Significant Figures and pH (pOH as well)

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Here is the example:

Calculate the pH of a solution where the [H+] is 0.00100 M.
This could also be a pOH problem. The point being made below about significant figures is the same.

OK, you say, that's pretty easy, the answer is 3. After all 0.00100 is 10¯3 and the negative log of 10¯3 is 3.

You would probably be awarded partial credit for your answer. Why? Because the pH is not written to reflect the number of significant figures in the concentration.

Notice that there are three sig figs in 0.00100. (Hopefully you remember significant figures, since you probably studied them months ago before getting to acid base stuff. THEY ARE STILL IMPORTANT!)

So, our pH value should also reflect three significant figures.

However, there is a special rule to remember with pH (and pOH) values. The whole number portion DOES NOT COUNT when figuring out how many digits to write down.

Let's phrase that another way: in a pH (and a pOH), the only place where significant figures are contained is in the decimal portion.

So, the correct answer to the above problem is 3.000. Three sig figs and they are all in the decimal portion, NOT (I repeat NOT) in the whole number portion.

Here is a comment I saw online. The kid said the pH was 10.7 and was graded with some points off; I don't know how many. The comment the kid made was that 10.7 was three significant figures.

WRONG!! The 10 does not count. The correct answer would have had three figures in the decimal portion, as in 10.730 or 10.711.

The whole number portion of a pH (or a pOH) not counting towards sig figs is related to the two parts of a logarithm: the characteristic and the mantissa. The characteristic (the 10 in 10.7) only sets where the decimal point is in the value the logarithm represents. All the significant figures are encoded in the mantissa, which is the entire decimal portion.

You may look up more about the two parts of a logarithm on your own. The ChemTeam will spare you stories about using a slide rule and his six-place logarithm table from the days before calculators.

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