The pH of a solution is given by
the formula pH is equal to negative log of 𝑎 sub H+, where 𝑎 sub H+ is the
concentration of hydrogen ions. Determine the concentration of
hydrogen ions in a solution whose pH is 8.4.
When the pH is equal to 8.4, 8.4 is
equal to negative log of 𝑎 sub H+. We are trying to work out this
value which is the concentration of hydrogen ions. We recall that when a logarithm is
written without a base, it is assumed to be base 10. Log 𝑥 is the same as log base 10
of 𝑥. We can multiply both sides of our
equation by negative one such that negative 8.4 is equal to log base 10 of 𝑎 sub
H+. We know that a logarithmic function
is the inverse of an exponential function. If 𝑥 is equal to log base 𝑎 of
𝑦, then 𝑎 to the power of 𝑥 is equal to 𝑦. This means that 10 to the power of
negative 8.4 is equal to 𝑎 sub H+. The concentration of hydrogen ions
is therefore equal to 10 to the power of negative 8.4.