Calculate solution concentration in mol/L. Solve for molarity from moles and volume, find moles from molarity and volume, or calculate dilution problems using C₁V₁ = C₂V₂.
Molarity (M) is the number of moles of solute dissolved per litre of solution. M = moles / litres. A 1 M solution contains 1 mole of solute in 1 litre of solution.
M = n / V, where M is molarity in mol/L, n is moles of solute, and V is volume in litres. Rearranged: n = M × V, and V = n / M.
Molarity (M) = moles / volume of solution (in litres). Molality (m) = moles / mass of solvent (in kg). Molarity changes with temperature (volume expands); molality does not.
When diluting a solution, the initial moles must equal the final moles. C₁V₁ = C₂V₂ where C is concentration and V is volume. Use this to find the final volume needed to reach a target concentration.
Calculate moles needed: 0.1 mol/L × 1 L = 0.1 mol. Find mass: 0.1 mol × 58.44 g/mol (molar mass of NaCl) = 5.844 g. Dissolve 5.844 g of NaCl in water and make up to exactly 1 litre.
Molar mass is the mass of one mole of a substance in grams. It equals the sum of atomic masses of all atoms in the formula. NaCl = 23 + 35.5 = 58.5 g/mol. You need molar mass to convert between grams and moles.
Biology commonly uses millimolar (mM, 10⁻³ M), micromolar (μM, 10⁻⁶ M), and nanomolar (nM, 10⁻⁹ M) for very dilute solutions. Blood glucose is approximately 5 mM, and hormone concentrations are often in the nM range.