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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:

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?

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    $\begingroup$ And this is why I always told people to be careful about looking for help online. Personally, I've found that it's way worse that 50% for quantum mechanics problems... $\endgroup$ – chipbuster Jun 6 '18 at 8:03
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    $\begingroup$ Yes, you got it right. The web is dark and full of errors. $\endgroup$ – Ivan Neretin Jun 6 '18 at 13:23
  • $\begingroup$ @IvanNeretin I see what you've done here :D Nice pun. BTW I'm afraid OP already asked about it earlier. This question is kinda waste of time. Question is trivial, and no idea why someone would even dig through all these pseudo "resources". Also difference between 2.69 and 2.73 as far as pH goes is negligible and approximate calculations are employed often. Approximation isn't equal to error as every value describing physical world is approximate unless it's a constant made to be precise. $\endgroup$ – Mithoron Jun 6 '18 at 19:00
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    $\begingroup$ I'm voting to close this question as off-topic because it's essentially a rant how people on internet are usually wrong, not a question. $\endgroup$ – Mithoron Jun 6 '18 at 20:11
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    $\begingroup$ I had read your meta post yesterday and was planning to convert this into a proper Q&A, however, this isn't the way I would have done it. Your question: "am I missing something, or are half of the sources out there just wrong?" has the obvious answer that the sources are wrong. In fact, you've labeled them as being incorrect or correct yourself. I fail to see what is being asked, thus. $\endgroup$ – Gaurang Tandon Jun 7 '18 at 3:54
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...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.

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  • $\begingroup$ Well I figured that in most cases the question is asking about accuracy to two or three significant figures (that's what is used in the answers given), so you can ignore anything that's less significant than that (e.g. the auto-ionization of water), but you have to factor in anything that will make the answer incorrect at two-significant-figures accuracy (e.g., the second proton of H2SO4 at 0.001 M). $\endgroup$ – Bennett Jun 7 '18 at 7:10
  • $\begingroup$ I agree if they are giving answers to more precision than is justified by the ignoring of the weak-acid equilibria, that is a significant mistake. Goes back to the often neglected, boring, but important treatment of "appropriate precision" in calculated values. All that sig dig stuff students hate, ha ha. $\endgroup$ – Christopher Grayce Jun 7 '18 at 21:22

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