# 7.11.2 The pH Scale

Hydronium ion concentration in molarity is more conveniently expressed on a logarithmic scale known as the pH scale. The pH of a solution is defined as the negative logarithm to base 10 of the activity (aH+) of hydrogen ion.

In dilute solutions (< 0.01 M), activity of hydrogen ion (H+) is equal in magnitude to molarity represented by [H+]. It should be noted that activity has no units and is defined as: [H+] / mol L-1

From the definition of pH, the following can be written,

pH = -log aH+ = -log{[H+]/ mol L-1}

Thus, an acidic solution of HCl (10–2 M) will have a pH = 2.

Similarly, a basic solution of NaOH having [OH] =10 –4 M and [H3O+] = 10–10 M will have a pH = 10. At 25 °C, pure water has a concentration of hydrogen ions, [H+] = 10–7 M.

Hence, the pH of pure water is given as: pH = -log(10-7) = 7

Acidic solutions possess a concentration of hydrogen ions, [H+] > 10–7 M, while basic solutions possess a concentration of hydrogen ions, [H+] < 10–7 M. thus, we can summarise that

Acidic solution has pH < 7

Basic solution has pH > 7

Neutral solution has pH = 7

Now again, consider the equation Kw = [H3O+][OH-] = (1 × 10-7)2 = 1 × 10-14 M2 at 298 K

Kw = [H3O+][OH-] = 10-14

Taking negative logarithm on both sides of equation, we obtain

-log Kw = -log {[H3O+][OH-]}

= -log [H3O+] -log[OH-]

= -log 10-14

pKw = pH + pOH = 14

Note that although Kw may change with temperature the variations in pH with temperature are so small that we often ignore it.

pKw is a very important quantity for aqueous solutions and controls the relative concentrations of hydrogen and hydroxyl ions as their product is a constant.

It should be noted that as the pH scale is logarithmic, a change in pH by just one unit also means change in [H+] by a factor of 10.

Similarly, when the hydrogen ion concentration, [H+] changes by a factor of 100, the value of pH changes by 2 units. Now you can realise why the change in pH with temperature is often ignored.

Measurement of pH of a solution is very essential as its value should be known when dealing with biological and cosmetic applications.

The pH of a solution can be found roughly with the help of pH paper that has different colour in solutions of different pH. Now-a-days pH paper is available with four strips on it.

The different strips have different colours (Figure) at the same pH. The pH in the range of 1-14 can be determined with an accuracy of ~0.5 using pH paper.

For greater accuracy pH meters are used. pH meter is a device that measures the pH-dependent electrical potential of the test solution within 0.001 precision. pH meters of the size of a writing pen are now available in the market.