Concentration
High-Yield Summary
- Molarity (M) = mol solute / L solution — the MCAT's default concentration unit.
- Dilution adds solvent without changing moles of solute, so M₁V₁ = M₂V₂ relates concentration and volume before/after dilution.
- Molality (m) = mol solute / kg solvent — doesn't change with temperature (unlike molarity), so it's preferred for thermodynamic calculations.
- Percent by weight = (mass solute / mass solution) × 100; mole fraction (X) = mol component / total mol.
- Normality (N) = equivalents solute / L solution = M × n, where n is equivalents per mole (the valence factor, e.g. n=2 for diprotic H₂SO₄).
Key Terms
- Molarity (M)
- Moles of solute per liter of solution — M = mol solute / L solution.
- Molality (m)
- Moles of solute per kilogram of solvent — m = mol solute / kg solvent; temperature-independent.
- Mole fraction (X)
- Moles of one component divided by total moles of all components in the solution.
- Equivalent
- A measure of reactive capacity — for acids/bases, the amount supplying one mole of H⁺ or OH⁻; for redox, one mole of electrons.
- Normality (N)
- Equivalents of solute per liter of solution — N = equivalents solute / L solution = M × n.
Dilution Equation
M₁V₁ = M₂V₂
- M₁, V₁ = molarity and volume of the concentrated (stock) solution before dilution
- M₂, V₂ = molarity and volume of the solution after dilution
- Works because moles of solute (M × V) is conserved during dilution — only volume changes, so molarity drops.
- Worked example: need 500 mL of 1.5 M HCl from 6.0 M stock → V₁ = (1.5 × 0.500)/6.0 = 0.125 L = 125 mL of stock, then dilute to 500 mL total.
Normality
N = equivalents solute / L solution = M × n
- n = equivalents per mole (valence factor) — 1 for monoprotic, 2 for diprotic, etc.
- Worked example: 0.500 M H₂SO₄ (diprotic, n=2) → N = 0.500 × 2 = 1.00 N.
Four Concentration Units Compared
| Unit | Formula / notes |
|---|---|
| Molarity (M) | mol solute / L solution — changes with temperature (volume expands/contracts). |
| Molality (m) | mol solute / kg solvent — temperature-independent; preferred for thermo. |
| Percent by weight (%) | (mass solute / mass solution) × 100 — common in industrial contexts. |
| Mole fraction (X) | mol component / total mol — used for gas mixtures and solutions. |
Must-Know Points
- Molarity and molality diverge as concentration increases — they're only numerically close for dilute solutions near water's density (1 kg/L).
- A monoprotic acid like HCl: 1 mole = 1 equivalent. A diprotic acid like H₂SO₄: 1 mole = 2 equivalents.
- Worked example (1.00 mol NaCl in 1.000 kg water, 1.02 L total): M = 0.980 M, m = 1.00 m, % = 5.53%, X(NaCl) = 0.0177.
Common MCAT Trap
- Molality's denominator is kg of SOLVENT, not solution — don't include solute mass when calculating molality.
- Don't assume M and m are interchangeable at higher concentrations — they diverge because molarity's volume denominator shifts with both temperature and solute packing.
- Normality depends on the reaction context — the same solution can have different N values for different reactions (e.g., acid-base vs. redox) since n (equivalents/mole) changes with the reactive unit being counted.
Quick Recall
Why does M₁V₁ = M₂V₂ hold true during dilution?
Why is molality preferred over molarity for thermodynamic calculations involving temperature changes?
What is the normality of a 0.100 M H₃PO₄ solution?