Question bd6c1

May 19, 2015

I usually don't follow this rule, although I admit I should, but pH and pOH values should take into account the number of sig figs given for the concentration of ${H}^{+}$ and OH""^(-)#, respectively.

However, there's a little trick to remember. For pH and pOH values, only the digits after the decimal count as being significant.

In your example, you have $\left[{H}^{+}\right] = 8.25 \cdot {10}^{- 9}$. This number has 3 significant figures, 8, 2, and 5. If you take the negative log you should get

$p {H}_{\text{sol}} = - \log \left(\left[{H}^{+}\right]\right) = - \log \left(8.25 \cdot {10}^{- 9}\right) = 8.08355$

You would be tempted to say that, rounded to three sig figs, the answer should be

$p {H}_{\text{sol}} = 8.08$ $\to$ you'd be wrong!

You need to take 3 sig figs after the decimal, so the answer becomes

$p {H}_{\text{sol}} = 8.084$ $\to$ the three sig figs are 0, 8, and 4.

Another example. If you have $\left[{H}^{+}\right] = \text{0.1 M}$, you'd be tempted to say that the pH is

$p {H}_{\text{sol}} = - \log \left(0.1\right) = 1$ $\to$ with one sig fig.

But again, you'd be wrong because you actually need to have 1 dig fig after the decimal, like this

$p {H}_{\text{sol}} = - \log \left(0.1\right) = 1.0$ $\to$ one sig fig, which is 0.

This is just a result of how sig figs are calculated for logs and antilogs. Read more about that here (towards the bottom of the page)

http://web.campbell.edu/faculty/fetterman/Significant%20Figures.htm

and here

http://www.chemteam.info/AcidBase/pH&sig-figs.html