Intermediate

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Ionic Equilibrium — Acids, Bases & pH

Master Ionic Equilibrium for JEE & NEET. Covers Arrhenius, Brønsted-Lowry, Lewis theories, Ka, Kb, Kw, pH of strong/weak acids and bases, Ostwald's dilution law.

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Ionic equilibrium governs the behaviour of acids, bases, and salts in aqueous solution — one of the most practically important areas of chemistry. The Arrhenius, Brønsted-Lowry, and Lewis theories provide a hierarchy of definitions for acids and bases, while the ionisation constants $K_{a}$ and $K_{b}$ quantify how strongly a species donates or accepts protons. pH calculations — for strong and weak acids/bases, and the relationship between $K_{a}$ , $K_{b}$ , and $K_{w}$ — appear in virtually every JEE and NEET chemistry paper. This topic requires both conceptual clarity (which theory applies, what conjugate pairs are) and numerical fluency (solving ICE tables, applying approximations correctly).

1. Theories of Acids and Bases

Theory	Acid	Base	Limitation
Arrhenius	Gives $H^{+}$ in water	Gives ${OH}^{-}$ in water	Only in aqueous solution; ${NH}_{3}$ base not explained
Brønsted-Lowry	Proton donor	Proton acceptor	Requires proton transfer; doesn't cover Lewis acids
Lewis	Electron pair acceptor	Electron pair donor	Broadest; includes ${BF}_{3}$ , ${AlCl}_{3}$ , metal ions

Conjugate pairs: When an acid donates a proton, the species formed is its conjugate base. ${CH}_{3} COOH / {CH}_{3} {COO}^{-}$ is a conjugate acid-base pair. Stronger acid → weaker conjugate base.

Amphoteric species — act as both acid and base: $H_{2} O$ , ${HCO}_{3}^{-}$ , ${HPO}_{4}^{2 -}$ , ${HS}^{-}$ .

2. Ionisation of Water and $K_{w}$

$H_{2} O ⇌ H^{+} + {OH}^{-} K_{w} = [H^{+}] [{OH}^{-}] = 1 \times 10^{- 14} at 25 ° C$

In pure water: $[H^{+}] = [{OH}^{-}] = 1 \times 10^{- 7} M$
$K_{w}$ is temperature-dependent: increases with temperature (endothermic ionisation).
At higher $T$ : $K_{w} > 10^{- 14}$ → $[H^{+}] > 10^{- 7}$ → pH of pure water $< 7$ (still neutral).
$K_{a} \times K_{b} = K_{w}$ for conjugate acid-base pair.

3. pH Scale and Definitions

$pH = - \log [H^{+}] pOH = - \log [{OH}^{-}] pH + pOH = 14 (at 25°C)$

Solution type	Condition	pH (at 25°C)
Acidic	$[H^{+}] > [{OH}^{-}]$	$< 7$
Neutral	$[H^{+}] = [{OH}^{-}]$	$= 7$
Basic	$[H^{+}] < [{OH}^{-}]$	$> 7$

4. Strong Acids and Bases — pH Calculations

Strong acids/bases are completely dissociated — use concentration directly.

Strong acid (e.g., HCl, $H_{2} {SO}_{4}$ , ${HNO}_{3}$ ): $[H^{+}] = C_{acid}$

Example: $0.01 M HCl$ : $[H^{+}] = 0.01 M$ ; $pH = - \log (0.01) = 2$

Strong base (e.g., NaOH, KOH): $[{OH}^{-}] = C_{base}$ ; $pOH = - \log C_{base}$ ; $pH = 14 - pOH$

Example: $0.001 M NaOH$ : $[{OH}^{-}] = 10^{- 3}$ ; $pOH = 3$ ; $pH = 14 - 3 = 11$

5. Weak Acids — Ionisation Constant $K_{a}$ and pH

For $HA ⇌ H^{+} + A^{-}$ :

$K_{a} = \frac{[H^{+}] [A^{-}]}{[HA]} = C α^{2} (Ostwald's dilution law, for α ≪ 1)$

where $C$ = initial concentration, $α$ = degree of ionisation.

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

Worked Example

$0.1 {M CH}_{3} COOH$ , $K_{a} = 1.8 \times 10^{- 5}$ :

$[H^{+}] = \sqrt{1.8 \times 10^{- 5} \times 0.1} = \sqrt{1.8 \times 10^{- 6}} = 1.34 \times 10^{- 3} M$

$pH = - \log (1.34 \times 10^{- 3}) = 2.87$

$α = [H^{+}] / C = 1.34 \times 10^{- 3} / 0.1 = 0.0134 = 1.34 %$

Strength of Acids and Bases

Stronger acid = larger $K_{a}$ = smaller $p K_{a}$ . Stronger base = larger $K_{b}$ = smaller $p K_{b}$ .

For conjugate pair: $K_{a} \times K_{b} = K_{w} \Rightarrow p K_{a} + p K_{b} = 14$ (at 25°C).

Stronger the acid → weaker its conjugate base.

6. Polyprotic Acids

Acids with more than one ionisable proton. For $H_{2} {SO}_{4}$ : first ionisation complete (strong), second partial (weak).

For $H_{3} {PO}_{4}$ : $K_{a 1} ≫ K_{a 2} ≫ K_{a 3}$ — each successive ionisation is weaker. For pH calculations, only $K_{a 1}$ matters (the subsequent ionisations contribute negligibly to $[H^{+}]$ ).

pH Calculation Flowchart

Type	Formula for $[H^{+}]$	Example
Strong acid	$[H^{+}] = C$	0.01M HCl → pH = 2
Weak acid	$[H^{+}] = \sqrt{K_{a} C}$	0.1M AcOH → pH = 2.87
Strong base	$[{OH}^{-}] = C$ ; pH = 14 − pOH	0.001M NaOH → pH = 11
Weak base	$[{OH}^{-}] = \sqrt{K_{b} C}$ ; pH = 14 − pOH	0.1M NH₃ ( $K_{b} = 1.8 \times 10^{- 5}$ ) → pH = 11.13

JEE / NEET Power Tips — Ionic Equilibrium

$[H^{+}] = \sqrt{K_{a} \cdot C}$ is only valid when $α ≪ 1$ (approximately $< 5 %$ ). If $K_{a} / C > 0.01$ , the approximation breaks down — use the quadratic formula. Always check: if $α < 5 %$ , the approximation is fine.
$K_{a} \times K_{b} = K_{w}$ for a conjugate pair. This means $p K_{a} + p K_{b} = 14$ . So if you know $K_{a}$ of acetic acid, you instantly know $K_{b}$ of acetate ion: $K_{b} = K_{w} / K_{a} = 10^{- 14} / 1.8 \times 10^{- 5} = 5.6 \times 10^{- 10}$ .
Increasing temperature increases $K_{w}$ , decreasing pH of neutral water below 7. Pure water is always neutral (even if $pH < 7$ at high $T$ ) because $[H^{+}] = [{OH}^{-}]$ still holds. "Neutral" means $[H^{+}] = [{OH}^{-}]$ , not pH = 7.
Lewis acids include: ${BF}_{3}$ , ${AlCl}_{3}$ , ${FeCl}_{3}$ , metal ions ( ${Fe}^{3 +}$ , ${Cu}^{2 +}$ ). They are electron pair acceptors but are NOT Brønsted-Lowry acids. A very common JEE MCQ tests this distinction.

Practice Questions

Q1 (NEET): Calculate the pH of a 0.1 M solution of acetic acid. ( $K_{a} = 1.8 \times 10^{- 5}$ )

Explanation:

For a weak acid, the hydrogen ion concentration can be approximated using Ostwald's dilution law:
$[H^{+}] = \sqrt{K_{a} \cdot C}$

$[H^{+}] = \sqrt{1.8 \times 10^{- 5} \cdot 0.1} = \sqrt{1.8 \times 10^{- 6}}$
$[H^{+}] = 1.34 \times 10^{- 3}$ M

Now, calculate the pH:
$pH = - \log (1.34 \times 10^{- 3}) = 3 - \log (1.34)$
$pH = 3 - 0.127 = 2.87$

Verification of approximation: Degree of dissociation $α = \frac{1.34 \times 10^{- 3}}{0.1} = 0.0134$ (or 1.34%). Since $α < 5 %$ , the approximation $[HA] \approx C$ is perfectly valid.

Q2 (JEE Main): The $K_{a}$ of acetic acid is $1.8 \times 10^{- 5}$ . Find the $K_{b}$ of the acetate ion ( ${CH}_{3} {COO}^{-}$ ).

Explanation:

For any conjugate acid-base pair in aqueous solution, the product of their dissociation constants equals the ionic product of water ( $K_{w}$ ):
$K_{a} \cdot K_{b} = K_{w}$

Assuming standard temperature (25°C), $K_{w} = 1.0 \times 10^{- 14}$ .
$K_{b} = \frac{K_{w}}{K_{a}} = \frac{1.0 \times 10^{- 14}}{1.8 \times 10^{- 5}}$

$K_{b} = 5.56 \times 10^{- 10}$

Q3 (NEET MCQ): Which of the following is a Lewis acid but NOT a Brønsted-Lowry acid?

A) $HCl$
B) ${BF}_{3}$
C) ${NH}_{4}^{+}$
D) $H_{2} O$

Answer: B) ${BF}_{3}$ .

Explanation: ${BF}_{3}$ (Boron trifluoride) has an incomplete octet on the central Boron atom (only 6 valence electrons), allowing it to accept an electron pair. This makes it a Lewis acid. However, it does not possess any protons ( $H^{+}$ ) to donate, meaning it cannot act as a Brønsted-Lowry acid. $HCl$ and ${NH}_{4}^{+}$ are both proton donors (so they are Brønsted-Lowry acids). Water ( $H_{2} O$ ) is amphoteric.

Q4 (Board): The pH of pure water at 60°C is roughly 6.51 (which is less than 7). Does this mean pure water at 60°C is acidic?

Explanation:

No — it is still perfectly neutral.

The auto-ionisation of water ( $H_{2} O ⇌ H^{+} + {OH}^{-}$ ) is an endothermic process. According to Le Chatelier's Principle, increasing the temperature to 60°C drives the reaction forward, increasing the value of $K_{w}$ to roughly $1.0 \times 10^{- 13}$ .

Consequently, the concentration of both ions increases: $[H^{+}] = [{OH}^{-}] = \sqrt{K_{w}} \approx 3.16 \times 10^{- 7}$ M. Because $[H^{+}]$ is greater than $10^{- 7}$ , the pH drops below 7. However, the fundamental definition of neutrality is that $[H^{+}] = [{OH}^{-}]$ , which remains true. A pH of 7 only defines neutrality specifically at 25°C.

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DifficultyIntermediate

Est. Read Time24 minutes

CategoryEquilibrium

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Ionic Equilibrium — Acids, Bases & pH

1. Theories of Acids and Bases

2. Ionisation of Water and $K_{w}$

3. pH Scale and Definitions

4. Strong Acids and Bases — pH Calculations

5. Weak Acids — Ionisation Constant $K_{a}$ and pH

Worked Example

Strength of Acids and Bases

6. Polyprotic Acids

pH Calculation Flowchart

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Ionic Equilibrium — Acids, Bases & pH

1. Theories of Acids and Bases

2. Ionisation of Water and Kw

3. pH Scale and Definitions

4. Strong Acids and Bases — pH Calculations

5. Weak Acids — Ionisation Constant Ka and pH

Worked Example

Strength of Acids and Bases

6. Polyprotic Acids

pH Calculation Flowchart

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2. Ionisation of Water and $K_{w}$

5. Weak Acids — Ionisation Constant $K_{a}$ and pH