In a quick addition to this post and this post, here’s a note about pH and significant figures. Firstly the ‘rule’.

*When taking the log of a number that is expressed in scientific notation (as hydrogen (hydronium) ion and hydroxide ion concentration often will be), the number of significant figures in the mantissa of the number are correctly replicated AFTER the decimal point in the log value.*

e.g., in terms of significant figures, in a pH calculation where the [H_{3}O^{+}] = **2.22** x 10^{-3 }M^{
}

(i.e., where there are 3 significant figures in the mantissa), then

pH = -log (**2.22** x 10^{-3}) = 2.**654**

(i.e., three significant figures are replicated *after* the decimal point)

If you would like a math explanation of this, see this simple explanation.

Because this is a ‘math thing’, this is actually almost certainly highly *irrelevant* to the AP chemistry exam, since I never recall a question where the one point for significant figures on the whole exam, was ever applied to a pH calculation, but you never know!

Good post, Adrian. I have grown to really dislike teaching significant figures over the last few years. My students always give me a look that says, “you have to be making up all of this stuff on the spot.” That is more or less how I feel. I don’t even teach it in AP Chemistry anymore. I just tell students to use three significant figures all the time and they will be right about 99% of the time.

In the UK, this is taught in math(s) class, not chemistry or physics – another thing I prefer!

I have had to teach Algebra II a few times during my career and the general rule I was told to use is “round to the tenths place.” Zero mention of significant figures.

The use of significant figure rules are very generalized. It is like trying to make a rule or a polynomial equation to fit some obscure curve. What really needs to be taught is the precision limits of our instrumentation and lab-ware.

I wouldn’t disagree.

When calculating hydronium concentration from pH, you would get an incorrect answer if you followed rules for sig digs.

e.g., pH 4.6, hydronium would be 2.5 x 10-5

but if rounded to one sig dig (since 4.6 has one sig dig) you would report 3. x 10-5, way off !

Can anyone explain this?

“Can anyone explain this?”

Yes, significant figures are a nightmare!

pH 4.6 is two significant digits meaning two decimal digits in the concentration. So that would be 2.51 x 10-5