Ionisation of water

Ionisation of water

We have learnt that when an acidic or a basic substance is dissolved in water, depending upon its nature, it can either donate (or) accept a proton. In addition to that the pure water itself has a little tendency to dissociate. i.e, one water molecule donates a proton to an another water molecule. This is known as auto ionisation of water and it is represented as below.

In the above ionisation, one water molecule acts as an acid while the another water molecule acts as a base.

The dissociation constant for the above ionisation is given by the following expression

The concentration of pure liquid water is one. i.e, [H₂O]² = 1

 K_w = [H₃O⁺ ][OH^- ] .    ....(8.4)

Here, K_w represents the ionic product (ionic product constant) of water

It was experimentally found that the concentration of H₃O⁺ in pure water is 1×10^-7 at 25^oC . Since the dissociation of water produces equal number of H₃O⁺ and OH^- , the concentration of OH^- is also equal to 1×10^-7 at 25^oC.

Therefore, the ionic product of water at 25^oC is

K_w = [H₃O]⁺[OH^-]                ......(8.4)

K_w = (1 × 10^-7 )(1 × 10^-7 )

= 1 ×10^-14.

Like all equilibrium constants, K_w  is also a constant at a particular temperature. The dissociation of water is an endothermic reaction. With the increase in temperature, the concentration of H ₃O⁺ and OH- also increases, and hence the ionic product also increases.

In neutral aqueous solution like NaCl solution, the concentration of H₃O⁺ is always equal to the concentration of OH^- whereas in case of an aqueous solution of a substance which may behave as an acid (or) a base, the concentration of H₃O⁺ will not be equal to [OH^-].

We can understand this by considering the aqueous HCl as an example. In addition to the auto ionisation of water, the following equilibrium due to the dissociation of HCl can also exist.

HCl + H₂O ↔ H₃O ⁺ + Cl^-

In this case, in addition to the auto ionisation of water, HCl molecules also produces H₃O⁺ ion by donating a proton to water and hence [H₃O⁺]>[OH^-]. It means that the aqueous HCl solution is acidic. Similarly, in basic solution such as aqueous NH₃ , NaOH etc….. [OH^–]>[H₃O⁺].

Example 8.1

Calculate the concentration of OH^- in a fruit juice which contains 2 ×10^-3 M, H₃O⁺ ion. Identify the nature of the solution.

Given that H₃O⁺ = 2 ×10^-3 M

K_w = [H₃O⁺ ][OH ^- ]

∴[OH - ]= Kw /[H₃O⁺ ] = [1 ××10^-14] / [2 x 10 ³] =5 ×10^-12 M

 2 ×10^-3 >> 5 ×10^-12

 i.e., [H₃O⁺ ] >> [OH^-], hence the juice is acidic in nature

Evaluate yourself – 5

At a particular temperature, the K_w of a neutral solution was equal to 4 ×10^-14. Calculate the concentration of [H₃O⁺ ] and [OH^- ].

Answer:

Given solution is neutral

∴ [ H₃O⁺ ] = [OH^- ]

Let [H₃O⁺ ] = x ; then [OH^- ] = x

K_w = [H₃O⁺ ][OH^- ]

4× 10^-14 = x . x

 x² = 4 × 10^-14

 x = √ 4 × 10^-14  = 2 ×10^-7