Acids, Bases and Salt Preparation

This topic covers the properties of acids and bases, pH, strong and weak acids, buffers, and methods Of salt preparation. It is essential for both Ordinary and Higher Level.

Definitions of Acids and Bases (OL/HL)

Arrhenius Definition

• Acid: produces \mathrm{H^+ (or \mathrm{H_3\mathrm{O^+) in water.
• Base: produces \mathrm{OH^- in water.

Bronsted-Lowry Definition (HL)

• Acid: proton (\mathrm{H^+) donor.
• Base: proton acceptor.

Conjugate Acid-Base Pairs (HL)

When an acid donates a proton, it forms its conjugate base. When a base accepts a proton, it forms Its conjugate acid.

\mathrm{HA + \mathrm{H_2\mathrm{O \rightleftharpoons \mathrm{H_3\mathrm{O^+ + \mathrm{A^-

• \mathrm{HA and \mathrm{A^- form a conjugate pair.
• \mathrm{H_2\mathrm{O and \mathrm{H_3\mathrm{O^+ form a conjugate pair.

Example (HL): Identify the conjugate acid-base pairs in:

\mathrm{NH_3 + \mathrm{H_2\mathrm{O \rightleftharpoons \mathrm{NH_4^+ + \mathrm{OH^-

\mathrm{NH_3/\mathrm{NH_4^+ and \mathrm{H_2\mathrm{O/\mathrm{OH^-.

Lewis Definition (HL)

• Acid: electron pair acceptor.
• Base: electron pair donor.

Strong and Weak Acids and Bases (OL/HL)

Strong Acids

Completely dissociate in water: \mathrm{HCl$$\mathrm{HNO_3$$\mathrm{H_2\mathrm{SO_4 (first Dissociation).

\mathrm{HCl + \mathrm{H_2\mathrm{O \to \mathrm{H_3\mathrm{O^+ + \mathrm{Cl^-

Weak Acids

Partially dissociate in water: \mathrm{CH_3\mathrm{COOH$$\mathrm{HF$$\mathrm{H_2\mathrm{CO_3.

\mathrm{CH_3\mathrm{COOH + \mathrm{H_2\mathrm{O \rightleftharpoons \mathrm{H_3\mathrm{O^+ + \mathrm{CH_3\mathrm{COO^-

Strong Bases

Completely dissociate: \mathrm{NaOH$$\mathrm{KOH$$\mathrm{Ca(OH)_2.

Weak Bases

Partially dissociate: \mathrm{NH_3.

\mathrm{NH_3 + \mathrm{H_2\mathrm{O \rightleftharpoons \mathrm{NH_4^+ + \mathrm{OH^-

The pH Scale (OL/HL)

\mathrm{pH = -\log_{10}[\mathrm{H_3\mathrm{O^+]

At 25^\circ\mathrm{C: [\mathrm{H_3\mathrm{O^+][\mathrm{OH^-] = 10^{-14}.

pH	[H3O+]	Description
0	1\mathrm{ M	Strongly acidic
7	10^{-7}\mathrm{ M	Neutral
14	10^{-14}\mathrm{ M	Strongly basic

Example (OL): Find the pH of a 0.01\mathrm{ M solution of \mathrm{HCl.

[\mathrm{H_3\mathrm{O^+] = 0.01 = 10^{-2}\mathrm{ M \implies \mathrm{pH = 2

Example (HL): Find the pH of a 0.10\mathrm{ M solution of \mathrm{CH_3\mathrm{COOH ($K_a = 1.8 \times 10^{-5}$).

K_a = \frac{[\mathrm{H_3\mathrm{O^+][\mathrm{CH_3\mathrm{COO^-]}{[\mathrm{CH_3\mathrm{COOH]} = \frac{x^2}{0.10 - x} \approx \frac{x^2}{0.10} X = \sqrt{0.10 \times 1.8 \times 10^{-5}} = \sqrt{1.8 \times 10^{-6}} = 1.34 \times 10^{-3}\mathrm{ M \mathrm{pH = -\log(1.34 \times 10^{-3}) = 2.87

Acid Dissociation Constant ($K_a$) (HL)

K_a = \frac{[\mathrm{H_3\mathrm{O^+][\mathrm{A^-]}{[\mathrm{HA]} \mathrm{pK_a = -\log K_a

The larger the $K_a$The stronger the acid.

Relationship: \mathrm{pH + \mathrm{pOH = 14 at 25^\circ\mathrm{C.

pH Calculations (HL)

Strong Monoprotic Acid

\mathrm{pH = -\log[\mathrm{H_3\mathrm{O^+]

Strong Diprotic Acid

For \mathrm{H_2\mathrm{SO_4 (first dissociation complete):

[\mathrm{H_3\mathrm{O^+] = 2c \quad (\mathrm{if both protons dissociate fully)

Dilution

$$C_1 V_1 = c_2 V_2$$

Example (HL): 25 mL of 0.10\mathrm{ M \mathrm{HCl is diluted to 250 mL. Find the new pH.

C_2 = \frac{0.10 \times 25}{250} = 0.010\mathrm{ M \mathrm{pH = -\log(0.010) = 2

Buffers (HL)

A buffer solution resists changes in pH when small amounts of acid or base are added. It consists of A weak acid and its conjugate base (or a weak base and its conjugate acid).

Buffer pH Equation (Henderson-Hasselbalch)

\mathrm{pH = \mathrm{pK_a + \log\frac{[\mathrm{A^-]}{[\mathrm{HA]}

Example (HL): A buffer contains 0.10\mathrm{ M \mathrm{CH_3\mathrm{COOH and 0.15\mathrm{ M \mathrm{CH_3\mathrm{COONa. Find the pH. (\mathrm{pK_a = 4.76)

\mathrm{pH = 4.76 + \log\frac{0.15}{0.10} = 4.76 + \log 1.5 = 4.76 + 0.18 = 4.94

How Buffers Work

When acid (\mathrm{H^+) is added: the conjugate base reacts with \mathrm{H^+Removing it.

\mathrm{CH_3\mathrm{COO^- + \mathrm{H_3\mathrm{O^+ \to \mathrm{CH_3\mathrm{COOH + \mathrm{H_2\mathrm{O

When base (\mathrm{OH^-) is added: the weak acid reacts with \mathrm{OH^-Neutralising it.

\mathrm{CH_3\mathrm{COOH + \mathrm{OH^- \to \mathrm{CH_3\mathrm{COO^- + \mathrm{H_2\mathrm{O

Neutralisation Reactions (OL/HL)

Acid + Base $\to$ Salt + Water

Example (OL):

\mathrm{HCl + \mathrm{NaOH \to \mathrm{NaCl + \mathrm{H_2\mathrm{O \mathrm{H_2\mathrm{SO_4 + 2\mathrm{NaOH \to \mathrm{Na_2\mathrm{SO_4 + 2\mathrm{H_2\mathrm{O

Salt Preparation (OL/HL)

Methods of Preparation

1. Acid + Metal:

\mathrm{Zn + \mathrm{H_2\mathrm{SO_4 \to \mathrm{ZnSO_4 + \mathrm{H_2

2. Acid + Base (neutralisation):

\mathrm{HCl + \mathrm{NaOH \to \mathrm{NaCl + \mathrm{H_2\mathrm{O

3. Acid + Carbonate:

\mathrm{HCl + \mathrm{CaCO_3 \to \mathrm{CaCl_2 + \mathrm{H_2\mathrm{O + \mathrm{CO_2

4. Acid + Insoluble Base (titration method):

Add the acid to the insoluble base (e.g., \mathrm{CuO) until no more dissolves. Filter and Evaporate.

5. Precipitation (mixing two solutions):

\mathrm{AgNO_3 + \mathrm{NaCl \to \mathrm{AgCl + \mathrm{NaNO_3

Choosing the Method

Desired salt	Method
Sodium, potassium, ammonium salts	Titration or evaporation
Soluble salts of other metals	Metal + acid or base + acid
Insoluble salts	Precipitation

Indicators (OL/HL)

Indicator	Colour in acid	Colour in base	pH range
Litmus	Red	Blue	4.5 — 8.3
Methyl orange	Red	Yellow	3.1 — 4.4
Phenolphthalein	Colourless	Pink	8.3 — 10.0
Universal indicator	Various	Various	1 — 14

Choosing an Indicator for Titrations (HL)

The indicator must change colour within the pH range of the equivalence point.

• Strong acid + strong base: any indicator (pH change large).
• Strong acid + weak base: methyl orange (equivalence pH < 7).
• Weak acid + strong base: phenolphthalein (equivalence pH > 7).
• Weak acid + weak base: no suitable indicator.

Common Pitfalls

1. Strong vs weak — strong acids/bases dissociate completely; weak ones partially.
2. pH of weak acids — do not assume [\mathrm{H^+] = c; use $K_a$.
3. Buffer calculations — the Henderson-Hasselbalch equation uses the ratio of base to acid.
4. Diprotic acids — each mole can donate two protons.
5. Indicator choice — match the indicator range to the equivalence point pH.

Practice Questions

Ordinary Level

1. Define acid and base using the Arrhenius definition.
2. Find the pH of a 0.001\mathrm{ M solution of \mathrm{NaOH.
3. Write the balanced equation for the reaction between \mathrm{HNO_3 and \mathrm{KOH.
4. Describe how to prepare a sample of \mathrm{ZnSO_4 crystals from zinc and dilute sulfuric acid.

Higher Level

1. Calculate the pH of a 0.15\mathrm{ M solution of \mathrm{HF ($K_a = 6.8 \times 10^{-4}$).
2. Calculate the pH of a buffer containing 0.20\mathrm{ M \mathrm{NH_3 and 0.25\mathrm{ M \mathrm{NH_4\mathrm{Cl ($K_b = 1.8 \times 10^{-5}$).
3. Explain why the pH of a 0.01\mathrm{ M solution of \mathrm{HCl is 2 but the pH of a 0.01\mathrm{ M solution of \mathrm{CH_3\mathrm{COOH is greater than 2.
4. 50 mL of 0.10\mathrm{ M \mathrm{NaOH is added to 50 mL of 0.10\mathrm{ M \mathrm{CH_3\mathrm{COOH. Calculate the pH of the resulting solution.

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pH Calculations in Detail (HL)

Strong Monoprotic Acid

Since strong acids dissociate completely, [\mathrm{H^+] = c (the acid concentration).

\mathrm{pH = -\log c

Worked Example 5 (HL): Find the pH of a 0.0025 \mathrm{ M solution of \mathrm{HNO_3.

\mathrm{pH = -\log(0.0025) = 2.60

Strong Diprotic Acid

For \mathrm{H_2\mathrm{SO_4The first proton dissociates completely. The second proton has $K_{a2} = 1.2 \times 10^{-2}$.

Worked Example 6 (HL): Find the pH of 0.010 \mathrm{ M \mathrm{H_2\mathrm{SO_4Accounting for Both protons.

First proton: [\mathrm{H^+] = 0.010 \mathrm{ M (complete dissociation).

Second proton: \mathrm{HSO_4^- \rightleftharpoons \mathrm{H^+ + \mathrm{SO_4^{2-}

K_{a2} = \frac{[\mathrm{H^+][\mathrm{SO_4^{2-}]}{[\mathrm{HSO_4^-]} = 1.2 \times 10^{-2}

Let $x$ = additional [\mathrm{H^+] from second dissociation:

$1.2 \times 10^{-2} = \frac{(0.010 + x)(x)}{(0.010 - x)}$

Solving the quadratic: x \approx 0.0046 \mathrm{ M.

[\mathrm{H^+]_{\mathrm{total} = 0.010 + 0.0046 = 0.0146 \mathrm{ M

\mathrm{pH = -\log(0.0146) = 1.84

Dilution Calculations

Worked Example 7 (HL): 25 mL of 0.10 \mathrm{ M \mathrm{HCl is diluted to 250 mL. Find the new PH.

c_2 = \frac{0.10 \times 25}{250} = 0.010 \mathrm{ M

\mathrm{pH = -\log(0.010) = 2.00

pH of Strong Bases

Worked Example 8 (HL): Find the pH of a 0.001 \mathrm{ M solution of \mathrm{NaOH.

[\mathrm{OH^-] = 0.001 \mathrm{ M

\mathrm{pOH = -\log(0.001) = 3

\mathrm{pH = 14 - 3 = 11

pH of Weak Acids: Detailed Treatment

Worked Example 9 (HL): Calculate the pH of a 0.15 \mathrm{ M solution of \mathrm{HF ($K_a = 6.8 \times 10^{-4}$). Check the validity of the approximation.

Without approximation:

$K_a = \frac{x^2}{0.15 - x} = 6.8 \times 10^{-4}$

$x^2 + 6.8 \times 10^{-4}x - 6.8 \times 10^{-4} \times 0.15 = 0$

$x^2 + 6.8 \times 10^{-4}x - 1.02 \times 10^{-4} = 0$

Using the quadratic formula: x = 9.9 \times 10^{-3} \mathrm{ M.

\mathrm{pH = -\log(9.9 \times 10^{-3}) = 2.00

Check: $c/K_a = 0.15/(6.8 \times 10^{-4}) = 220 > 100$So the approximation [\mathrm{H^+] \approx \sqrt{K_a \times c} gives essentially the same result.

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Buffers in Detail (HL)

How Buffers Work: Quantitative Treatment

Worked Example 10 (HL): Calculate the pH of a buffer containing 0.20 \mathrm{ M \mathrm{NH_3 And 0.25 \mathrm{ M \mathrm{NH_4\mathrm{Cl ($K_b = 1.8 \times 10^{-5}$).

First find $pK_a$ for \mathrm{NH_4^+:

$K_a = \frac{K_w}{K_b} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}$

$pK_a = 9.26$

Using Henderson-Hasselbalch:

\mathrm{pH = pK_a + \log\frac{[\mathrm{NH_3]}{[\mathrm{NH_4^+]} = 9.26 + \log\frac{0.20}{0.25} = 9.26 - 0.10 = 9.16

Buffer Capacity and pH Range

A buffer is most effective when:

1. The concentrations of acid and conjugate base are high ( greater than 0.10 M)
2. The ratio [\mathrm{A^-]/[\mathrm{HA] is between 0.1 and 10, giving an effective range of \mathrm{pH = pK_a \pm 1

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Salt Hydrolysis (HL)

pH of Salt Solutions

Salt formed from	Resulting pH	Reason
Strong acid + strong base	7	Neither ion hydrolyses
Strong acid + weak base	Less than 7	Cation hydrolyses
Weak acid + strong base	Greater than 7	Anion hydrolyses
Weak acid + weak base	Depends	Compare $K_a$ and $K_b$

Worked Example 11 (HL): Explain why \mathrm{Na_2\mathrm{CO_3 solution is alkaline.

\mathrm{CO_3^{2-} is the conjugate base of the weak acid \mathrm{HCO_3^-. In water:

\mathrm{CO_3^{2-} + \mathrm{H_2\mathrm{O \rightleftharpoons \mathrm{HCO_3^- + \mathrm{OH^-

The production of \mathrm{OH^- makes the solution alkaline.

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Titration Curves (HL)

Strong Acid-Strong Base

• Initial pH: low (strong acid)
• Equivalence point: pH = 7
• Sharp change near equivalence point

Weak Acid-Strong Base

• Initial pH: higher than strong acid at same concentration
• Buffer region present (weak acid and conjugate base coexist)
• Half-equivalence point: pH = $pK_a$
• Equivalence point: pH greater than 7

Strong Acid-Weak Base

• Equivalence point: pH less than 7

Worked Example 12 (HL): 50 mL of 0.10 \mathrm{ M \mathrm{NaOH is added to 50 mL of 0.10 \mathrm{ M \mathrm{CH_3\mathrm{COOH. Calculate the pH of the resulting solution.

At the equivalence point, all \mathrm{CH_3\mathrm{COOH is converted to \mathrm{CH_3\mathrm{COO^-.

n(\mathrm{CH_3\mathrm{COO^-) = 0.10 \times 0.050 = 0.0050 \mathrm{ mol

[\mathrm{CH_3\mathrm{COO^-] = \frac{0.0050}{0.100} = 0.050 \mathrm{ M

$K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}$

[\mathrm{OH^-] = \sqrt{5.56 \times 10^{-10} \times 0.050} = 5.27 \times 10^{-6} \mathrm{ M

\mathrm{pOH = 5.28, \quad \mathrm{pH = 8.72

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Common Pitfalls (Extended)

1. Strong vs weak — strong acids/bases dissociate completely; weak ones partially.
2. pH of weak acids — do not assume [\mathrm{H^+] = c; use $K_a$.
3. Buffer calculations — the Henderson-Hasselbalch equation uses the ratio of base to acid.
4. Diprotic acids — each mole can donate two protons.
5. Indicator choice — match the indicator range to the equivalence point pH.
6. pH of water at different temperatures — pure water has pH 7 at $25°C$ only.
7. $K_a$ vs. $K_b$ — remember the relationship $K_a \times K_b = K_w$.

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Practice Questions (Extended)

5. Write the balanced equation for the reaction between \mathrm{HNO_3 and \mathrm{KOH.
6. Describe how to prepare a sample of \mathrm{ZnSO_4 crystals from zinc and dilute sulfuric acid.
7. Calculate the pH of a 0.25 \mathrm{ M solution of \mathrm{CH_3\mathrm{COOH ($K_a = 1.8 \times 10^{-5}$) and the percentage dissociation.
8. A buffer contains 0.15 \mathrm{ M \mathrm{HCOOH ($pK_a = 3.75$) and 0.20 \mathrm{ M \mathrm{HCOONa. Calculate the pH and the pH after adding 0.01 \mathrm{ mol of \mathrm{NaOH to 1 \mathrm{ L of the buffer.
9. Explain why \mathrm{Na_2\mathrm{CO_3 solution is alkaline.
10. Sketch the pH titration curve for 25 \mathrm{ mL of 0.10 \mathrm{ M \mathrm{NH_3 titrated with 0.10 \mathrm{ M \mathrm{HCl. Label the equivalence point, buffer region, and the half-equivalence point.
11. Calculate $K_a$ for a 0.050 \mathrm{ M weak acid solution with pH 2.80.
12. Explain the difference between the Arrhenius, Bronsted-Lowry, and Lewis definitions of acids and bases, giving an example of a reaction that illustrates each definition.
13. A student prepares a buffer by mixing 100 \mathrm{ mL of 0.20 \mathrm{ M \mathrm{CH_3\mathrm{COOH with 50 \mathrm{ mL of 0.20 \mathrm{ M \mathrm{NaOH. Calculate the pH of the resulting buffer.
14. Describe the method of salt preparation by precipitation, giving an example.

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Lewis Acid-Base Theory (HL)

Definition

• Lewis acid: electron pair acceptor.
• Lewis base: electron pair donor.

Examples

Lewis acid: \mathrm{BF_3 (boron has an empty $p$ orbital), \mathrm{AlCl_3, \mathrm{H^+ (has No electrons), \mathrm{Cu^{2+} (can accept electron pairs).

Lewis base: \mathrm{NH_3 (lone pair on nitrogen), \mathrm{H_2\mathrm{O (lone pairs on oxygen), \mathrm{OH^- (lone pair and negative charge), \mathrm{Cl^- (lone pairs and negative charge).

Comparison of Acid-Base Theories

Theory	Acid definition	Base definition	Scope
Arrhenius	Produces \mathrm{H^+ in water	Produces \mathrm{OH^- in water	Aqueous solutions only
Bronsted-Lowry	Proton donor	Proton acceptor	Includes non-aqueous systems
Lewis	Electron pair acceptor	Electron pair donor	Widest scope, includes proton-free reactions

Example: The reaction between \mathrm{BF_3 and \mathrm{NH_3 is a Lewis acid-base reaction but NOT a Bronsted-Lowry reaction (no proton transfer):

\mathrm{BF_3 + \mathrm{NH_3 \to \mathrm{F_3\mathrm{B:\mathrm{NH_3

\mathrm{BF_3 accepts the lone pair from nitrogen (Lewis acid), \mathrm{NH_3 donates the lone pair (Lewis base). A dative covalent bond is formed.

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Salt Preparation Methods in Detail (OL/HL)

Method 1: Acid + Metal

Suitable for: Salts of moderately reactive metals (above hydrogen in reactivity series).

Example: Preparation of \mathrm{ZnSO_4:

1. Add excess zinc to dilute sulfuric acid.
2. Filter to remove excess zinc.
3. Evaporate the filtrate to crystallisation point.
4. Cool to form crystals.
5. Filter and dry crystals.

\mathrm{Zn + \mathrm{H_2\mathrm{SO_4 \to \mathrm{ZnSO_4 + \mathrm{H_2

Note: Very reactive metals (Na, K) react too violently. Unreactive metals (Cu, Ag) do not react With dilute acids.

Method 2: Acid + Base (Neutralisation)

Suitable for: Soluble salts of sodium, potassium, and ammonium.

Example: Preparation of \mathrm{NaCl:

1. Titrate \mathrm{NaOH with \mathrm{HCl using phenolphthalein to find the exact volume needed.
2. Repeat without indicator, adding exactly the right volume of acid.
3. Evaporate and crystallise.

Method 3: Acid + Carbonate

Suitable for: Most metal salts where the carbonate is available.

Example: Preparation of \mathrm{CaCl_2:

\mathrm{CaCO_3 + 2\mathrm{HCl \to \mathrm{CaCl_2 + \mathrm{H_2\mathrm{O + \mathrm{CO_2

Add excess \mathrm{CaCO_3 to \mathrm{HClFilter, evaporate, crystallise.

Method 4: Acid + Insoluble Base

Suitable for: Salts of metals with insoluble oxides or hydroxides (e.g., Cu, Fe, Zn).

Example: Preparation of \mathrm{CuSO_4:

\mathrm{CuO + \mathrm{H_2\mathrm{SO_4 \to \mathrm{CuSO_4 + \mathrm{H_2\mathrm{O

Warm \mathrm{CuO with dilute \mathrm{H_2\mathrm{SO_4Filter, evaporate, crystallise.

Method 5: Precipitation

Suitable for: Insoluble salts.

Example: Preparation of \mathrm{PbI_2:

\mathrm{Pb(NO_3)_2 + 2\mathrm{KI \to \mathrm{PbI_2\mathrm{(s) + 2\mathrm{KNO_3

Mix solutions, filter the precipitate, wash with distilled water, dry.

Choosing the Correct Method

Desired salt	Solubility of salt	Recommended method
\mathrm{NaCl	Soluble	Neutralisation (titration)
\mathrm{CuSO_4	Soluble	Acid + insoluble base
\mathrm{ZnSO_4	Soluble	Acid + metal or acid + base
\mathrm{PbI_2	Insoluble	Precipitation
\mathrm{CaCO_3	Insoluble	Cannot be prepared by aqueous methods

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Strength vs. Concentration (OL/HL)

Common Misconception

A common error is to confuse strength with concentration.

• Concentration: how much acid/base is dissolved (mol/L).
• Strength: how completely it dissociates.

Example: 0.01 M \mathrm{HCl (strong) has [\mathrm{H^+] = 0.01 M, pH = 2. 0.10 M \mathrm{CH_3\mathrm{COOH (weak) has [\mathrm{H^+] \approx 0.0013 M, pH = 2.9.

Despite the weak acid being 10 times more concentrated, its pH is higher because it is only Partially dissociated.

Dilution Effect on pH

• Diluting a strong acid by a factor of 10 increases pH by 1.
• Diluting a weak acid by a factor of 10 increases pH by 0.5 (approximately, because the degree of dissociation increases upon dilution).

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Summary Table: Acid-Base Concepts

Concept	Formula	Key Point
pH	\mathrm{pH = -\log[\mathrm{H^+]	Lower = more acidic
$K_w$	[\mathrm{H^+][\mathrm{OH^-] = 10^{-14}	At $25°C$
$K_a$	\frac{[\mathrm{H^+][\mathrm{A^-]}{[\mathrm{HA]}	Higher = stronger acid
$pK_a$	$-\log K_a$	Lower = stronger acid
Henderson-Hasselbalch	\mathrm{pH = pK_a + \log\frac{[\mathrm{A^-]}{[\mathrm{HA]}	Buffer pH
$K_a \times K_b$	$= K_w$	Conjugate pair relationship

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Practice Questions (Further Extended)

15. Define acid and base using the Arrhenius definition.
16. Find the pH of a 0.001 \mathrm{ M solution of \mathrm{NaOH.
17. Explain why \mathrm{NH_4\mathrm{Cl solution has a pH less than 7.
18. Calculate the mass of \mathrm{AgNO_3 required to prepare 250 \mathrm{ mL of 0.10 \mathrm{ M solution.
19. Describe how you would prepare a pure, dry sample of lead(II) sulfate.
20. Explain why \mathrm{HCl is a strong acid but \mathrm{HF is a weak acid, despite fluorine being more electronegative than chlorine.
21. Calculate the pH at the half-equivalence point when 25 \mathrm{ mL of 0.10 \mathrm{ M \mathrm{CH_3\mathrm{COOH is titrated with \mathrm{NaOH.
22. A solution of \mathrm{H_2\mathrm{SO_4 has pH 1.30. Calculate the concentration of the acid, assuming the first proton dissociates completely and the second is negligible.
23. Explain, with equations, how a buffer containing \mathrm{CH_3\mathrm{COOH and \mathrm{CH_3\mathrm{COONa resists pH change when (a) a small amount of \mathrm{HCl is added, and (b) a small amount of \mathrm{NaOH is added.

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Polyprotic Acids (HL)

Acids that can donate more than one proton are called polyprotic acids.

Carbonic Acid (\mathrm{H_2\mathrm{CO_3)

\mathrm{H_2\mathrm{CO_3 \rightleftharpoons \mathrm{H^+ + \mathrm{HCO_3^- \quad K_{a1} = 4.3 \times 10^{-7}

\mathrm{HCO_3^- \rightleftharpoons \mathrm{H^+ + \mathrm{CO_3^{2-} \quad K_{a2} = 4.8 \times 10^{-11}

Note: $K_{a1} \gg K_{a2}$. The first dissociation is much stronger than the second because removing \mathrm{H^+ from a negatively charged ion (\mathrm{HCO_3^-) is harder than from a neutral molecule (\mathrm{H_2\mathrm{CO_3).

Phosphoric Acid (\mathrm{H_3\mathrm{PO_4)

$K_{a1} = 7.5 \times 10^{-3}, \quad K_{a2} = 6.2 \times 10^{-8}, \quad K_{a3} = 4.8 \times 10^{-13}$

Each successive dissociation constant is smaller by a factor of approximately $10^5$.

Sulfuric Acid (\mathrm{H_2\mathrm{SO_4)

K_{a1} = \mathrm{very large (complete), \quad K_{a2} = 1.2 \times 10^{-2}

The first proton dissociates completely (strong acid), but the second does not.

Biological Buffer Systems

The carbonic acid-bicarbonate buffer system maintains blood pH at approximately 7.4:

\mathrm{H_2\mathrm{CO_3 \rightleftharpoons \mathrm{H^+ + \mathrm{HCO_3^- \quad pK_{a1} = 6.37

Although the blood pH of 7.4 is outside the optimal range ($pK_a \pm 1 = 5.37$ to $7.37$), the System works because:

1. The body constantly removes \mathrm{CO_2 through respiration
2. The kidneys regulate \mathrm{HCO_3^- levels
3. Haemoglobin acts as an additional buffer

The phosphate buffer system (\mathrm{H_2\mathrm{PO_4^-/\mathrm{HPO_4^{2-}, $pK_{a2} = 7.21$) is Important intracellularly.

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Environmental Chemistry of Acids and Bases

Acid Rain

Rain with pH less than 5.6 (normal rain is slightly acidic due to dissolved \mathrm{CO_2).

Causes: \mathrm{SO_2 and \mathrm{NO_x from fossil fuel combustion react with atmospheric Water:

\mathrm{SO_2 + \mathrm{H_2\mathrm{O \to \mathrm{H_2\mathrm{SO_3

2\mathrm{SO_2 + \mathrm{O_2 \to 2\mathrm{SO_3 \quad \mathrm{then \quad \mathrm{SO_3 + \mathrm{H_2\mathrm{O \to \mathrm{H_2\mathrm{SO_4

Effects: Damage to buildings (limestone dissolves), acidification of lakes (harmful to aquatic Life), damage to forests (nutrient leaching).

Neutralisation of Acid Rain

Lakes can be treated with limestone (\mathrm{CaCO_3):

\mathrm{CaCO_3 + 2\mathrm{H^+ \to \mathrm{Ca^{2+} + \mathrm{H_2\mathrm{O + \mathrm{CO_2

However, this is a temporary solution. Reducing emissions at source is the long-term answer.

Worked Examples

Example 1: Mole calculation

Calculate the number of moles in $12.0\,\text{g}$ of $\text{NaOH}$ ($M_r = 40.0$).

Solution:

$n = \frac{m}{M_r} = \frac{12.0}{40.0} = 0.300\,\text{mol}$

Example 2: Reacting masses

$\text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2$

What mass of $\text{CaCl}_2$ is produced from $10.0\,\text{g}$ of $\text{CaCO}_3$? ($M_r[\text{CaCO}_3] = 100$, $M_r[\text{CaCl}_2] = 111$)

Solution:

$n(\text{CaCO}_3) = \frac{10.0}{100} = 0.100\,\text{mol}$

From the equation, ratio is $1:1$, so $n(\text{CaCl}_2) = 0.100\,\text{mol}$.

$m(\text{CaCl}_2) = 0.100 \times 111 = 11.1\,\text{g}$