Hydrogen Ion Concentration

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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 < 7

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 < 10^-3.5 < 10^-2.0 < 10^-1.5

Hence, the strength of acids follows the order, D < B < C < AWeakest                  Strongest

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