EXAM STRATEGY & IMPORTANT QUESTIONS GUIDE

Definition:
Pharmaceutical analysis is the branch of analytical chemistry that identifies, determines, quantifies and purifies drugs, pharmaceutical raw materials, intermediates and finished dosage forms. It ensures that every product complies with the standards laid down by the IP, BP or USP.

Scope of Pharmaceutical Analysis:
The scope of pharmaceutical analysis covers every stage in the life of a medicine.
1. Identification and assay🔊 of active pharmaceutical ingredients (API).
2. Determination of purity and impurity profile.
3. Stability testing — shelf-life and degradation products.
4. Pharmacokinetic🔊 and bioavailability measurements.
5. Process monitoring during manufacture (IPQC).
6. Forensic and toxicological analysis of biological samples.

Techniques of Analysis:
Qualitative analysis tells us what is present in a sample — colour tests, melting-point determination, spot tests and planar chromatography are common examples.

Quantitative analysis tells us how much is present and has two main branches:

• Classical (chemical) methods — titrimetry🔊 and gravimetry🔊.
• Instrumental methods — electrometric🔊 (potentiometry, conductometry, polarography🔊); spectroscopy🔊 (UV, IR, AAS, NMR); chromatography🔊 (HPLC, GC, TLC); MS.

Methods of Expressing Concentration:

Term	Definition	Formula / Unit
Normality🔊 (N)	Gram-equivalents of solute per litre of solution	N = g-equivalents / L
Molarity🔊 (M)	Moles of solute per litre of solution	M = mol / L
Molality🔊 (m)	Moles of solute per kilogram of solvent	m = mol / kg
Mole fraction (χ)	Moles of component / total moles	Dimensionless
% w/w	Weight of solute / weight of solution × 100	g / 100 g
% w/v	Weight of solute / volume of solution × 100	g / 100 mL
% v/v	Volume of solute / volume of solution × 100	mL / 100 mL
ppm	Parts per million — dilute concentrations	mg / kg (or µg / g)

Primary Standard — Definition + Criteria:
A primary standard🔊 is a highly pure and stable chemical of accurately known composition that can be used directly to prepare a standard solution by accurate weighing.

A good primary standard must satisfy the following criteria:
1. High purity (≥ 99.9 %).
2. Stable — non-hygroscopic🔊, unaffected by air, CO₂ or light.
3. High equivalent weight — minimises weighing errors.
4. Readily soluble in the titration solvent.
5. Gives a sharp, stoichiometric🔊 reaction with the titrant.

Examples: anhydrous Na₂CO₃, K₂Cr₂O₇, potassium hydrogen phthalate (KHP), oxalic acid🔊 dihydrate, Na₂C₂O₄, AgNO₃, iodine.

Secondary Standard:
A secondary standard🔊 is a solution whose concentration is established by titration against a primary standard. Secondary standards fail one or more of the primary-standard criteria (they may be hygroscopic, volatile or unstable) and therefore cannot be prepared with exact concentration by weighing.

Examples: NaOH (hygroscopic + absorbs CO₂), HCl (volatile), KMnO₄ (self-decomposes on storage), Na₂S₂O₃ (slowly oxidised by air and light).

(a) Preparation + Standardisation of 0.1 N NaOH:
Preparation: Dissolve about 4.0 g of NaOH pellets in freshly boiled and cooled distilled water, transfer to a 1000 mL volumetric flask and make up to mark. Store in a polyethylene bottle fitted with a soda-lime guard tube to absorb atmospheric CO₂.
Standardisation: Titrate against primary standard KHP (MW 204.22).
Accurately weigh about 0.5 g of KHP, dissolve in 25 mL water, add two drops of phenolphthalein🔊, and titrate with the NaOH solution until a permanent pale-pink end-point appears.
Calculation: N_NaOH = (weight of KHP × 1000) / (204.22 × volume of NaOH in mL).

(b) Preparation + Standardisation of 0.1 N HCl:
Preparation: Dilute 8.5 mL of concentrated HCl (specific gravity 1.18, ~11.7 N) to 1000 mL with distilled water.
Standardisation: Titrate against primary standard anhydrous Na₂CO₃, which must be dried at 270 °C for 1 hour before use.
Accurately weigh about 0.15 g of Na₂CO₃, dissolve in 50 mL water, add methyl orange🔊 indicator, and titrate with the HCl solution to a red end-point.
Reaction: Na₂CO₃ + 2 HCl → 2 NaCl + H₂O + CO₂.
Calculation: N_HCl = (weight of Na₂CO₃ × 1000) / (53 × volume of HCl in mL).

(c) Preparation + Standardisation of 0.1 N KMnO₄:
Preparation: Dissolve about 3.2 g of KMnO₄🔊 in 1000 mL of water, boil for about 1 hour, cool, filter through sintered glass (to remove MnO₂), and store in an amber bottle.
Standardisation: Titrate against primary standard oxalic acid dihydrate.
Accurately weigh about 0.63 g of oxalic acid, dissolve in water, add dilute H₂SO₄, warm to 70 °C and titrate with KMnO₄ until a permanent pale-pink colour appears (KMnO₄ is its own indicator).
Reaction: 2 KMnO₄ + 5 H₂C₂O₄ + 3 H₂SO₄ → K₂SO₄ + 2 MnSO₄ + 10 CO₂ + 8 H₂O.
Calculation: N_KMnO₄ = (weight of oxalic acid × 1000) / (63.03 × volume of KMnO₄ in mL).

Definition of Error:
An error is the difference between the observed (measured) value and the true or accepted value of a quantity. It is usually expressed either as an absolute error (E = observed − true) or as a relative error (E/true × 100%). Errors are classified broadly into three groups described below.

1. Determinate (Systematic) Errors:
Determinate errors 🔊 have a definable cause and a definite sign, so they are reproducible and can be detected and removed. They are subdivided as follows.

(a) Instrumental errors arise from an uncalibrated balance, cracked glassware, a faulty burette, or an aged detector.
(b) Reagent or chemical errors occur when impure reagents, atmospheric CO₂ dissolved in NaOH, or a decomposed KMnO₄ solution alter the stoichiometry of the reaction.
(c) Operational or personal errors include incorrect reading of the meniscus, parallax 🔊, colour blindness of the analyst, and delayed end-point recognition.
(d) Method errors are the most serious because they are inherent in the procedure itself — for example, incomplete or non-stoichiometric reaction, indicator error, or interfering side reactions.

2. Indeterminate (Random) Errors:
Indeterminate errors 🔊 are accidental and have no single definable cause. They arise from small uncontrollable variations in temperature, air currents, vibrations and the analyst's own estimation of the final digit. Such errors follow a Gaussian 🔊 distribution around the mean and can only be minimised by performing replicate measurements and averaging.

3. Gross (Mistake) Errors:
Gross errors are outright human blunders, such as spilling a portion of the sample, misreading a figure, or mis-labelling a bottle. The only remedy is to reject the result and repeat the analysis.

Accuracy versus Precision:
Although students often confuse the two, accuracy and precision describe different qualities of a measurement, as the following table shows.

Feature	Accuracy	Precision
Meaning	Closeness of the result to the true value	Closeness of repeated results to one another
Measured by	Absolute or relative error	Standard deviation or RSD
Mainly affected by	Determinate (systematic) errors	Indeterminate (random) errors
Improved by	Calibration, blank, control sample	Replicate analysis, better technique

A simple analogy is the dart-board: hitting the bull's-eye repeatedly represents accuracy, while grouping the darts close together (even if off-centre) represents precision.

Significant Figures:
The significant figures of a measurement are all the digits that are known with certainty plus the first uncertain digit. They reflect both the precision of the instrument and the reliability of the result. The commonly followed rules are as follows.
(i) All non-zero digits are significant.
(ii) Zeros lying between non-zero digits are significant (for example 2.005 has four).
(iii) Leading zeros are not significant (0.0045 has only two).
(iv) Trailing zeros after a decimal point are significant (2.500 has four).
(v) In addition or subtraction, the result is rounded to the least number of decimal places of the original values.
(vi) In multiplication or division, the result is rounded to the least number of significant figures.

Methods of Minimising Errors:
Errors can never be completely eliminated, but the following measures reduce them to an acceptable level.
(1) Calibration 🔊 of all volumetric glassware and instruments (balance, pipette, burette, volumetric flask, spectrophotometer).
(2) Use of a blank determination, in which all reagents except the sample are carried through the procedure to correct for reagent impurities.
(3) Use of a control determination, in which a pure substance of known composition is analysed in parallel with the sample.
(4) Running the analysis in triplicate or more replicates and reporting the mean, which minimises random error.
(5) Use of SRM or pharmacopoeial reference substances.
(6) Independent cross-checking of the result by a second, different analytical method.
(7) Rejection of outlier values using statistical tests such as the Q-test.

Definition:
A pharmacopoeia is an official, legally binding compendium issued by a recognised national authority that lays down the standards of identity, purity, strength, quality and storage for drugs, excipients and dosage forms manufactured or imported into the country.

Major Pharmacopoeias:
The following table compares the six pharmacopoeias most frequently consulted in analytical practice.

Pharmacopoeia	Abbr.	Country / Region	Issuing Authority	Latest Edition
Indian Pharmacopoeia	IP	India	Indian Pharmacopoeia Commission, Ghaziabad	IP 2022
British Pharmacopoeia	BP	United Kingdom	British Pharmacopoeia Commission, MHRA	BP 2024
United States Pharmacopeia–National Formulary	USP–NF	United States of America	USP Convention, Rockville	USP 46–NF 41
European Pharmacopoeia	Ph.Eur.	Europe (37 member states)	EDQM, Strasbourg	11th Edition
Japanese Pharmacopoeia	JP	Japan	PMDA	JP 18
International Pharmacopoeia	Ph.Int.	Global (recommended)	WHO, Geneva	11th Edition

Brief Notes on IP, BP and USP:
The Indian Pharmacopoeia (IP) is the legally enforceable standard for drugs marketed in India. It is published by the Indian Pharmacopoeia Commission, Ghaziabad, under the Ministry of Health and Family Welfare, and is revised every few years with supplements.
The British Pharmacopoeia (BP) is published annually by the British Pharmacopoeia Commission of the MHRA and includes all current monographs of the European Pharmacopoeia along with British-specific texts.
The United States Pharmacopeia (USP), issued jointly with the National Formulary as USP–NF, is published by the non-governmental USP Convention at Rockville, Maryland. It is updated continuously through official supplements.

Sources of Impurities in Medicinal Agents:
Impurities may enter a drug substance at any stage from raw material to final packaging. The principal sources are given below.
(1) Raw materials may themselves contain chemically related impurities that pass into the final product.
(2) Reagents and solvents used during manufacture may leave residues, traces of heavy metals or organic solvents.
(3) The manufacturing process contributes impurities through incomplete reaction, side products, catalyst residues and thermal degradation.
(4) Equipment used in production can release impurities through corrosion of iron vessels or leaching from copper and other metals.
(5) Atmospheric contamination by CO₂, oxygen, moisture and light causes oxidation, hydrolysis and photolysis.
(6) During storage, exposure to heat, light and humidity promotes hydrolysis, oxidation, photolysis and polymerisation.
(7) Microbial contamination produces degradation products and endotoxins, particularly in syrups, creams and parenteral products.
(8) Packaging materials such as rubber closures, plastic liners and glass containers may contribute plasticisers (phthalates), leachable metal ions, or alkali from soft glass.

Definition and General Principle:
A limit test is a semi-quantitative test that detects and controls the small amount of impurity likely to be present in a pharmaceutical substance. The opalescence 🔊, turbidity or colour produced by the test sample is matched against that produced by a standard solution containing a known, officially permitted amount of the impurity. The comparison is carried out in matched Nessler cylinders 🔊 viewed vertically against a white background. If the test reading is equal to or less than the standard, the sample complies with the pharmacopoeia.

1. Limit Test for Chlorides (Cl⁻):
Principle: Chloride ions react with AgNO₃ in the presence of dilute HNO₃ to form a white, curdy precipitate of silver chloride that appears as an opalescence.
Cl⁻ + AgNO₃ → AgCl↓ (white) + NO₃⁻ Procedure: Equal volumes of the test solution and of the standard chloride solution (prepared from NaCl to give a known Cl⁻ content) are placed in two matched Nessler cylinders. To each, 1 mL of dilute HNO₃ and 1 mL of AgNO₃ solution are added. The cylinders are mixed, kept aside for 5 minutes, and the opalescence is compared. If the test is not more opalescent than the standard, the sample passes the test.

2. Limit Test for Sulphates (SO₄²⁻):
Principle: Sulphate ions react with BaCl₂ in the presence of dilute HCl to form a fine white turbidity of barium sulphate. A small amount of K₂SO₄ is added to seed uniform nucleation and make the turbidity reproducible.
SO₄²⁻ + BaCl₂ → BaSO₄↓ (white) + 2 Cl⁻ Procedure: Equal volumes of the test solution and the standard sulphate solution (0.1087 g of K₂SO₄ per litre, which supplies the officially permitted level of SO₄²⁻) are placed in matched Nessler cylinders. To each is added 2 mL of ethanolic BaCl₂ solution, 1 mL of dilute HCl and 0.15 mL of the standard potassium sulphate reagent. The cylinders are mixed, allowed to stand for 5 minutes, and the turbidities are compared against a dark background.

3. Limit Test for Iron (Fe):
Principle: In an ammoniacal medium (approximately pH 9), ferric ions (Fe³⁺) combine with thioglycollic acid to form a stable pink to violet coloured complex. If the sample contains ferrous ions, they are first oxidised to ferric by citric acid, and the thioglycollic acid then reduces Fe³⁺ back to Fe²⁺ within the complex, producing the colour.
2 Fe³⁺ + 2 HSCH₂COOH → [Fe(SCH₂COO)]²⁺ + 2 H⁺ Procedure: The sample is dissolved in water, and iron-free citric acid, thioglycollic acid 🔊 and dilute ammonia are added. The resulting colour is compared in a Nessler cylinder with a standard solution containing 20 µg of iron, treated in the same way. The test colour must not be deeper than the standard.

4. Limit Test for Arsenic (As) — Gutzeit Test:
Principle: In the Gutzeit test 🔊, arsenic compounds in the sample are reduced to arsine gas (AsH₃) by nascent hydrogen liberated from zinc and dilute H₂SO₄. The arsine gas then reacts with mercuric chloride paper to give a yellow to brown stain, the intensity of which depends on the amount of arsenic present.
As³⁺ + 3 H → AsH₃↑;  AsH₃ + 2 HgCl₂ → As(HgCl)₃ (yellow-brown stain) Apparatus: The Gutzeit apparatus consists of a wide-mouthed bottle in which the reaction is carried out, fitted with a glass tube that holds a plug of lead acetate cotton (which absorbs any H₂S interference) and, at its upper end, a strip of mercuric chloride paper on which the stain develops.
Procedure: The sample, zinc, potassium iodide, SnCl₂ and dilute H₂SO₄ are placed in the bottle and the apparatus is assembled quickly. Reaction is allowed to proceed for 40 minutes at 40 °C. The stain on the mercuric chloride paper is then compared with a standard arsenic stain obtained from 10 µg of arsenic treated in the same way; the test stain must not be darker.

Theories of Acid-Base Indicators:
Two classical theories are used to explain why indicators change colour when the pH of the solution changes.

1. Ostwald's Ionisation Theory (1894). According to this theory, an indicator is a weak organic acid or a weak organic base whose undissociated (molecular) form has one colour and whose ionised form has a different colour. A change in pH shifts the following equilibrium.
HIn ⇌ H⁺ + In⁻  (two different colours) Applying the Henderson–Hasselbalch 🔊 equation gives pH = pK_In + log([In⁻]/[HIn]). The eye can distinguish the colour change only when the ratio of the two forms is approximately 10 : 1, so the working range of an indicator is pK_In ± 1.

2. Quinonoid (Chromophoric) Theory. The colour change is explained as a structural rearrangement of the indicator molecule between two tautomers 🔊 — the benzenoid form and the quinonoid form — which absorb light at different wavelengths. For example, phenolphthalein 🔊 exists as a colourless lactone (benzenoid) in acidic solution and changes to a pink quinonoid form in alkali.

Common Acid-Base Indicators (pH ranges):

Indicator	pH range	Acid colour	Base colour
Methyl orange	3.1 – 4.4	Red	Yellow
Methyl red	4.4 – 6.2	Red	Yellow
Bromothymol blue	6.0 – 7.6	Yellow	Blue
Phenol red	6.8 – 8.4	Yellow	Red
Phenolphthalein	8.3 – 10.0	Colourless	Pink
Thymolphthalein	9.3 – 10.5	Colourless	Blue

Classification of Acid-Base Titrations and Neutralisation Curves:
Acid-base titrations are classified according to the strength of the acid and the base being titrated, and each class gives a characteristic pH-versus-volume curve.

1. Strong acid versus strong base (example: HCl versus NaOH). The neutralisation curve shows a sharp vertical rise from approximately pH 4 to pH 10 around the equivalence point (pH 7). Any indicator whose working range lies between pH 4 and 10 — such as methyl orange, methyl red or phenolphthalein — can be used.

2. Weak acid versus strong base (example: acetic acid versus NaOH). The equivalence point lies in the alkaline region near pH 8.7, because the conjugate base of the weak acid is hydrolysed. Phenolphthalein (pH 8.3 – 10) is the indicator of choice.

3. Strong acid versus weak base (example: HCl versus NH₄OH). The equivalence point falls in the acidic region near pH 5.3 because the conjugate acid of the weak base undergoes hydrolysis. Methyl orange or methyl red is suitable.

4. Weak acid versus weak base (example: acetic acid versus ammonia). The curve shows no sharp inflection, so visual indicators are unreliable; the end-point is determined by a potentiometric 🔊 or conductometric method.

Principle:
In water, very weak acids (with K_a < 10⁻⁸) and very weak bases (with K_b < 10⁻⁸) do not give a sharp end-point because the self-ionisation of water (K_w = 10⁻¹⁴) is comparable in magnitude. When the titration is performed in a suitable non-aqueous solvent, the Brønsted 🔊 proton-transfer equilibrium is shifted so that the analyte behaves as a much stronger acid or base, producing a sharp end-point.

Classification of Non-aqueous Solvents:
Non-aqueous solvents are classified according to their ability to donate or accept protons.

1. Protogenic (acidic) solvents readily donate protons and therefore enhance the basicity of weak bases dissolved in them. Common examples are anhydrous glacial acetic acid 🔊, formic acid and sulphuric acid.
2. Protophilic (basic) solvents accept protons and therefore enhance the acidity of weak acids dissolved in them. Examples include pyridine, ethylenediamine and liquid ammonia.
3. Amphiprotic solvents can both donate and accept protons, for example methanol, ethanol and water itself.
4. Aprotic (inert) solvents neither donate nor accept protons and have no self-ionisation; examples are benzene, chloroform, carbon tetrachloride and dioxane. They are used as diluents to adjust the dielectric constant of the medium.

A levelling solvent 🔊 reduces all strong acids (or bases) to the strength of its own lyonium (or lyate) ion, while a differentiating solvent preserves the relative strength differences between acids (or bases).

Common Titrants:
For weak bases, the standard titrant is 0.1 M perchloric acid (HClO₄) dissolved in glacial acetic acid, with crystal violet as indicator. For weak acids, the standard titrant is 0.1 M sodium methoxide (CH₃ONa) in a mixture of methanol and benzene, with thymol blue as indicator.

Estimation of Sodium Benzoate (salt of a weak acid):
Sodium benzoate is the sodium salt of a weak acid, and in glacial acetic acid it behaves as a base that accepts a proton from perchloric acid.
Procedure: Accurately weigh about 0.3 g of the sample and dissolve it in 30 mL of anhydrous glacial acetic acid together with 10 mL of chloroform. Add two drops of crystal violet indicator and titrate against 0.1 M perchloric acid until the solution turns from violet to blue-green. Carry out a blank determination in parallel.
C₆H₅COO⁻Na⁺ + HClO₄ + CH₃COOH → C₆H₅COOH + NaClO₄ + CH₃COOH Each millilitre of 0.1 M HClO₄ is equivalent to 0.01441 g of sodium benzoate (molecular weight 144.1).

Estimation of Ephedrine Hydrochloride (salt of a weak base):
Ephedrine hydrochloride is the hydrochloride salt of a weak base; the chloride ion must first be masked with mercuric acetate to prevent it from interfering with the titration.
Procedure: Accurately weigh about 0.4 g of the sample and dissolve it in 30 mL of glacial acetic acid. Add 10 mL of mercuric acetate solution, which converts the reactive Cl⁻ into un-ionised HgCl₂. Add crystal violet indicator and titrate with 0.1 M HClO₄ until the end-point changes from violet to blue-green. Carry out a blank determination in parallel.
2 (C₁₀H₁₅NO·HCl) + Hg(CH₃COO)₂ → 2 C₁₀H₁₅NO·CH₃COOH + HgCl₂
C₁₀H₁₅NO·CH₃COOH + HClO₄ → C₁₀H₁₅NO·HClO₄ + CH₃COOH Each millilitre of 0.1 M HClO₄ is equivalent to 0.02017 g of ephedrine hydrochloride.

Principle:
In a precipitation titration, the analyte and the titrant combine to form an insoluble precipitate. The end-point is detected by an indicator that produces a visible colour change immediately after the analyte has been completely precipitated, indicating that the next drop of titrant is in slight excess.

1. Mohr's Method (Direct Titration):
In Mohr's method, chloride or bromide is titrated directly with AgNO₃ in a neutral or slightly alkaline medium (pH 6.5 – 9) using K₂CrO₄ as indicator.
AgNO₃ + NaCl → AgCl↓ (white) + NaNO₃ After all the chloride has been precipitated, the first slight excess of Ag⁺ combines with chromate to give reddish-brown silver chromate, which signals the end-point.
2 Ag⁺ + CrO₄²⁻ → Ag₂CrO₄↓ (reddish-brown) Limitations: The method cannot be used in acidic medium, because chromate is converted to dichromate, nor in strongly alkaline medium, where silver precipitates as Ag₂O.

2. Volhard's Method (Back-Titration in Acidic Medium):
In Volhard's method, a known excess of AgNO₃ is added to the chloride solution and the unreacted Ag⁺ is then back-titrated with standard ammonium or potassium thiocyanate 🔊 using ferric ammonium sulphate as indicator.
Cl⁻ + excess AgNO₃ → AgCl↓ + remaining Ag⁺
Ag⁺ + SCN⁻ → AgSCN↓ (white)
SCN⁻ (excess) + Fe³⁺ → [FeSCN]²⁺ (blood-red) — end-point The titration is performed in dilute HNO₃ medium, which prevents hydrolysis of Fe³⁺.
Difficulty with chloride: AgCl is slightly more soluble than AgSCN, so SCN⁻ can displace Cl⁻ from the precipitate and give a fading end-point. This is overcome either by filtering off AgCl before back-titration, or by adding nitrobenzene (see modified method).

3. Modified Volhard's Method:
In the modified procedure, nitrobenzene is added to the solution before back-titration. The nitrobenzene coats the AgCl precipitate and prevents it from re-dissolving during back-titration, giving a stable end-point.

4. Fajans Method (Adsorption Indicator):
Fajans method uses adsorption indicators such as fluorescein 🔊, dichlorofluorescein and eosin 🔊, which adsorb onto the surface of the precipitate at the equivalence point.
Before the end-point, the AgCl precipitate carries a negative surface charge (because Cl⁻ is in excess), so the negatively charged indicator does not adsorb. After the end-point, the surface becomes positively charged (because Ag⁺ is in excess), and the indicator is adsorbed to give a pink colour on the precipitate.
The titration is performed in a neutral or weakly acidic medium, and dextrin is added to prevent flocculation of the precipitate.

Estimation of Sodium Chloride by Mohr's Method:
Principle: Sodium chloride is titrated directly with standard AgNO₃ using K₂CrO₄ as indicator; the reddish-brown colour of Ag₂CrO₄ signals the end-point.
NaCl + AgNO₃ → AgCl↓ + NaNO₃ Procedure: Accurately weigh about 0.05 g of NaCl and dissolve it in 25 mL of water. Add 1 mL of 5 % potassium chromate solution and titrate against standard 0.1 M silver nitrate until the first permanent reddish-brown colour persists.
Calculation: Each millilitre of 0.1 M AgNO₃ is equivalent to 0.005844 g of NaCl (molecular weight 58.44). Percentage purity = (V × N × 0.05844 × 100) / weight of sample.

Principle:
Complexometric titration is based on the formation of a stable, water-soluble 1 : 1 complex between the metal ion and the chelating titrant.
Mⁿ⁺ + EDTA⁴⁻ → [M–EDTA]⁽ⁿ⁻⁴⁾ The dissociation constants of the four carboxylate and two amine groups of EDTA decide the pH at which a particular metal can be titrated; hence pH control by a suitable buffer is essential for a sharp end-point.

Classification of Complexometric Titrations:
1. Direct titration. The analyte is titrated directly with a standard solution of EDTA at the appropriate pH using a suitable metal-ion indicator. This is the simplest approach and is used for Ca²⁺, Mg²⁺, Zn²⁺ and similar ions.
2. Back-titration. A known excess of EDTA is added to the sample and the unreacted EDTA is back-titrated with standard MgCl₂ or ZnSO₄. This is used when the reaction between analyte and EDTA is slow or when a suitable indicator is not available (for example, Al³⁺ reacts very slowly with EDTA).
3. Replacement (substitution) titration. The analyte displaces another metal from its preformed EDTA complex, and the liberated metal is then titrated with EDTA. This is used when no direct indicator exists for the analyte, for example determination of Ca²⁺ via Mg–EDTA.
4. Alkalimetric (indirect) titration. The H⁺ liberated when the metal ion reacts with disodium EDTA is titrated with standard alkali using an acid-base indicator.

Metal Ion Indicators (Metallochromic Dyes):
Metallochromic 🔊 indicators are organic dyes that form coloured complexes with metal ions which are less stable than the corresponding metal–EDTA complex. At the end-point, the EDTA removes the metal from the indicator, giving a distinct colour change. The metal–indicator complex must be less stable than the metal–EDTA complex, the colour contrast must be clear, and the indicator must function at the pH of the titration.

Indicator	Metal + pH	Free colour → Complex colour
EBT (Eriochrome Black T)	Mg²⁺, Zn²⁺, Pb²⁺ at pH 10	Blue → Wine-red
Murexide	Ca²⁺ at pH 12	Violet → Red
Xylenol orange	Zn²⁺, Bi³⁺, Th⁴⁺ at pH 5–6	Yellow → Red
Calcon	Ca²⁺ in 0.1 M NaOH	Blue → Red

Masking and Demasking:
Masking is the addition of a reagent that selectively complexes an interfering metal ion so that it is no longer available to react with EDTA. For example, potassium cyanide masks Cu²⁺, Zn²⁺ and Ni²⁺, allowing Mg²⁺ and Ca²⁺ to be titrated selectively; triethanolamine masks Al³⁺ and Fe³⁺.
Demasking is the process of releasing a previously masked metal so that it too can be titrated. For example, formaldehyde releases zinc from its cyanide complex for a subsequent titration with EDTA.

Estimation of Magnesium Sulphate:
Principle: At pH 10, maintained by an ammonium chloride / ammonia buffer, magnesium ions react quantitatively with disodium EDTA to form a stable Mg–EDTA complex. Before the end-point, the indicator EBT is bound to some Mg²⁺ as a wine-red complex; at the end-point, EDTA strips the magnesium from the indicator, releasing the free blue form of EBT.
Mg²⁺ + EDTA²⁻ → [Mg–EDTA]²⁻ Procedure: Accurately weigh about 0.3 g of MgSO₄·7H₂O and dissolve it in water. Add 10 mL of ammonium chloride / ammonia buffer (pH 10) and two drops of EBT indicator. Titrate against 0.05 M disodium EDTA until the colour changes from wine-red to a pure blue.
Calculation: Each millilitre of 0.05 M disodium EDTA is equivalent to 0.01232 g of MgSO₄·7H₂O (molecular weight 246.5).

Principle:
In gravimetric analysis, the analyte is converted to a pure, insoluble compound of definite stoichiometric composition. This precipitate is then filtered, washed, dried or ignited to constant weight, and finally weighed. The amount of analyte is calculated from the weight of the precipitate by multiplying by a gravimetric factor.

Steps in Gravimetric Analysis:
The following eight steps are common to most gravimetric assays.
(1) Sample preparation involves accurate weighing of the sample and its dissolution in a suitable solvent.
(2) Precipitation is carried out by adding the precipitating reagent slowly to a hot, dilute solution, which favours the formation of a few large, pure crystals rather than many small ones.
(3) Digestion, the process of allowing the precipitate to stand warm in its mother liquor, permits small crystals to dissolve and redeposit on larger ones, thereby purifying the precipitate (Ostwald ripening 🔊).
(4) Filtration is performed through sintered glass, a Gooch crucible or ashless filter paper (for example Whatman 42) depending on whether the precipitate is to be dried or ignited.
(5) Washing with a suitable wash liquid (often containing a common ion to minimise dissolution) removes adsorbed impurities.
(6) Drying or ignition is carried out to constant weight at a specified temperature to obtain the weighing form of the precipitate.
(7) Weighing is done in a covered crucible after cooling in a desiccator 🔊.
(8) Calculation of the amount of analyte is then carried out using the appropriate gravimetric factor.

Co-precipitation and Post-precipitation:
Co-precipitation is the contamination of a precipitate by normally soluble substances that are carried down along with the analyte during precipitation. It occurs in four principal ways.
(a) Surface adsorption — foreign ions are adsorbed on the surface of the precipitate.
(b) Occlusion — impurity ions become trapped inside the crystal during its rapid growth.
(c) Mechanical entrapment — small pockets of the mother liquor are enclosed within the precipitate.
(d) Isomorphous replacement — an impurity of similar ionic size replaces the analyte in the crystal lattice.
Co-precipitation is minimised by using dilute solutions, slow addition of the precipitating reagent, adequate digestion, thorough washing and, where necessary, reprecipitation.

Post-precipitation is the deposition of an impurity on the surface of an already formed precipitate, particularly when the impurity itself precipitates slowly (for example, magnesium oxalate depositing on calcium oxalate). It is minimised by reducing the contact time between the precipitate and the mother liquor and by filtering as soon as possible.

Estimation of Barium Sulphate:
Principle: Barium ions react quantitatively with dilute sulphuric acid to give a highly insoluble, ignition-stable precipitate of barium sulphate.
BaCl₂ + H₂SO₄ → BaSO₄↓ + 2 HCl Procedure: Accurately weigh the sample of a barium salt and dissolve it in water containing a little dilute HCl (to prevent precipitation of carbonate). Heat the solution to about 70 °C and add dilute H₂SO₄ slowly with constant stirring to produce the precipitate. Digest the mixture on a water bath for about one hour, then filter through ashless Whatman No. 42 paper. Wash the precipitate with small quantities of hot water until free of chloride, transfer to a pre-weighed silica crucible, and ignite at 800 °C to constant weight. Cool in a desiccator and weigh.
Calculation: Weight of Ba = weight of BaSO₄ × (137.33 / 233.39); the gravimetric factor for Ba from BaSO₄ is therefore 0.5884.

Principle:
Primary aromatic amines react with nitrous acid, generated in situ from sodium nitrite and hydrochloric acid, at ice-bath temperature (0 – 5 °C) to form a water-soluble diazonium salt 🔊.
Ar–NH₂ + NaNO₂ + 2 HCl → Ar–N₂⁺Cl⁻ + NaCl + 2 H₂O

Procedure:
(1) The weighed sample of the primary aromatic amine (for example sulphanilamide 🔊) is dissolved in dilute HCl.
(2) The solution is cooled to 0 – 5 °C in an ice bath.
(3) It is then titrated slowly with standard 0.1 M sodium nitrite.
(4) The end-point is detected with an external starch-iodide paper: a drop of the titrated solution placed on the paper turns immediately blue when the nitrite is in slight excess, because the free HNO₂ liberates iodine from the iodide, and iodine combines with starch to give the blue colour.
(5) Persistence of the blue colour after one minute confirms the end-point.

Conditions to be Maintained:
The temperature must be kept between 0 and 5 °C because higher temperatures cause the diazonium salt to decompose. A three- to four-fold excess of HCl is required to ensure complete reaction. The titration is carried out slowly with continuous stirring, and an external indicator (starch-iodide paper) is preferred to an internal one to avoid side reactions with the indicator.

Applications:
Diazotisation titration is used mainly for the assay of sulphonamides such as sulphanilamide, sulphadiazine and sulphamerazine; for local anaesthetics such as procaine HCl and benzocaine; for antimalarials such as primaquine; for isoniazid (a hydrazine derivative); for dapsone; and for dye intermediates. Each millilitre of 0.1 M sodium nitrite is equivalent to 0.01722 g of sulphanilamide (molecular weight 172.2).

Oxidation and Reduction:
Oxidation is the loss of electrons by a species, which corresponds to an increase in its oxidation state — for example, Fe²⁺ → Fe³⁺ + e⁻. Reduction is the opposite process, namely the gain of electrons and a decrease in oxidation state, as in Ce⁴⁺ + e⁻ → Ce³⁺.
An oxidising agent is itself reduced in the process (for example KMnO₄, K₂Cr₂O₇, Ce⁴⁺ and I₂), whereas a reducing agent is itself oxidised (for example Na₂S₂O₃, oxalic acid, Fe²⁺ and Sn²⁺). A useful memory aid is the phrase "LEO says GER" — Loss of Electrons is Oxidation, Gain of Electrons is Reduction.

Classification of Redox Titrations:
Redox titrations are classified on the basis of the titrant used.
(1) Permanganometry 🔊 uses KMnO₄ as titrant and is self-indicating in acidic medium (pale pink at end-point).
(2) Cerimetry uses ceric ammonium sulphate and ferroin 🔊 as indicator.
(3) Iodimetry is a direct titration with standard iodine solution using starch indicator.
(4) Iodometry is an indirect titration; iodine liberated from KI by an oxidiser is titrated with Na₂S₂O₃.
(5) Bromatometry uses KBrO₃ (with KBr) in acidic medium and methyl orange or methyl red as indicator.
(6) Dichrometry uses K₂Cr₂O₇ in acidic medium and diphenylamine as redox indicator.
(7) Andrew's titration uses KIO₃ in concentrated HCl medium.

Cerimetry:
Principle: The cerium(IV) ion is reduced to cerium(III), with an E° of +1.44 V in sulphuric acid. It is a strong, single-electron oxidant and the standard solution is very stable.
Ce⁴⁺ + e⁻ → Ce³⁺ Titrant: 0.1 N ceric ammonium sulphate prepared in dilute H₂SO₄.
Indicator: Ferroin — the tris(o-phenanthroline) complex of iron(II) — which is red in its Fe(II) form and pale blue in its Fe(III) form; the end-point is the disappearance of the red colour.
Advantages over KMnO₄: the cerium(IV) solution is much more stable, the reaction involves only a one-electron transfer (so no intermediate oxidation states), the titration can be carried out in HCl, H₂SO₄ or HNO₃ medium, and the pale yellow colour of the titrant does not interfere with the end-point.
Applications: assay of ferrous sulphate, paracetamol (after acid hydrolysis), hydroquinone and vitamin C.

Iodimetry versus Iodometry:
Although the names sound similar, iodimetry and iodometry differ in almost every way, as shown in the following table.

Feature	Iodimetry (direct)	Iodometry (indirect)
Nature of analyte	Reducing agent	Oxidising agent
Titrant	Standard I₂ solution	Standard Na₂S₂O₃
Main reaction	I₂ + 2 e⁻ → 2 I⁻	Analyte + 2 KI → I₂; then 2 Na₂S₂O₃ + I₂ → Na₂S₄O₆ + 2 NaI
Indicator addition	Starch added at the start	Starch added near the end-point
End-point colour	Appearance of blue	Disappearance of blue
Typical examples	Vitamin C, As₂O₃	Copper sulphate, bleaching powder, H₂O₂, MnO₂

In iodometry, starch is added only near the end-point, because the starch-iodine complex formed in the presence of a large amount of iodine is difficult to decompose and would give a false high reading.

Bromatometry:
Titrant: 0.1 N potassium bromate (a primary standard) containing an excess of potassium bromide.
In acidic medium, the bromate and bromide react to liberate bromine in situ, which then brominates the analyte.
KBrO₃ + 5 KBr + 6 HCl → 3 Br₂ + 6 KCl + 3 H₂O Indicators: methyl orange or methyl red, which are irreversibly bleached by the first slight excess of bromine at the end-point.
Applications: assay of 8-hydroxyquinoline, phenol, resorcinol, salicylic acid and isoniazid.

Dichrometry:
Titrant: 0.1 N potassium dichromate, which is a true primary standard (stable, non-hygroscopic, can be weighed directly).
In acidic medium, the dichromate ion is reduced to the green chromium(III) ion with a six-electron change.
Cr₂O₇²⁻ + 14 H⁺ + 6 e⁻ → 2 Cr³⁺ + 7 H₂O  (E° = +1.33 V) Because the orange-to-green colour change is gradual, an external diphenylamine 🔊 or barium diphenylaminesulphonate indicator is used, which turns violet at the end-point.
Applications: estimation of Fe²⁺ in iron ore and the pharmacopoeial assay of ferrous sulphate.

Titration with KIO₃ (Andrew's Titration):
Titrant: 0.025 M potassium iodate dissolved in concentrated HCl.
In concentrated HCl, iodate combines with iodide and chloride to form iodine monochloride (ICl), involving a six-electron change per mole of KIO₃.
KIO₃ + 2 I⁻ + 6 H⁺ + 4 Cl⁻ → ICl + 3 H₂O + K⁺ End-point detection: a small volume of CCl₄ or chloroform is added; the organic layer shows the violet colour of free iodine which disappears when all iodide has been converted to colourless ICl.
Applications: assay of hydrazine, arsenic, antimony, mercury and vitamin C.

Principle:
The conductance (G) of a solution is the reciprocal of its electrical resistance, G = 1/R, and its SI unit is the siemens (S). For an electrolyte solution, the conductance depends on three factors: the number of ions per unit volume (concentration), the charge on each ion, and the ionic mobility (which in turn depends on the size, charge and solvation of the ion and on the temperature of the solution).
The specific conductance (κ, in S cm⁻¹) is obtained by multiplying G by the cell constant (ℓ/a), and the molar conductance (Λ_m, in S cm² mol⁻¹) is given by Λ_m = 1000 κ / C, where C is the molar concentration. During a titration, the ionic composition of the solution changes distinctly before and after the equivalence point, producing a characteristic break in the conductance-versus-volume plot.

Instrumentation:
The main components of a conductometer are listed below.
(1) A conductivity cell consisting of two platinum electrodes coated with platinum black to minimise polarisation, fixed at a known separation in the solution. The cell constant (ℓ/a) is calibrated using standard 0.1 N KCl.
(2) An alternating-current source (typically 50 – 3000 Hz); a direct current cannot be used because it would cause electrolysis of the solution at the electrodes.
(3) A Wheatstone (Kohlrausch) bridge with a null detector such as a headphone or magic-eye tube, or a modern digital conductivity meter.
(4) A thermostat, because conductance changes by about 2 % per degree Celsius.

Conductometric Titration Curves:
1. Strong acid versus strong base (HCl versus NaOH). A characteristic V-shaped curve is obtained. Before the end-point, the highly mobile H⁺ ions are replaced by the less mobile Na⁺ ions, so the conductance falls. After the end-point, excess OH⁻ ions (which are also highly mobile) build up and the conductance rises sharply. The sharp minimum gives the equivalence point.
2. Weak acid versus strong base (acetic acid versus NaOH). The conductance first shows a slight dip as the free H⁺ is neutralised, then rises steadily as the highly conducting sodium acetate is formed, and rises more steeply once excess OH⁻ appears.
3. Strong acid versus weak base. The conductance falls steadily as H⁺ is replaced by the weakly conducting cation of the weak base, and then remains almost constant after the end-point.
4. Mixture of strong and weak acid versus strong base. Two inflection points appear, corresponding to the successive neutralisation of the strong acid first and then the weak acid.
5. Precipitation titration (for example, AgNO₃ versus KCl). The inflection is sharp only when the ion being removed has a markedly different mobility from the ion replacing it.

Applications:
Conductometry is widely used for acid-base titrations, especially of a weak acid against a weak base where visual indicators give no sharp end-point, and for precipitation titrations. It is also used to determine the solubility of sparingly soluble salts such as BaSO₄ and AgCl, the basicity of organic acids, the ionic product of water (K_w), the purity of deionised water, and the CMC of surfactants.

Principle:
A potentiometric cell consists of an indicator electrode, whose potential depends on the activity of the analyte, and a reference electrode, whose potential remains constant, both dipping into the analyte solution and connected through a salt bridge. The cell potential is given by E_cell = E_ind − E_ref, and is related to the activity of the analyte by the Nernst 🔊 equation.
E = E° − (0.059 / n) log ([Red] / [Ox])  (at 25 °C)

Reference Electrodes:
1. Standard Hydrogen Electrode (SHE). It consists of a platinised platinum foil dipping into 1 M H⁺ solution and saturated with hydrogen gas at 1 atm. Its potential is defined as 0.0000 V and it is used as the primary reference. Its disadvantages are fragility and the need for a continuous supply of hydrogen gas.
2. Silver–silver chloride electrode. A silver wire coated with a layer of AgCl is immersed in saturated KCl. Its potential is +0.197 V (saturated). It is simple, stable and non-toxic.
AgCl + e⁻ ⇌ Ag + Cl⁻ 3. Saturated calomel electrode (SCE). It consists of mercury in contact with mercurous chloride (calomel) and saturated KCl. Its potential is +0.244 V, and although very stable, its use is declining because of the toxicity of mercury.
Hg₂Cl₂ + 2 e⁻ ⇌ 2 Hg + 2 Cl⁻

Indicator Electrodes:
1. Class I metal electrodes. A metal is in direct contact with a solution of its own ion, and its potential responds to the metal ion activity. Examples include silver in Ag⁺ and copper in Cu²⁺ solution.
2. Class II metal electrodes. A metal is in contact with a sparingly soluble salt of the metal, and the potential responds to the anion of that salt. The Ag/AgCl electrode in a chloride solution is a typical example, giving a response to Cl⁻ activity.
3. Class III (redox) electrodes. An inert platinum electrode is dipped into a solution containing both members of a redox couple, and its potential depends on the ratio of the two oxidation states, for example Pt in a Fe³⁺/Fe²⁺ mixture.
4. Glass electrode. This is the basis of the modern pH meter. It consists of an internal Ag/AgCl reference immersed in 0.1 M HCl within a thin glass bulb; when the bulb is dipped into the sample, a potential develops across the glass membrane that is proportional to log [H⁺].
5. Ion-selective electrodes (ISE). These have a membrane that is selective for a single ion such as F⁻, Ca²⁺, Na⁺ or K⁺.

End-Point Determination Methods:
(1) A direct plot of E versus volume of titrant gives an S-shaped curve, and the inflection point corresponds to the equivalence point.
(2) The first-derivative plot (ΔE/ΔV versus V) shows a sharp peak at the end-point.
(3) The second-derivative plot (Δ²E/ΔV² versus V) passes through zero at the end-point, giving the most precise location.
(4) Gran's plot uses a linearised transformation of the data; extrapolating the straight line to the x-intercept gives the equivalence volume accurately, even for dilute solutions.

Applications:
Potentiometry is used for pH determination, for acid-base, redox, precipitation and complexometric titrations in coloured or turbid solutions where visual indicators fail, for ion-selective assays (such as fluoride in toothpaste or calcium in serum), and for the direct measurement of redox potentials in biological and industrial samples.

Principle:
A steadily increasing direct-current voltage is applied between the dropping mercury electrode (cathode) and a reference electrode (saturated calomel electrode or mercury pool acting as anode) immersed in the analyte solution containing a supporting electrolyte. The resulting current is measured and plotted against applied voltage to give a polarogram. At the half-wave potential (E_1/2), which is characteristic of each analyte, the current rises sharply and then levels off at a plateau called the limiting diffusion current (i_d).
The half-wave potential gives qualitative information (the identity of the analyte), while the diffusion current gives quantitative information (its concentration).

Ilkovic Equation:
The diffusion current is described quantitatively by the Ilkovic equation:
i_d = 607 × n × D^½ × m^2/3 × t^1/6 × C where n is the number of electrons transferred, D is the diffusion coefficient of the analyte (cm²/s), m is the mercury flow-rate (mg/s), t is the drop time (s), C is the molar concentration (mmol/L) and i_d is in µA.
At constant n, D, m and t, the equation reduces to i_d ∝ C, which forms the basis of quantitative polarography.

Dropping Mercury Electrode (DME):
The DME consists of a glass capillary through which mercury flows slowly from a reservoir under gravity; the drop grows, then falls away every 3 – 5 seconds, giving a continuously refreshed electrode surface. Its advantages are the reproducible fresh surface, a high hydrogen overvoltage that allows measurements at very negative potentials, and the ready formation of amalgams with many metals. Its disadvantages are the toxicity of mercury and the fact that it cannot be used at strongly positive potentials, where mercury itself is oxidised.
The RPE is a solid platinum electrode rotated at 600 – 3000 rpm; the forced convection gives a reproducible diffusion layer and permits work at positive potentials.

Applications:
Polarography is used for the determination of metal ions (Cu²⁺, Cd²⁺, Pb²⁺, Zn²⁺) in pharmaceutical and biological samples; for vitamin assays (riboflavin, ascorbic acid, nicotinamide); for reducible organic functional groups such as nitro, carbonyl, conjugated C=C and disulphide; for the assay of drugs such as chloramphenicol and metronidazole; for trace analysis of heavy-metal impurities; and for the study of complex formation and stability constants.

0.1 N Sodium Thiosulphate (Na₂S₂O₃·5H₂O):
Preparation: Dissolve 25 g of Na₂S₂O₃·5H₂O in 1000 mL of freshly boiled and cooled distilled water (to remove dissolved CO₂ and oxygen), add 0.1 g of Na₂CO₃ as a stabiliser and store in an amber bottle.
Standardisation: Against primary-standard potassium dichromate. In acidic medium K₂Cr₂O₇ liberates iodine from potassium iodide, and the liberated iodine is then titrated with the thiosulphate solution using starch indicator (added near the end-point).
K₂Cr₂O₇ + 6 KI + 14 HCl → 2 CrCl₃ + 3 I₂ + 8 KCl + 7 H₂O
I₂ + 2 Na₂S₂O₃ → 2 NaI + Na₂S₄O₆

0.1 N Sulphuric Acid:
Preparation: Carefully add 2.8 mL of concentrated H₂SO₄ (approximately 36 N) to about 500 mL of distilled water with continuous stirring (always add acid to water, never the reverse) and dilute to 1000 mL.
Standardisation: Against anhydrous sodium carbonate as primary standard, using methyl orange as indicator.
Na₂CO₃ + H₂SO₄ → Na₂SO₄ + H₂O + CO₂

0.1 N Oxalic Acid:
Oxalic acid (COOH)₂·2H₂O is a true primary standard and its solution can be prepared directly from the weighed solid. Dissolve 6.303 g of crystalline oxalic acid (molecular weight 126.07, equivalent weight 63.03) in 1000 mL of distilled water. No further standardisation is necessary.

0.1 N Ceric Ammonium Sulphate:
Preparation: Dissolve 64 g of Ce(NH₄)₄(SO₄)₄·2H₂O in about 500 mL of water containing 30 mL of concentrated H₂SO₄ and dilute to 1000 mL.
Standardisation: Against arsenic trioxide (As₂O₃) as primary standard, using ferroin indicator. Sodium oxalate may also be used as primary standard. The typical reaction during titration of a ferrous sample is shown below.
Ce⁴⁺ + Fe²⁺ → Ce³⁺ + Fe³⁺

Definition:
The significant figures of a measured quantity are all the digits that are known with certainty together with the first digit that is uncertain.

Rules for Counting Significant Figures:
(1) All non-zero digits are significant (for example 123.45 has five significant figures).
(2) Zeros lying between non-zero digits are significant (for example 2005 has four significant figures).
(3) Leading zeros are not significant (for example 0.00452 has three significant figures).
(4) Trailing zeros after a decimal point are significant (for example 2.500 has four significant figures).
(5) Trailing zeros in a whole number without a decimal point are ambiguous, so scientific notation is preferred (for example, 1500 may have two, three or four significant figures depending on context).
(6) Exact numbers from counting or definition (for example, 12 eggs in a dozen; the number 100 in a percentage) are considered to have an infinite number of significant figures.

Rules for Arithmetic Operations:
Addition and subtraction: the result is rounded to the least number of decimal places of any of the operands. For example, 12.11 + 18.0 + 1.013 = 31.123, which must be reported as 31.1 because 18.0 has only one decimal place.
Multiplication and division: the result is rounded to the least number of significant figures of any operand. For example, 3.2 × 3.652 = 11.6864, which is reported as 12 because 3.2 has only two significant figures.
Rounding: if the digit to be dropped is less than 5 the previous digit is left unchanged; if it is greater than 5 the previous digit is increased by one; and if it is exactly 5 the previous digit is rounded to the nearest even number (the banker's rounding convention).