Ionization of water, pH and pH scale

Pure water being a weak electrolyte under goes self ionization to a small extent as follows:

The equilibrium constant for this reaction is:

The concentration of unionized water is taken as constant because the degree on ionization of water is very small. So we can write this equation as:

where K_w is a constant and is known as the ionic product of water whose value is 1.008 x 10^-14 mol² L^-2at 298 K. In pure water the concentration of H₃O⁺ and OH^- are equal and so we can write,

[H₃O⁺] = [OH^-]

If, K_w = [H₃O⁺] [OH^-] = 1.008 x 10^-14 mol² L^-2 then,

[H₃O⁺] [OH^-] = 1.008 x 10^-14

[H₃O⁺]² = 1.008 x 10^-14

Thus in pure water [H₃O⁺] = [OH^-] = 1.0 x 10^-7 mol L^-1 at 298 K

Effect of temperature on K

The value of Kw varies with the change in temperature. The values of [H₃O⁺] and [OH^-] are always equal to each other at all temperatures but the values of K_w are different at different temperatures. The value of K_w increases with the rise in temperature. This is because increase in temperature will shift the equilibrium in the forward direction producing large concentrations of [H₃O⁺] and [OH^-] ions (Le Chatelier's principle).

Hence, K_w increases with rise in temperature.

In acidic solution

When an acidic solution of HCl is added to a pure neutral solution of water, the concentration of [H₃O⁺] becomes larger than 1.0 x 10^-7 mol L^-1. The dissociation equilibrium of water shifts in the reverse direction (Le Chatelier's principle). The excess [OH^-] ions combine with hydronium ions to form undissociated water molecules so that the value of K_w remains constant in the solution. The concentration of [OH^-] ions will then be equal to

The concentration of [H₃O⁺] is more than the concentration of the [OH^-] ions in acidic solution.

When a few drops of a base like NaOH is added to pure water, the concentration of [OH^-] increases and that of hydrogen ions decreases. The concentration of [H₃O⁺] can be calculated as:

Thus in basic solution the concentration of [OH^-] will be greater than of [H₃O⁺].

It can be concluded that the hydronium and hydroxyl ions are always present in solution whether they are acidic or basic. However their concentrations differ.

Problem

6. Calculate the hydronium and hydroxyl ion concentrations in (i) 0.01 M HCl (ii) 0.001 M NaOH solution at 298 K.

Solution

(i) HCl completely ionizes as:

The concentration of hydronium ions is equal to that of hydrochloric acid,

[H₃O⁺] = [HCl]

[HCl] = 0.01M = 1 x 10^-2 mol L^-1

The ionic product of water is K_w = [H₃O⁺] [OH^-]

Thus [H₃O⁺] = 1 x 10^-2 mol L^-1 and [OH^-] = 1 x 10^-12 mol L^-1

(ii) NaOH ionizes completely as:

NaOH_(aq) Na⁺_(aq) + OH^-_(aq)

The concentration of [OH^-] is equal to that of NaOH i.e.,

[NaOH] = [OH^-]

[NaOH] = 0.001 M = 1 x 10^-3 mol L^-1

[OH^-] = 1 x 10^-3 mol L^-1

K_w = [H₃O⁺] [OH^-]

Thus, [OH^-] = 1 x 10^-3 mol L^-1and [H₃O⁺] = 1 x 10^-11 mol L^-1.

Ph and ph scale

In 1909, Sorensen introduced a term for expressing the concentration of hydrogen ions, which give an idea about the acidic and basic characters of the aqueous solution. This term was called 'pH' which means the 'power of hydrogen ions'. The pH is defined as "the negative logarithm of the H₃O⁺ ion concentration in moles per litre".

For neutral solution at 298 K,

[H₃O⁺] = [OH^-] = 1.0 x 10^-7 mol L^-1

so that, pH = -log [H₃O⁺] = -log (1.0 x 10^-7) = 7

Substituting different values for [H₃O⁺] in the above relation we have,

For acidic solution pH <>

For basic solution pH > 7

For neutral solution pH = 7

A scale called as the pH scale is devised to express the acidic and basic properties of solution in terms of the pH value.

Fig: 8.1 - The pH scale

From the scale it is clear that for solutions with

pH between 0 to 2 strongly acidic

pH between 2 to 4 moderately acidic

pH between 4 to 7 weakly acidic

pH between 7 to 10 weakly basic

pH between 10 to 12 moderately basic

pH between 12 to 14 strongly basic.

Problems

6. Calculate the pH value of (i) 0.001 M HCl and (ii) 0.01 M NaOH

Solution

(i) Since HCl is a strong acid, it completely ionizes and therefore, H₃O⁺ ions concentration is equal to that of the acid itself i.e.,

[H₃O⁺] = [HCl] = 0.001 M = 1 x 10^-3 M

now, pH = -log [H₃O⁺]

pH = -log [1 x 10^-3]

= -(-3) log 10 = 3 (log 10 =1)

(ii) Since NaOH is a strong base, it completely ionizes and therefore, OH^- ions concentration is equal to that of the base itself i.e.,

[OH^-] = [NaOH] = 0.01 M = 1 x 10^-2 M

K_w = [H₃O⁺] [OH^-]

pH = -log [H₃O⁺]

pH = -log [1 x 10^-12]

= -(-12) log 10 = 12

7. Calculate the pH of a solution whose hydronium ion concentration is 6.2 x 10^-9 mol L^-1.

Solution

[H₃O⁺] = 6.2 x 10^-9 M

pH = -log [H₃O⁺]

pH = -log [6.2 x 10^-9]

= -(log 6.2 - 9 log 10)

= -log 6.2 + 9 x 1 (log 6.2 = 0.79)

= 9 - 0.79 = 8.21

8. Acid A, B, C and D have the following pKa values: A = 1.5, B = 3.5, C = 2.0, D = 5.0. Arrange these acids in the increasing order of acid strength.

Solution

We know that,

pK_a = -log K_a or K_a = 10^-pKa

Therefore, for the given acids,

K_a (A) = 10^-1.5 K_a (B) = 10^-3.5

K_a (C) = 10^-2.0 K_a (D) = 10^-5.0

Since, 10^-5.0 <>^-3.5 <>^-2.0 <>^-1.5

Hence, the strength of acids follows the order, D <>

9. The value of K_w is 9.55 x 10^-14 at a certain temperature. Calculate the pH of water at this temperature.

Solution

K_w = 9.55 x 10^-14

For water [H₃O⁺] = [OH^-]

If, K_w = [H₃O⁺] [OH^-] = 9.55 x 10^-14 then,

[H₃O⁺] [H₃O⁺] = 9.55 x 10^-14

[H₃O⁺]² = 9.55 x 10^-14

pH = -log [H₃O⁺]

pH = -log [3.09 x 10^-7]

= -(log 3.09 + log 10^-7)

= -(0.49 - 7) = 6.51

10. What is the pH of a solution whose hydrogen ion concentration is 0.005 x 10^-3 kg dm^-3?

Solution

In the solution [H⁺] = 0.005 x 10^-3 kg dm^-3 = 0.005 x 10^-3x 10³Lm^-3

= 0.005 g dm^-3 = 0.005 mol dm^-3

11. The pH of blood is maintained at 7.4 due to the presence of HCO^-₃ and H₂CO₃. If K_a of H₂CO₃ in blood is 8 x 10^-7 calculate the ratio [HCO^-₃]:[H₂CO₃] in blood.

Solution

pH = 7.4= -log[H⁺]

log[H⁺]= -7.4 = 8.6 [H⁺]= 3.98 x 10^-8 4 x 10^-8 M