Ask ten students halfway through PCT 202 what separates a linctus from an elixir and most of them hesitate. That hesitation costs marks, because this course loves the small distinction: syrup against elixir, powder against granule, homolytic against heterolytic thinking carried over from chemistry, and the difference between a strength that reads "% w/v" and one that reads "1 in 1000". Get those clean and half the paper looks after itself. This page is a student-written study companion for PCT 202 – Pharmaceutical Preparations & Calculations, a compulsory course for ABUAD 200 Level Pharmacy students in the second semester, College of Pharmacy.
The course really has two personalities. One is descriptive: how a drug becomes a usable medicine, from solutions and their colligative behaviour, through phase equilibria and freeze-drying, to the solid dosage forms of powders, granules, tablets and capsules. The other is quantitative: the calculations a pharmacist runs every day, ratio and proportion, specific gravity, percentage strength and alligation. The summaries below turn both halves of the syllabus into plain-English notes, with original practice questions and fully worked answers so you can check each idea has stuck. The complete study workbook sits in the interactive reader at the end as a free bonus to the notes on this page.
- Course: PCT 202 – Pharmaceutical Preparations & Calculations
- College / Department: College of Pharmacy, Pharmaceutics
- Level / Semester: 200 Level, Second Semester
- Topics covered: Dispensing and the nature of solutions, formulation and excipients, solubility and its factors, colligative properties, liquids in liquids and the distribution law, syrups, elixirs and linctuses, body-cavity and topical solutions, phases and the phase rule, one- and two-component systems, eutectics and freeze-drying, powders, granules, tablets and capsules, then the calculations syllabus: units, ratio and proportion, specific gravity, percentage and ratio strength, dilution and alligation
- Best for: Continuous assessment + final exam revision
Part One: Pharmaceutical Solutions
1. Dispensing and the Nature of a Solution
Dispensing is the branch of pharmaceutics that covers mixing, preparing, presenting and supplying a medicine in a form the patient can actually use, whether that is a solution, a suspension, a tablet or an ointment. Good dispensing rests on knowing how a preparation is made, labelled, packaged, stored, dosed and kept stable in the patient's hands.
A pharmaceutical solution is a homogeneous, single-phase system in which one or more solutes dissolve in a solvent. The solvent, almost always a liquid, is the continuous phase, and the solute, which may be solid, liquid or gas, breaks down into individual ions or molecules spread evenly through it. Usually the solvent far outweighs the solute, with Syrup BP the famous exception, where sucrose makes up about 66.7% and the solvent only about 33.3%. Exam tip: the reason a solution gives such reliable dosing is worth a line of its own. Because it is molecularly homogeneous, every measured portion carries the same amount of drug, so quote that dose-uniformity point whenever a question asks why solutions are chosen.
2. Formulating a Solution: the Excipients
Turning a drug into a palatable, stable liquid takes more than the active and the vehicle. A working formulation usually draws on several classes of additive, each with a defined job: co-solvents such as propylene glycol and glycerol to push a poorly soluble drug into solution, buffers such as citrates and phosphates to hold pH, sweeteners such as sucrose (or sorbitol for diabetics), flavours and colourants for acceptability and identification, preservatives such as benzoic acid against microbial spoilage, antioxidants such as tocopherol against oxidation, and viscosity enhancers such as povidone to fix flow and mouth-feel.
The vehicle itself is chosen on clarity, viscosity, toxicity, odour, compatibility, palatability and colour. Antioxidants earn their place particularly where vitamins or essential oils can oxidise, a reaction that light or trace metals like copper and iron can set off. Exam tip: learn the excipients as a two-column list, additive against reason, and be ready to name one typical example for each, because the classic question gives you a role and asks for the class that fills it.
3. Why Solutions? Advantages, Drawbacks and Uses
Solutions are easier to swallow than solids, which suits paediatric and geriatric patients, and they act faster because the drug is already dissolved and skips the disintegration and dissolution a tablet must undergo. They dose uniformly, sit more gently on the gastric mucosa, and allow flexible dosing. Against that, they are bulky and heavy, a broken bottle loses the whole dose at once, they are chemically less stable and shorter-lived than solids, the watery vehicle invites microbial growth so a preservative is usually needed, unpleasant tastes stand out, and accurate dosing depends on a proper measure and some patient technique.
They are formulated for many routes: oral (mixtures, elixirs, linctuses, draughts, syrups, drops), mouth and throat (mouthwashes, gargles, throat paints and sprays), external (collodions, liniments, lotions, paints), body cavities (douches, enemas, ear and nasal drops) and parenteral (intramuscular, intravenous, subcutaneous). Exam tip: keep the advantages and disadvantages as a balanced pair of lists, and match a route to its dosage form, since "give two oral and two external solution types" is an easy structured mark.
4. Solubility and Types of Solution
Solubility is the amount of a substance that will dissolve in a stated amount of solvent to give a saturated solution at a set temperature. It matters even for solid dosage forms, since any drug must dissolve in body fluids before absorption. Solutions can pair any two states, but the solid-in-liquid type dominates pharmacy. By degree of saturation there are three: a saturated solution sits in equilibrium with excess solute; an unsaturated one holds less than saturation allows; and a supersaturated one holds more than saturation allows in a metastable state that crystallises out on seeding, shaking or scratching, as sodium thiosulphate and sodium acetate do on cooling.
Strength is expressed three ways: % w/w (grams of solute per 100 g of solution), % w/v (grams per 100 mL of solution) and % v/v (millilitres per 100 mL of solution). Where a figure is unhelpful, the pharmacopoeia falls back on descriptive terms set by the parts of solvent needed to dissolve one part of solute, from "very soluble" (less than 1 part) down to "practically insoluble" (more than 10,000 parts). Exam tip: memorise the descriptive-term ladder with its part ranges, and be able to say in one line what makes a supersaturated solution metastable, because that is the detail examiners probe.
5. Factors Affecting Solubility
Five factors move solubility. Temperature raises the solubility of an endothermic solute but lowers it for an exothermic one, so calcium hydroxide, calcium citrate, paraldehyde and most gases actually dissolve less as things heat up. Particle size matters because a smaller particle has more surface area, so micronising a drug speeds dissolution, and barium sulphate roughly doubles its solubility when its size falls from 1.8 µm to 0.1 µm. Pressure barely touches solids and liquids but strongly affects gases, following Henry's law, M = kP, at constant temperature.
The nature of the solvent sets how much solute it can hold, and added substances can shift that. pH is the pharmacist's lever: a weak acid such as aspirin dissolves better in alkaline media, where it forms a soluble salt, and precipitates in acid, while a weak base does the reverse. Exam tip: the endothermic-versus-exothermic temperature rule catches people out, so pair it with its named exceptions, and remember the pH effect explains why so many drugs are formulated as salts.
6. Colligative Properties of Solutions
Colligative properties depend only on the number of solute particles present, not on their chemical nature. For a non-volatile solute there are four. Lowering of vapour pressure follows Raoult's law: the relative lowering equals the mole fraction of solute, ΔP/P° = X₂. Elevation of boiling point follows ΔTb = Kbm, because a lowered vapour pressure needs a higher temperature to reach 760 mmHg. Depression of freezing point follows ΔTf = Kfm, since the solute lowers the solvent's escaping tendency. Osmotic pressure is the pressure needed to stop solvent crossing a semi-permeable membrane into the more concentrated side.
The numbers reward practice. Dissolving 171.2 g sucrose in 1000 g water at 20°C gives a relative lowering of 0.0089 and a vapour pressure of 17.379 mmHg. A 0.200 m solution showing a 0.103° rise gives Kb = 0.515, and a 1.3 m sucrose solution with Kf = 2.1 depresses the freezing point by 2.73°C. Osmotic pressure is the one that reaches the clinic, since it underpins isotonic parenteral and eye products. Exam tip: write out the four properties with their governing equation, then rehearse one boiling-point and one freezing-point calculation by hand, because a numerical colligative question is almost guaranteed.
7. Liquids in Liquids: What Decides Miscibility
A liquid-in-liquid solution is one liquid dispersed evenly in another. Pairs are miscible when they blend completely and immiscible when they split into layers. The governing idea is "like dissolves like": liquids of similar polarity and structure mix freely, so benzene and toluene or ethanol and water blend, while oil and water separate. The deeper reason is that liquids mix when their intermolecular forces match, water with other hydrogen-bonding liquids, hydrocarbons with each other through weak dispersion forces.
Alcohols show this neatly because they are amphipathic, with a water-loving hydroxyl end and a fat-loving chain. When the chain is short the hydroxyl wins, so methanol and ethanol mix fully with water, but a long chain tips the balance toward the hydrocarbon and cuts water solubility. Raising temperature can improve the mutual miscibility of two partly miscible liquids. Exam tip: keep two short example lists ready, miscible pairs (ethanol in water, HCl in water) against immiscible pairs (oil and water, benzene and water), and use the amphipathic-alcohol argument to explain the trend down a homologous series.
8. Distribution Between Immiscible Liquids
In 1891 Walther Nernst set out the distribution, or partition, law: when a solute that dissolves in each of two immiscible liquids is shaken with both, it spreads so that the ratio of its concentrations in the two phases stays constant at a fixed temperature. That constant is the partition coefficient, a dimensionless number usually worked out from solubilities or molar concentrations. The law holds only under four conditions: constant temperature, dilute solutions, no reaction between solute and solvent, and the solute in the same molecular state in both phases, with no association or dissociation.
The idea runs through pharmacy. It explains solvent extraction, is the basis of chromatography, guides formulation when you predict a drug's solubility across solvents, and describes drug absorption, where a drug must partition from watery gut contents into a lipid membrane and back into blood, then distribute from blood into tissues by its affinity for each. Exam tip: the four conditions for Nernst's law are a favourite recall question, so memorise them as a set, then be ready to give two pharmaceutical applications of partitioning.
9. Oral Solutions: Syrups, Elixirs and Linctuses
These three trip students precisely because they look similar. A syrup is a concentrated, viscous solution of sugar in water, needing at least about 65% sucrose to preserve itself and reaching up to about 85% in a simple syrup; add a drug and it is a medicinal syrup. An elixir is a clear, pleasantly flavoured solution of a potent drug that acts mainly in the gut, and it usually needs 10 to 20% alcohol to hold essential oils in solution, though paediatric elixirs swap alcohol for propylene glycol. A linctus is a viscous oral solution that soothes cough in the throat, rich in syrup and glycerol for their demulcent effect, taken in small 5 mL doses and labelled to be swallowed slowly without water.
The contrasts are the exam. A syrup is sweeter, more viscous and better at masking taste but less stable and unsuitable for diabetics, while an elixir is less sweet, less viscous, alcohol-containing, clear and more stable. A linctus and an elixir differ mainly by site of action, throat against gastrointestinal tract, and by typical actives, expectorants and sedatives against antibiotics and antihistamines. Codeine Linctus and Piperazine Citrate Elixir are the standard worked formulae. Exam tip: build the syrup-elixir-linctus comparison as a table with rows for alcohol, sweetness, viscosity, clarity, stability and site of action, then reproduce it cold, because "distinguish between" here is almost a given.
10. Solutions for the Mouth and Body Cavities
Paints carry an active to skin or mucosa on a brush, usually as an antiseptic or local analgesic; a skin paint uses a volatile vehicle such as ethanol that dries to a film, while a throat paint uses a viscous vehicle such as glycerol to hold the drug in place, as Mandl's compound iodine paint does. Gargles are concentrated aqueous solutions diluted with warm water and held in the throat, while mouthwashes are similar solutions used on the lining of the mouth, both carrying antiseptic, deodorant or astringent agents.
The specialised cavity preparations each have a rule worth knowing: eye preparations must be sterile with careful attention to tonicity, ear preparations use water, glycerol, propylene glycol or alcohol as cleansers and wax softeners, nasal solutions sit near pH 6.8 and isotonic to protect the cilia, and enemas and douches are large volumes warmed to body temperature before use. Exam tip: tie each preparation to its one non-negotiable requirement, sterility for the eye, near-neutral pH for the nose, warmth for enemas, because that specific pairing is where the marks sit rather than in the general definition.
11. Topical Solutions: Collodions, Lotions and Liniments
A collodion is a solution of pyroxylin in ether or ethanol that dries to a flexible film (castor oil supplies the flexibility) and seals minor cuts or holds a drug like salicylic acid against the skin. It is highly inflammable, so it is dispensed in small amber, tightly closed containers and labelled for external use only, keep away from naked flames. A lotion is usually a solution applied without friction to unbroken skin as an antiseptic, antipruritic or protective; after the solvent evaporates it leaves a film and the evaporation itself cools, with ethanol boosting the cooling and glycerol keeping the skin moist.
A liniment is applied with friction to unbroken skin to ease sprains and strains, either alcoholic (rubefacient and penetrating) or oily (milder, better for massage). The liniment-against-lotion contrast is clean: a liniment absorbs faster, has low viscosity and goes on with friction for pain, while a lotion is more viscous, more cosmetic and goes on without friction for protection. Irrigation solutions, which wash wounds, must be sterile and pyrogen-free. Exam tip: remember that a collodion contains pyroxylin and is flammable, and be ready to contrast a liniment and a lotion by application method and purpose, since that distinction is the reliable question here.
Part Two: Phase Equilibria
12. Phases, Equilibrium and the Phase Rule
A phase is a homogeneous part of a system with uniform physical and chemical properties, and it can be solid, liquid or gas; a pure compound such as water can exist in all three, each with its own separable boundary. A system reaches equilibrium when its free energy is at a minimum and its properties stop changing with time at constant temperature, pressure and volume. Phase equilibrium is simply the reversible balance struck when phases coexist, though only for a while, since ice survives far longer in cold water than in boiling water.
The Gibbs phase rule pins this down with one equation, F = C - P + 2, where F is the degrees of freedom, C the number of components and P the number of phases. It gives the smallest number of variables (temperature, pressure, concentration) you can change without creating or destroying a phase. The key relationship is that more phases in equilibrium leave fewer degrees of freedom. Exam tip: memorise F = C - P + 2 and what each letter means, then practise plugging in numbers, because most phase-rule marks come from a clean substitution rather than from theory.
13. One-Component Phase Diagrams
For a one-component system such as water, the pressure-temperature diagram is carved by three curves that meet at one point: the fusion curve (solid and liquid in balance), the vaporisation curve (liquid and vapour) and the sublimation curve (solid and vapour). The areas between the curves are single-phase regions of ice, water or vapour, and the meeting point is the triple point, where all three phases coexist, fixed for water at 0.0098°C and 4.58 mmHg.
Applying the phase rule shows the pattern cleanly. In a single-phase area, F = 1 - 1 + 2 = 2, so the system is bivariant and temperature and pressure vary independently. On a two-phase curve, F = 1 - 2 + 2 = 1, univariant, so fixing temperature fixes pressure. At the three-phase triple point, F = 1 - 3 + 2 = 0, invariant, so nothing can change without losing a phase. Exam tip: learn the three cases as area, line and point with their F values of 2, 1 and 0, and be ready to name the curves, because a labelled water diagram is a standard exam figure.
14. Two-Component Systems and Eutectics
Add a second component and the counting changes. Sodium chloride dissolved in water is a one-phase, two-component system, for which F = 2 - 1 + 2 = 3, the three variables being temperature, pressure and concentration. Once excess solid salt is present, the system has two components and two phases, a condensed system that behaves as a eutectic.
A eutectic mixture is a homogeneous mixture of two or more components that do not react to form a new compound but melt or solidify together at a single temperature lower than the melting point of any pure component, as sodium chloride and water do. Exam tip: memorise the eutectic definition word for word, especially the "single temperature lower than any pure component" clause, and be able to redo the F = 3 calculation for a salt solution, since that pairing of definition and phase-rule sum is the typical question.
15. Sublimation and Freeze-Drying
Sublimation is the direct move from solid to gas without a liquid stage, which for water happens below the triple point and, unlike evaporation, needs no heat input. This is the basis of freeze-drying, or lyophilisation, which preserves a sample by freezing it and then removing the ice as vapour under vacuum, giving a porous product that rehydrates quickly and almost completely. It runs in three stages: freezing (rapid freezing gives small crystals that spare structure but slow vapour flow, slow freezing gives large crystals that dry faster but can damage cells), primary drying (the ice sublimes and is collected on condensers) and secondary drying (residual unfrozen water is removed).
The trade-off is cost. Freeze-drying causes minimal damage to heat-labile materials, produces a friable structure and preserves activity, but the equipment is expensive, the energy demand high and the process slow. That is why it is reserved for high-value products: microbial cultures, coffee and tea, egg and milk products, and injections too unstable in solution, which are supplied as powders for reconstitution just before use. Exam tip: learn the three stages in order and pair each freeze-drying advantage with a matching disadvantage, then remember that rapid versus slow freezing changes crystal size and therefore both drying speed and structural damage.
Part Three: Powders, Tablets and Capsules
16. Powders as a Dosage Form
A powder is a dry solid of finely divided particles, roughly 10 to 1000 µm, made by crushing, grinding or comminution. Its large surface area and properties like particle size, shape, density and flowability shape how well it packs and processes into granules, tablets, capsules and suspensions, and can change a drug's solubility and bioavailability. Powders serve both as excipients and as a dosage form, chemically stable and good for large soluble doses, though awkward to carry, hard to taste-mask and unsuitable for potent low-dose or gastric-irritant drugs.
They come in two forms. Bulk powders pack all the material into one container, so the dose depends on the spoon, humidity and patient technique, which limits them to drugs with a wide therapeutic window, a large dose and a pleasant taste; effervescent powders are a bulk type with a bicarbonate-acid couple, and external bulk powders include dusting powders and dry-powder inhalers. Divided powders pack each dose separately in paper, foil or plastic, which protects volatile or hygroscopic material far better. Exam tip: the bulk-versus-divided contrast turns on dose accuracy, so state plainly that divided powders are more accurate because each dose is measured at manufacture, not by the patient.
17. Granules and Granulation
Because powders of different particle size can segregate on storage and give a non-uniform product, mixed powders are often granulated. Granules are dry aggregates of powder particles, tough enough to handle, taken orally as they are, chewed or dispersed in liquid, and best for low-toxicity, high-dose drugs such as methylcellulose. Granulation is carried out to prevent segregation, improve flow, improve compaction before tableting, cut the dust hazard of toxic materials, limit caking of slightly hygroscopic materials, and pack more weight into less volume.
Granules are more chemically stable than liquids, which is why reconstitutable antibiotic syrups keep for two to three years dry but only one to two weeks once mixed, and they dissolve faster than tablets or capsules. Against that, bulk granules are inconvenient to self-administer, unpleasant tastes are hard to mask, and dosing by spoon is inaccurate for potent low-dose drugs. Exam tip: the reasons for granulating are a classic list question, so memorise the six of them, and pair "prevent segregation" and "improve flow" as the two most examiners expect first.
18. Tablets and Their Types
The USP defines tablets as solid dosage forms of medicinal substances, with or without diluents, made by compression or moulding, and the overwhelming majority are compressed tablets formed by steel punches and dies pressing powders or granulations. The types are the exam target. A compressed tablet is the simplest, uncoated form. A sugar-coated tablet masks taste and protects oxidation-sensitive drugs, while a film-coated tablet does the same with a thin water-soluble polymer applied much faster, now the first choice.
Beyond those, an enteric-coated tablet resists gastric fluid but dissolves in the intestine to protect acid-labile drugs or delay release; a multiple-compressed or layered tablet separates incompatible actives; a controlled-release tablet spreads the dose over time; a tablet for solution is dissolved before use and labelled not to be swallowed; an effervescent tablet fizzes off carbon dioxide as its own disintegrant; and buccal or sublingual tablets are held in the cheek or under the tongue for direct absorption, as nitroglycerin is. Exam tip: learn each tablet type as a one-line "key feature" and keep the enteric-coated and controlled-release entries sharp, because "why enteric coat a tablet" is a common short answer.
19. Capsules
A capsule encloses the drug in a hard or soft soluble shell, traditionally gelatin but increasingly hydroxypropyl methylcellulose, which holds less moisture (useful for hydrolytic drugs) and suits vegetarians. Gelatin itself comes from hydrolysed collagen, Type A from pork skin by acid processing and Type B from bone and skin by alkaline processing. A hard-gelatin capsule lets the prescriber pick a single drug or a combination at exactly the dose the patient needs, a flexibility tablets lack, and many patients find capsules easier to swallow.
Capsules are popular for a bundle of reasons worth listing: they mask taste and odour, look attractive, turn slippery when moist so they go down easily, resist mechanical stress when stored properly, need fewer additives than tablets, release their finely powdered contents rapidly and uniformly, can be opacified or coloured against light, are physiologically inert and easily digested, and need no complex machinery for a few extemporaneous capsules. Exam tip: know the gelatin Type A versus Type B distinction (acid pork skin against alkaline bone and skin) and be able to give four reasons capsules are popular, since that combination covers most capsule questions.
Part Four: Pharmaceutical Calculations
20. Units and the Rules of Accurate Calculation
Calculation runs through every part of pharmacy, and because each result bears on patient safety, accuracy is the whole point. Four rules keep work clean: always put a zero before a decimal point (0.5, never .5), never overwrite a figure but strike it out and rewrite, show the full procedure with any conversion factors, and per the USP carry all figures through the working and round only the final answer. Pharmacy uses the metric SI system, with the avoirdupois and historic apothecaries' systems appearing occasionally.
A handful of equivalents are worth memorising because they surface constantly: 1 inch is 2.54 cm, 1 fluid ounce is 29.57 mL, 1 pint is 473 mL, 1 gallon (US) is 3785 mL, 1 pound is 454 g, 1 kilogram is 2.2 lb, and 1 grain is 64.8 mg. Exam tip: the "zero before the decimal point" rule is not trivia, it prevents the dangerous ten-fold dosing error, so state it as a safety rule, and drill the common conversions until they are automatic.
21. Ratio and Proportion
A ratio compares the relative size of two quantities, so 1:2 reads "one is to two" and behaves like the fraction one half; multiplying or dividing both terms by the same number leaves its value unchanged. A proportion states that two ratios are equal, written a:b = c:d or a/b = c/d, where a and d are the extremes and b and c the means. The single principle to hold onto is that the product of the extremes equals the product of the means, so given any three terms the fourth follows.
The method is always the same: line up the ratios with units labelled so like sits over like, then cross-multiply and solve. If 3 tablets contain 975 mg of aspirin, then 12 tablets contain (12 × 975) / 3 = 3900 mg. Exam tip: the commonest slip is mismatched units, so write the unit beside every number in the proportion, and treat "product of the extremes equals product of the means" as the sentence that unlocks any proportion problem.
22. Density and Specific Gravity
Density is mass per unit volume, and for water it is 1 g/mL. Specific gravity is the ratio of the weight of a substance to the weight of an equal volume of water at the same temperature, a dimensionless number: below 1 means lighter than water, above 1 means heavier. The three relationships to keep are specific gravity = weight ÷ weight of equal volume of water, weight = volume × specific gravity, and volume = weight ÷ specific gravity.
It is measured from a known weight and volume, with a pyknometer, or by displacement, and it is used to convert between weight and volume, for instance in automated compounders preparing parenteral nutrition, and clinically in urinalysis, where normal urine sits between 1.010 and 1.025. To find the weight of 250 mL of sevoflurane with specific gravity 1.52: 250 mL of water weighs 250 g, so the weight is 250 × 1.52 = 380 g. Exam tip: the trick with every specific-gravity sum is to convert the volume in millilitres to the equal weight of water first, then multiply by the specific gravity, so practise that one move until it is second nature.
23. Percentage Strength
Percent means parts per hundred, so 50%, 50/100 and 0.5 are the same, and for calculation you turn a percent into a decimal by dividing by 100. The USP fixes three expressions with default uses: % w/v is grams per 100 mL, used for solids in liquids; % v/v is millilitres per 100 mL, used for liquids in liquids; and % w/w is grams per 100 g, used for mixtures of solids or semisolids. For w/v the solution is treated as having the density of water, so 100 mL counts as 100 g.
The calculations follow directly. A 5% dextrose solution gives 5 g per 100 mL, so 4000 mL needs 200 g. For w/w with a stated specific gravity, convert volume to weight first: 120 mL of a 20% w/w solution at specific gravity 1.15 weighs 138 g and so needs 138 × 0.20 = 27.6 g of drug. Alcohol dilution uses volume of stronger alcohol = (volume required × % required) ÷ % available, so 500 mL of 20% from 95% needs 105 mL of the 95%. Exam tip: memorise which default each expression carries (w/v for solids in liquids, v/v for liquids in liquids, w/w for solids), and always convert volume to weight before a w/w calculation when a specific gravity is given.
24. Ratio Strength, Dilution and Alligation
Very dilute preparations are stated as a ratio strength, parts of solute per parts of solution, such as 1 in 1000, which you convert to percent by dividing 100 by the second figure: 1 in 400 is 0.25%, 1 in 1000 is 0.1%. For a concentrate, the strength of the dilute solution equals the strength of the concentrate divided by the degree of dilution, so 1 part diluted with 7 parts of water gives a 1 in 8000 (0.0125%) solution.
Alligation handles mixtures of different strengths. Alligation medial finds the weighted-average strength of a known mixture, so 200 g at 10%, 50 g at 20% and 100 g at 5% gives 35 g of active in 350 g, which is 10% w/w. Alligation alternate finds the proportions needed to hit a target strength by pairing one component above and one below the target: to make 70% alcohol from 95% and 50%, you take (70 - 50) = 20 parts of the 95% and (95 - 70) = 25 parts of the 50%, a ratio of 20:25, or 4:5. Exam tip: keep the two alligations distinct, medial finds the strength of a known mix while alternate finds the mixing proportions for a target, and always place the desired strength in the centre of the working diagram.
Sample Practice Questions (With Answers)
Here are a few representative questions, written in our own words, with the reasoning explained so you understand the why, not just the answer:
Q1. A patient needs a clear, alcohol-containing oral liquid of a potent antibiotic that works in the gut. Is a syrup, an elixir or a linctus the right choice, and why?
Answer: An elixir. Elixirs are clear, pleasantly flavoured solutions of potent drugs (antibiotics and antihistamines) that act mainly in the gastrointestinal tract, and they carry 10 to 20% alcohol to hold ingredients in solution. A syrup would be sweeter, more viscous and often not clear, and a linctus is a viscous, throat-acting cough preparation rich in syrup and glycerol, so neither fits a clear gut-acting antibiotic.
Q2. A 0.200 molal solution raises the solvent's boiling point by 0.103°C. Find the molal boiling-point constant, and state which colligative law you used.
Answer: Boiling-point elevation follows ΔTb = Kbm, so Kb = ΔTb / m = 0.103 / 0.200 = 0.515. The elevation happens because a non-volatile solute lowers the solvent's vapour pressure, so a higher temperature is needed to reach the external pressure of 760 mmHg. It is a colligative property, depending only on the number of solute particles, not their identity.
Q3. State the conditions under which Nernst's distribution law holds, and name two pharmaceutical uses of partitioning.
Answer: The law holds only when the temperature is constant, both solutions are dilute, the solute does not react with either solvent, and the solute exists in the same molecular state in both phases (no association or dissociation). Two pharmaceutical uses: solvent extraction (separating a drug with a selective solvent) and drug absorption (a drug partitioning from watery gut contents into the lipid membrane and back into blood). Chromatography and formulation prediction are also valid answers.
Q4. Using the phase rule, work out the degrees of freedom at the triple point of water and say what the answer means.
Answer: Water is one component (C = 1) and at the triple point three phases coexist (P = 3), so F = C - P + 2 = 1 - 3 + 2 = 0. Zero degrees of freedom means the system is invariant: neither temperature nor pressure can change without destroying a phase, which is why the triple point is fixed at a single temperature and pressure (0.0098°C and 4.58 mmHg for water).
Q5. Find the weight of 150 mL of glycerol whose specific gravity is 1.26.
Answer: First convert the volume to the equal weight of water: 150 mL of water weighs 150 g. Then weight = volume × specific gravity = 150 × 1.26 = 189 g. Because glycerol has a specific gravity above 1, it is heavier than the same volume of water, which is why the answer exceeds 150 g.
Q6. In what proportion should a 20% benzocaine ointment be mixed with white soft paraffin base (0%) to make a 2.5% ointment?
Answer: Use alligation alternate, placing the target 2.5% in the centre. Parts of the 20% ointment = 2.5 - 0 = 2.5; parts of the 0% base = 20 - 2.5 = 17.5. The ratio is 2.5 : 17.5, which simplifies to 1 : 7, so one part of the 20% ointment to seven parts of base.
Q7. If 3 g of boric acid is made up to 240 mL of solution, what is the percentage strength in % w/v?
Answer: Percentage w/v is grams of solute per 100 mL of solution, so % w/v = (weight in g / volume in mL) × 100 = (3 / 240) × 100 = 1.25% w/v. The w/v expression is the default for a solid dissolved in a liquid, which is exactly the case here.
How to Study PCT 202 Effectively
- Master the distinctions first, because Part One and Part Three are examined on them: syrup against elixir against linctus, liniment against lotion, bulk against divided powder, and the tablet types. Learn each as a paired comparison table, not a single loose definition.
- Do not skim the calculations, drill them by hand. Rework the ratio and proportion, specific gravity, percentage strength and both alligation methods until you can set each one up from a blank page, since these are the marks you can guarantee.
- Treat the phase rule as a plug-in tool: memorise F = C - P + 2 and practise substituting for an area, a curve and a point on the water diagram until the answers 2, 1 and 0 come without thinking.
- Memorise the short lists as complete sets: the four colligative properties, the five factors affecting solubility, the four conditions for Nernst's law, the six reasons for granulation, and the three stages of freeze-drying.
- Anchor every idea to a real preparation or clinical use, because the applied angle carries extra marks: why a nasal solution sits near pH 6.8, why irrigation fluids must be sterile, why freeze-drying is kept for high-value injections.
- Understand the summaries here first, then read the full workbook in the reader below and attempt the practice questions from memory before your exam.
Download the Full PCT 202 Practice Workbook
The notes above already cover the whole syllabus, but if you want everything in one place, the full PCT 202 – Pharmaceutical Preparations & Calculations workbook is loaded in the reader just below: the side-by-side comparison tables for syrups, elixirs and linctuses, the excipient and solubility reference charts, the labelled water phase diagram, the complete tablet-type table, and every worked calculation from ratio and proportion through to alligation. Flip through it right here on the page, or save a copy so you can keep drilling the distinctions and the maths offline in the days before your paper.
Frequently Asked Questions
Is this PCT 202 material free?
It is. There is no paywall, sign-up or fee here; the PCT 202 notes, practice questions and downloadable workbook are all open to any student who needs them.
Do I need to be good at maths to pass PCT 202?
You need confident arithmetic rather than advanced maths. The calculations rest on ratio, proportion and percentages, so if you can set up a proportion and handle decimals carefully you can score well. The notes rebuild each calculation type with worked examples, so practise them by hand and the numerical half of the paper becomes the most reliable place to gain marks.
Will these exact questions appear in my exam?
They will not. Everything in the practice set was written from scratch for revision, so use it to rehearse the reasoning and the method, not as a forecast of the questions your lecturer will actually set.
What is the fastest way to revise PCT 202 before the paper?
Rebuild the key comparison tables from memory (syrup, elixir and linctus, then the tablet types), memorise the short lists such as the colligative properties and the freeze-drying stages, then redo the calculations for proportion, specific gravity, percentage strength and alligation by hand. Finish by attempting the practice questions without looking and reading the full workbook in the reader below.
About this resource: All summaries, explanations, study tips, and practice questions on this page were written, paraphrased, and adapted by the EverythingABUAD student team to support exam revision. This is an original study aid, not an official ABUAD document, and it is not a prediction of any future exam. Always cross-check with your lecturer's current course outline.
