite in the same ballpark, I agree)
Solving for x we get 0.00844, so pH is 2.07 - and I agree for most cases this is close enough to 2. But if you will try the same approach for 0.01 M solutions, pH will got up to 2.38, so we are almost 0.4 pH unit away, even if 0.02M buffer looks quite reasonable. HSO4- is a relatively strong acid, and it makes calculations difficult.
I would look at the "difficulty" from another point of view: that's just the way stronger acids (compared to for example acetic acid) do behave - and that's why they're giving acceptable buffers only with high concentrations (and that's why I was recommending 0.1 mol/L in the first place).
the reason is that they
do dissociate in a relevant manner - hence c ~ c
0 doesn't apply anymore and the situation becomes concentration - dependant ( and not only ratio acid : corresponding anion dependant)
on the other hand, the very calculation itself doesn't seem difficult to me
anyway, talking pH 2 or - even worse - pH 1 , these acids are the only game in town, so we'll have to roll with the punch
Note: I got the same pH using full blown equilibrium calculations using pH calculator built into Buffer Maker. I am not going to comment on the phsolver result - but the idea of entering Ka and Kb looks absurd for me, as they describe the same equilibrium (so it is enough to enter one of these numbers).
that's just the way you have to introduce a buffer in this calculator: entering the c
0 - values of the acid, the corresponding anion and their respective K values
Now, ionic strength. (...)
My personal experience with buffers is, that you'd better calculate a value of expectation first, and then start preparing the system by taking one component's solution (usually the corresponding anion) and add the second component under pH-control.
carbon dioxide, the real temperature, other impurities, quality/purity of the educts...
the list goes on and on
no use to calculate the theoretical pH to the third decimal with D.H. or other approaches (except for academic reasons, that is) , if those effects will spoil everything in the first decimal already.
... and my impression was, that teoporta was asking for practical help
I would NOT advise to use the standard Hendersson-Hasselbalch equation for calculations regarding sodium hydrogensulfate / di sodiumsulfate, as esp. the degree of dissociation of KHSO4 can't be neglected
But that is - basically - what you did, assuming 1:1 solution will yield pH close to pKa.
I didn't need a HH-
calculation for the
estimation of the buffer point, knowing that the rule of thumb "an acid will buffer at / near it's pKa" will be +/- valid for acids of medium strength in higher concentrations
I would propose to use a full law of mass action term for the calculation instead (see attachment) and solve the resulting equation
Agreed. That's what I did (even if for pedagogical purposes I posted ICE method here, but I checked it yields the same results).
Please see this thread - LaTeX can be entered directly into posts.
So, by the end of the day we both come down to the same recommendation, both with respect how to calculate this system and what needs to be done - except that i would recommend higher buffer strength than you do
but that's no basic disagreement, I take it
... and that is good for teoporta
regards
Ingo
p.s.: thank you for directing me to a thread explaining how to use LaTex in this forum: that's what I've been looking for