The pH Scale | Ionic Equilibrium Class 11

The pH Scale

Acidity, Basicity & Ionic Product of Water | Ionic Equilibrium

1. Definition & Concept

Introduced by Sorenson (1909), pH stands for "Potenz of Hydrogen" (Power of Hydrogen). It is a logarithmic scale used to specify the acidity or basicity of an aqueous solution.

$$ pH = -\log_{10} [H^+] \quad \text{or} \quad [H^+] = 10^{-pH} $$

$$ pOH = -\log_{10} [OH^-] \quad \text{or} \quad [OH^-] = 10^{-pOH} $$

Logarithmic Nature: A change of 1 unit in pH corresponds to a 10-fold change in $[H^+]$ concentration.

2. Ionic Product of Water ($K_w$)

Water undergoes self-ionization: $H_2O \rightleftharpoons H^+ + OH^-$.

$$ K_w = [H^+][OH^-] $$

At 25°C (298 K):

• $[H^+] = [OH^-] = 10^{-7} M$
• $K_w = 10^{-14}$
• Taking negative log: $pK_w = pH + pOH = 14$

The pH Scale at 25°C:

• Acidic: pH < 7 ($[H^+] > 10^{-7}$)
• Neutral: pH = 7 ($[H^+] = 10^{-7}$)
• Basic: pH > 7 ($[H^+] < 10^{-7}$)

3. Effect of Temperature

Ionization of water is Endothermic ($\Delta H > 0$).

Trend: As Temperature increases $\rightarrow$ Ionization increases $\rightarrow$ $K_w$ increases.

Example at 90°C:

• $K_w \approx 10^{-12}$
• Neutral Point: $[H^+] = \sqrt{K_w} = 10^{-6}$
• Neutral pH = 6
• Therefore, at 90°C, pH 6 is neutral, pH < 6 is acidic, pH > 6 is basic.

4. pH Calculations: Common Cases

A. Strong Acid/Base (Complete Dissociation)

For $10^{-2} M$ $HCl$: $[H^+] = 10^{-2} \Rightarrow pH = 2$.

For $10^{-2} M$ $NaOH$: $[OH^-] = 10^{-2} \Rightarrow pOH = 2 \Rightarrow pH = 14-2 = 12$.

B. Very Dilute Strong Acid (Common Ion Effect)

Example: $10^{-8} M$ $HCl$.

We cannot neglect $H^+$ from water ($10^{-7}$). Total $[H^+] \approx 1.1 \times 10^{-7}$.

Result: pH $\approx 6.98$ (Not 8, as acid cannot have pH > 7).

C. Weak Acid (Partial Dissociation)

For a weak acid ($HA$) with concentration $C$ and dissociation constant $K_a$:

$$ [H^+] = \sqrt{K_a \cdot C} $$ $$ pH = \frac{1}{2} (pK_a - \log C) $$

Practice Quiz

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