Acids Bases — Concepts, Formulas & Examples

Acids and bases are two of the most fundamental categories in chemistry. CBSE Class 10 introduces them practically; Class 11 adds theory (Arrhenius, Bronsted-Lowry, Lewis). NEET tests pH calculations and conjugate pairs almost every year.

Core Concepts

Arrhenius definition

An acid gives H $^+$ ions in water, a base gives OH $^-$ ions. HCl → H $^+$ + Cl $^-$ . NaOH → Na $^+$ + OH $^-$ . Limited to aqueous solutions.

Bronsted-Lowry definition

An acid is a proton donor; a base is a proton acceptor. Broader — works in non-aqueous solvents. Every acid has a conjugate base after losing a proton, and vice versa.

\text{HCl} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{Cl}^-

Here HCl donates H $^+$ (acid), H $_2$ O accepts it (base). Products: H $_3$ O $^+$ is conjugate acid of H $_2$ O, Cl $^-$ is conjugate base of HCl.

Conjugate pairs: Every Bronsted acid-base reaction involves two conjugate pairs. Strong acids have weak conjugate bases and vice versa.

Lewis definition

An acid is an electron pair acceptor; a base is an electron pair donor. The broadest definition — includes things like BF $_3$ as acids, which have no hydrogens.

Examples of Lewis acids: BF $_3$ , AlCl $_3$ , FeCl $_3$ , H $^+$ , metal cations. They have empty orbitals to accept electron pairs.

Examples of Lewis bases: NH $_3$ , H $_2$ O, ROH, amines, halide ions. They have lone pairs to donate.

Lewis theory explains why AlCl $_3$ is a catalyst in Friedel-Crafts reactions — it is a Lewis acid that accepts an electron pair from the chloride of RCl, generating the electrophile R $^+$ .

pH scale

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

For neutral water $[\text{H}^+] = 10^{-7}$ , so pH = 7.

$\text{pH} = -\log_{10}[\text{H}^+]$ . Neutral water has pH 7, acids below 7, bases above 7. Each unit is a factor of 10 in H $^+$ concentration.

Related scales:

$\text{pOH} = -\log_{10}[\text{OH}^-]$
$\text{pH} + \text{pOH} = 14$ (at 25°C)
$\text{p}K_w = 14$ where $K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}$

pH of common substances:

Substance	pH
Gastric acid	1.5
Lemon juice	2.0
Vinegar	3.0
Black coffee	5.0
Milk	6.5
Blood	7.35-7.45
Baking soda	9.0
Household bleach	13.0

Strong vs weak acids and bases

Strong acids dissociate completely: HCl, HNO $_3$ , H $_2$ SO $_4$ , HBr, HI, HClO $_4$ .

Weak acids dissociate partially: CH $_3$ COOH ( $K_a = 1.8 \times 10^{-5}$ ), HF, H $_2$ CO $_3$ , H $_3$ PO $_4$ .

For a weak acid HA with concentration $c$ and dissociation constant $K_a$ :

[\text{H}^+] = \sqrt{K_a \times c} \quad \text{(when } K_a \ll c\text{)}

\text{pH} = \frac{1}{2}(\text{p}K_a - \log c)

Degree of dissociation ( $\alpha$ ): For a weak acid, $\alpha = \sqrt{K_a/c}$ . Dilution increases $\alpha$ (Ostwald’s dilution law) — the weaker the acid, the more dilution helps dissociation.

Buffer solutions

A buffer resists changes in pH when small amounts of acid or base are added. Two types:

Acidic buffer: Weak acid + its salt (CH $_3$ COOH + CH $_3$ COONa)
Basic buffer: Weak base + its salt (NH $_4$ OH + NH $_4$ Cl)

\text{pH} = \text{p}K_a + \log\frac{[\text{salt}]}{[\text{acid}]}

For basic buffers: $\text{pOH} = \text{p}K_b + \log\frac{[\text{salt}]}{[\text{base}]}$

Blood maintains pH 7.35-7.45 using the carbonic acid-bicarbonate buffer system: H $_2$ CO $_3$ /HCO $_3^-$ .

Neutralisation

Acid + base → salt + water. $\text{HCl} + \text{NaOH} \to \text{NaCl} + \text{H}_2\text{O}$ . Exothermic. Basis of titration.

Enthalpy of neutralisation: For strong acid + strong base, $\Delta H = -57.1$ kJ/mol (constant, because the net reaction is always H $^+$ + OH $^-$ → H $_2$ O). For weak acid + strong base, $|\Delta H|$ is less than 57.1 because some energy is used to dissociate the weak acid.

Indicators

Change colour with pH. Litmus — red in acid, blue in base. Phenolphthalein — colourless in acid, pink in base. Methyl orange — red in acid, yellow in base.

Choosing the right indicator for titration:

Strong acid + strong base: pH at equivalence ~7. Any indicator works.
Weak acid + strong base: pH at equivalence > 7. Use phenolphthalein (range 8-10).
Strong acid + weak base: pH at equivalence < 7. Use methyl orange (range 3.1-4.4).
Weak acid + weak base: No sharp endpoint. Not titrated with simple indicators.

Worked Examples

HCl is strong, fully dissociated. $[\text{H}^+] = 0.01$ M. pH = $-\log(0.01) = 2$ .

Lemon juice contains citric acid, which releases H $^+$ ions. Sour taste receptors on the tongue detect H $^+$ .

Calculate pH of 0.1 M acetic acid ( $K_a = 1.8 \times 10^{-5}$ ).

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

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

A buffer contains 0.1 M CH $_3$ COOH and 0.1 M CH $_3$ COONa. $pK_a$ of acetic acid = 4.74.

pH = $pK_a + \log\frac{[\text{salt}]}{[\text{acid}]} = 4.74 + \log\frac{0.1}{0.1} = 4.74 + 0 = 4.74$

When salt and acid are in equal concentration, pH = $pK_a$ . This is the most effective buffer composition.

In the reaction BF $_3$ + NH $_3$ → F $_3$ B-NH $_3$ :

BF $_3$ has an empty p orbital — it accepts the lone pair from NH $_3$ . BF $_3$ is the Lewis acid, NH $_3$ is the Lewis base. No proton transfer occurs — Bronsted theory cannot explain this.

Common Mistakes

Saying pH is concentration. pH is -log of concentration.

Writing that all acids contain hydrogen in the formula. Lewis acids like BF $_3$ do not.

Confusing strong and concentrated. Strong means fully dissociated; concentrated means a lot of acid per volume.

Using the simple $[\text{H}^+] = c$ formula for weak acids. Weak acids only partially dissociate — use $[\text{H}^+] = \sqrt{K_a \times c}$ instead. Using $c$ directly gives a pH that is far too low.

Forgetting that the pH of neutral water changes with temperature. At 25°C, neutral pH = 7. At 37°C (body temperature), $K_w$ is larger, so neutral pH drops to about 6.8. Neutral means $[\text{H}^+] = [\text{OH}^-]$ , not pH = 7.

Exam Weightage and Revision

JEE Main 2024 tested buffer pH with Henderson-Hasselbalch. NEET 2023 asked about conjugate acid-base pairs. CBSE Class 10 boards ask about pH of common substances and indicators every year. This is a cross-cutting topic that appears from Class 10 through JEE/NEET.

When a question gives a scenario, identify the core mechanism first, then match it to the concepts above. Most wrong answers come from reading the scenario too quickly.

Memorise pH of common substances — gastric acid 1.5, lemon 2, vinegar 3, milk 6.5, blood 7.4, baking soda 9, bleach 13.

Practice Questions

Q1. What is the conjugate base of H $_2$ SO $_4$ ?

HSO $_4^-$ (hydrogen sulphate ion). H $_2$ SO $_4$ donates one proton to become HSO $_4^-$ . Further, the conjugate base of HSO $_4^-$ is SO $_4^{2-}$ (sulphate ion).

Q2. Calculate the pH of 0.001 M NaOH.

NaOH is strong, fully dissociated. $[\text{OH}^-] = 0.001 = 10^{-3}$ M. pOH = 3. pH = 14 - 3 = 11.

Q3. Why is BF $_3$ a Lewis acid even though it has no hydrogen?

BF $_3$ has an empty p orbital on boron (boron has only 6 electrons in its valence shell, not 8). This empty orbital can accept an electron pair from a donor like NH $_3$ . Accepting an electron pair = Lewis acid. No protons are involved.

Q4. Why does the enthalpy of neutralisation of weak acid + strong base differ from strong acid + strong base?

For strong acid + strong base, $\Delta H = -57.1$ kJ/mol. For weak acid + strong base, some energy is consumed in dissociating the weak acid (since it is not fully ionised). So the net heat released is less: e.g., $\Delta H$ for CH $_3$ COOH + NaOH $\approx -55.2$ kJ/mol. The difference (about 2 kJ/mol) is the energy of dissociation of the weak acid.

Q5. What indicator would you use for titrating NH $_4$ OH with HCl?

This is a weak base + strong acid titration. The equivalence point pH is less than 7 (acidic). Use methyl orange (pH range 3.1-4.4), which changes colour right around the acidic equivalence point. Phenolphthalein would not work because its range (8-10) is too basic.

FAQs

Why is water amphoteric? Water can act as both an acid (donate H $^+$ to become OH $^-$ ) and a base (accept H $^+$ to become H $_3$ O $^+$ ). In the autoionisation reaction: $2\text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-$ , one water molecule acts as an acid and the other as a base.

Can pH be negative? Yes. If $[\text{H}^+] > 1$ M, pH is negative. For example, 2 M HCl has $[\text{H}^+] = 2$ M, so pH = $-\log 2 = -0.3$ . Similarly, pH can exceed 14 if $[\text{OH}^-] > 1$ M.

What is the difference between $pK_a$ and pH? $pK_a$ is a property of the acid itself — it measures the strength of the acid (lower $pK_a$ = stronger acid). pH is a property of the solution — it measures how acidic or basic the solution is. A weak acid ( $pK_a = 5$ ) in concentrated solution can have a low pH (quite acidic).

Why do antacids work? Antacids are bases (like Mg(OH) $_2$ or NaHCO $_3$ ) that neutralise excess HCl in the stomach. $\text{Mg(OH)}_2 + 2\text{HCl} \rightarrow \text{MgCl}_2 + 2\text{H}_2\text{O}$ . This raises the pH of stomach contents and relieves acidity.

Acids and bases are everywhere — in your stomach, in your kitchen, in the rain. The chapter rewards connecting theory to the world around you.