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## The pH Scale

We usually deal with acid / base solution in the concentration range 10^{-1} to 10^{-2}M. To express the strength of such low concentrations, Sorensen introduced a logarithmic scale known as the pH scale. The term pH is derived from the French word ‘Purissance de hydrogene’ meaning, the power of hydrogen. pH of a solution is defined as the negative logarithm of base 10 of the molar concentration of the hydronium ions present in the solution.

pH = – log_{10}[H_{3}O^{+}] …………. (8.5)

The concentration of H_{3}O^{+} in a solution of known pH can be calculated using the following expression.

[H_{3}O^{+}] = 10^{-pH} (or) [H_{3}O^{+}] = antilog of (-pH) …………. (8.6)

Similarly, pOH can also be defined as follows

pOH = -log_{10}[OH^{–}] …………….. (8.7)

As discussed earlier, in neutral solutions, the concentration of [H_{3}O^{+}] as well as [OH^{+}] is equal to 1 × 10^{-7}M at 25°C . The pH of a neutral solution can be calculated by substituting this H_{3}O^{+ }concentration in the expression (8.5)

pH = – log_{10}[H_{3}O^{+}]

= – log_{10}10^{-7}

= (-7)(-1)log_{10}10 = +7(1) = 7 [∵log_{10}^{10} = 1]

Similary, we can calculate the pOH of a neutral solution using the expression (8.7), it is also equal to 7. The negative sign in the expression (8.5) indicates that when the concentration of [H_{3}O^{+}] increases the pH value decreases.

For example, if the [H_{3}O^{+}] increases from to 10^{-7} to 10^{-5M} the pH value of the solution decreases from 7 to 5. We know that in acidic solution, [H_{3}O^{+}]>[OH^{–}], i.e; [H_{3}O^{+}]>10^{-7}. So, we can conclude that acidic solution should have pH value less than 7 and basic solution should have pH value greater than 7.

**Relation Between pH and pOH**

A relation between pH and pOH can be established using their following definitions