are half of "H2SO4 pH sample problem" webpages just wrong, or am I wrong? I did a Google search for "h2so4 pH sample problem" and went through the results, and it looks like about 50% of the webpages "explaining" how to do this problem give the wrong answer when calculating the pH of a solution of $\ce{H2SO4}$.  The incorrect sources either (a) assume that each molecule of $\ce{H2SO4}$ donates only one proton (approximately true only at high concentrations); or (b) assume that each molecule of $\ce{H2SO4}$ donates both protons (approximately true only at low concentrations).  Only about half of the sources do the problem correctly by assuming that all $\ce{H2SO4}$ molecules donate the first proton and then using the second dissociation constant to compute the degree of dissociation of the second proton.

I'm no expert, so am I missing something, or are half of the sources out there just wrong?

Googling "h2so4 pH sample problem", here are the first eight hits after removing pages that did not contain an $\ce{H2SO4}$ sample problem, and how I scored them:


http://che1.lf1.cuni.cz/html/Calculations1112_II_handout.pdf -- says "For $\ce{H2SO4}$: $\ce{[H+]}$ = 2 $\times$ $\ce{[H2SO4]}$" -- incorrect.
https://www.quora.com/How-do-I-calculate-pH-of-10-3-M-H2SO4 -- the top-voted answer also says the concentration of $\ce{[H+]}$ is twice the molarity of $\ce{[H2SO4]}$ which 0.001, which is incorrect.  (This gives the incorrect answer of pH = 2.69; the correct answer is 2.73.)
https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Acids_and_Bases/Monoprotic_Versus_Polyprotic_Acids_And_Bases/Calculating_the_pH_of_the_Solution_of_a_Polyprotic_Base%2F%2FAcid -- uses the second dissociation constant correctly and an ICE chart -- correct
https://www.youtube.com/watch?v=gd8mYfiURx0 -- "Calculating the pH value of 1 M H2SO4" -- also assumes both protons are donated -- incorrect
https://www.youtube.com/watch?v=bfdbmT27L1c -- "Calculate pH of a Strong Acid" -- also assumes both protons are donated -- incorrect
https://web2.0calc.com/questions/what-is-the-ph-of-a-0-00050m-solution-of-h2so4_1 -- uses the second dissociation constant -- correct
If the pH is zero, what would be the normality of a sulphuric acid solution? -- I'm counting this as HALF-correct, because it is assumed that each $\ce{H2SO4}$ molecule donates only 1 proton.  This is approximately true at 1 M concentration, but I think it should be stated explicitly that the second proton doesn't get donated because the concentration is so high
http://www.sparknotes.com/chemistry/acidsbases/phcalc/problems/ -- correctly explains the partial donation of the second proton, so even though they don't show the working out, it's still correct


So it looks like even for just a slightly-non-trivial problem, almost a majority of free online help resources get the answer wrong.  Is there some subtlety I'm overlooking?
...and you didn't even get into the fact that almost all explanations will ignore the autodissociation of water!

In some cases your online resources will be wrong, of course, and it would be odd to expect uniform correctness in something people donate for free on the Internet (including here BTW).  So that's worth keeping in mind.

However, it's also the case that it is not always important to treat a problem in all its subtlety.  For example, the difference you get in the calculated pH of 1M H2SO4 by treating or ignoring the second dissociation equilibrium is likely to be smaller than your measurement error in a typical undergraduate lab.  So why bother?  On the other hand, if you were running a very careful experiment with 0.01 M H2SO4 you might well want to take those other equilibria into account, and if you were doing something super sensitive with 10^-7 M H2SO4 then you'll need to worry about the autoionization of water, too.

Generally we use the least complex model that gets us the answer consistent with our measurement limitations.  That maximizes insight and reduces the obfuscation of complex calculation, which can easily make it so we fail to recognize an erroneous answer.   This runs all through science and engineering, and it's why simple models have such great staying power even when they are superseded by more sophisticated understanding.  Naturally a concomitant is that the good scientist must become very adept at identifying the least complex model he can use.  That takes deep insight into the limitations of each model, the probable sources of error, the limits of measurement, and the quality of data on hand.  Being good at this is a much more important skill in the senior scientist than mastering the details of the most complex and realistic model there is.