The Mole, Concentration & Drug Doses

Atoms are so small that working with individual atoms is impractical. Chemists use a unit called the mole to work with amounts large enough to measure. One mole = 6.022 × 10²³ particles (Avogadro's number). This number is chosen so that one mole of any element has a mass in grams equal to its atomic mass in amu (atomic mass units). - 1 mole of carbon (atomic mass 12) = 12 grams - 1 mole of oxygen (atomic mass 16) = 16 grams - 1 mole of water (H₂O, molecular mass 18) = 18 grams Why does this matter? Reactions happen between individual atoms and molecules in fixed ratios. The mole lets us scale up to laboratory and clinical quantities while preserving those ratios. Clinical example: When you prescribe 500 mg of paracetamol (molecular weight 151.16 g/mol), you're giving the patient 500/151,160 = 0.00331 moles = 3.31 × 10²¹ molecules. That number would be impossible to work with directly — the mole makes it manageable.

Concentration measures how much of a substance is present in a given volume of solution. In medicine, getting concentrations right is literally a matter of life and death — underdosing fails to treat; overdosing can kill. Common concentration units: Molarity (mol/L or M): Moles of solute per litre of solution. Standard in chemistry and used in research. "A 1M NaCl solution" has 1 mole of NaCl per litre. Millimolar (mmol/L or mM): Used for electrolytes in blood. Normal serum sodium: 135–145 mmol/L. Normal serum potassium: 3.5–5.0 mmol/L. mg/dL (milligrams per decilitre): Common for blood tests in some countries. Blood glucose: 70–100 mg/dL fasting. Cholesterol: <200 mg/dL desirable. mg/L and µg/L: Used for drug levels in blood (therapeutic drug monitoring). Gentamicin (an antibiotic): trough level must stay below 2 mg/L to avoid kidney and hearing damage. %w/v (weight/volume %): Grams of solute per 100 mL of solution. Saline 0.9% = 0.9 g NaCl per 100 mL. Glucose 5% = 5 g glucose per 100 mL.

When a drug is administered, it doesn't just appear at its target at full concentration. It undergoes ADME: Absorption, Distribution, Metabolism, Excretion. Each stage is governed by chemistry. Absorption: How the drug enters the body. Oral drugs must survive stomach acid (some are destroyed — hence some drugs must be injected). Ionised drugs don't cross membranes well — pH of the gut, blood, and target tissue affects absorption. Distribution: Where the drug goes after absorption. Volume of distribution (Vd) describes how widely a drug spreads. A drug that stays in blood has a small Vd; one that penetrates deeply into tissues has a large Vd. Hydrophilic drugs stay in blood; lipophilic drugs accumulate in fat. Metabolism: The liver chemically modifies most drugs — usually making them more water-soluble so they can be excreted. First-pass metabolism dramatically reduces the amount of some oral drugs that reaches the circulation (e.g. only ~20% of orally administered morphine survives first-pass to reach the blood). Excretion: Mostly via the kidneys (into urine) or bile (into faeces). pH of urine affects drug excretion (recall acid trapping from the pH lesson). Patients with kidney failure can't excrete drugs normally — dose reduction is essential. Half-life (t½): The time for plasma drug concentration to halve. After 5 half-lives, ~97% of the drug has been eliminated. Knowing half-life allows calculation of dosing intervals — you need the next dose to arrive before the drug falls below its effective concentration.

Every drug has a therapeutic window — the concentration range between: - Minimum effective concentration (MEC): Below this, no therapeutic effect - Minimum toxic concentration (MTC): Above this, toxic effects begin The goal of dosing is to keep drug concentration within this window. Narrow therapeutic index drugs — drugs where the window between effective and toxic is very small — require careful monitoring: - Warfarin: INR 2–3 is therapeutic; <2 = risk of clot; >3–4 = bleeding risk. Diet, other drugs, genetics all affect it. - Digoxin: Treats heart failure and arrhythmias. Therapeutic: 0.5–2 ng/mL. Toxic: >2 ng/mL → nausea, dangerous arrhythmias, visual disturbances (yellow-green vision). - Lithium: Treats bipolar disorder. Therapeutic: 0.6–1.2 mmol/L. Toxic: >1.5 mmol/L → tremor, confusion; >2 mmol/L → seizures, cardiac arrest. - Gentamicin: Antibiotic effective against gram-negative bacteria but nephrotoxic and ototoxic at high levels. - Phenytoin: Anti-epileptic. Nystagmus and ataxia at toxic levels. Therapeutic drug monitoring (TDM): Blood samples are taken at specific times (usually just before the next dose — the "trough") to measure drug concentration. Dose is adjusted to keep the level within the therapeutic window. Essential for narrow-index drugs.

Doctors, nurses, and pharmacists perform concentration calculations constantly. Getting these wrong has caused patient deaths — unit confusion, decimal errors, and wrong routes of administration are all reported clinical errors. Key calculation types: Dose by weight: Most drugs are dosed per kg of body weight. A 70 kg patient prescribed amoxicillin 25 mg/kg/day divided into 3 doses: - Total daily dose = 25 × 70 = 1750 mg/day - Each dose = 1750 ÷ 3 = 583 mg (round to 500 mg) Concentration in solution: Drug comes as 250 mg/5 mL. Patient needs 500 mg. Volume to give = (500 × 5) / 250 = 10 mL. IV infusion rates: 1000 mL of saline to run over 8 hours. Rate = 1000 ÷ 8 = 125 mL/hour. In drops: if giving set delivers 20 drops/mL → 125 × 20 ÷ 60 = ~42 drops/minute. Dilutions: Stock solution is 1000 mg/L. Need 50 mg/L for a patient. Dilution factor = 1000/50 = 20. Take 1 part stock + 19 parts diluent (C₁V₁ = C₂V₂: 1000 × V₁ = 50 × 1000 mL → V₁ = 50 mL of stock into 1000 mL total). The chemistry of concentration, moles, and solutions sits at the very heart of safe medical practice. A student who understands this chemistry is already thinking like a doctor.