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248 ACIDS AND BASES

−3
If the pH is x, then the concentration will be 10 −x mol dm , so the acid concentration
−3
is 10 −4 mol dm .
SAQ 6.5 Without using a calculator, what is the pH of hydrochloric acid
of concentration 10 −5 mol dm −3 ?

Aside

Units

We encounter problems when it becomes necessary to take the logarithm of a con-
centration (which has units), since it contravenes one of the laws of mathematics. To
overcome this problem, we implicitly employ a ‘dodge’ by rewriting the equation as
[H 3 O ]
+
pH =− log 10
c O
−3
where the term c O is the standard state, which generally has the value of 1 mol dm .
The c O term is introduced merely to allow the units within the bracketed term above
to cancel. Throughout this chapter, concentrations will be employed relative to this
standard, thereby obviating the problem inherent with concentrations having units.

Justification Box 6.1

Sørenson introduced The definition of pH is given in Equation (6.20) as
this definition of pH in
+
1909. pH =− log [H ]
10
First we multiply both sides by ‘−1’:

+
−pH = log [H ]
10
and then take the antilog, to expose the concentration term. Correctly, the function
‘antilog’ means a mathematical operator, which performs the opposite job to the original
function. The opposite function to log is a type of exponential. As the log is written in
base 10, so the exponent must also be in base 10.
y
If y = log x,then x = 10 . This way we obtain Equation (6.21).
10

Sometimes we need to know the pH of basic solutions.