# Exercises: pH, Logs and [H^{+}]

For these execises you are advised to make use of your own
electronic calculator, however, log_{10} and antilog
tables or pop-up calculator are available by clicking
appropriately.
These examples have few formats, but the values are generated
by a random number generator. Each time that you reload the page
using your web browser reload button, fresh values will be loaded
and corresponding solution expected. Enter your solution in the
Answer box, remembering to use a - (minus) to signify 'bar', if
appropriate. Simple errors will trigger a text box indicating the
likely source of error, unforeseen errors may trigger unforeseen
responses.

### Format A

A 1 mol dm^{_3} solution of a strong acid
(ideal, monobasic) will have a [H^{+}] of 1 mol
dm^{_3}.
Example:

Calculate the pH of 0.005 mol dm^{_3} HCl.

0.005 mol dm^{_3} of a strong acid will
have a [H^{+}] of 0.005 mol
dm^{_3}.

[H^{+}] = 5 x 10^{_3} mol
dm^{_3}.

^{_}log_{10} [H^{+}] =
^{_}(log_{10} 5 x 10^{_3})

^{_}log_{10} [H^{+}] =
^{_}(-3.6990) = 2.3010

therefore pH = 2.3

**Notes on **^{_}(-3.6990) = 2.301

Log_{10} 5 x 10^{_3} =
(log_{10} 5 + log_{10}
10^{_3})

Log_{10} 5 x 10^{_3} = (0.6990 +
^{_}3) = -3.6990

^{_}(Log_{10} 5 x 10^{_3}) =
^{_}(0.6990 + ^{_}3) = ^{_}(-3.6990)

The nuisance of ^{_}logs is that the characteristic and
mantissa must be treated separately:

the positive mantissa must be subtracted from the negative
characteristic, so that:

^{_}(0.6990 + ^{_}3)

= ^{_}(^{_}3 + 0.6690)

= ^{_ _}3 ^{_} 0.6990

= +3 ^{_} 0.6990

= +2.3010

### Now try out a calculation yourself:

### Format B

Example:
Calculate the concentration of a solution of strong acid with
a pH of 4.6.

^{_}(log_{10} [H^{+}] = 4.6 (=
^{_}log_{10} [strong acid])

therefore log_{10} [H^{+}] = ^{_}4.6 =
-5.4

therefore [H^{+}] = antilog -5.4 = 2.512 x
10^{_5} mol dm^{_3}

Created and maintained by Robert Lancashire and Andrew
Pearson,

University of the West Indies, Mona Campus, Jamaica.

Comments to authors at Robert Lancashire and/or
Andrew Pearson.

Created Thursday May 2nd 1996. Last modified 22nd February 2015.

#### URL:
http://wwwchem.uwimona.edu.jm/courses/pH/phexerc.html