Understanding Molarity, Dilution, and Gas Laws
The chemistry formulas behind solution concentration, dilution calculations, and the ideal gas law, explained simply.
Solution chemistry comes down to tracking two things — how much solute you have, and how much solution it's dissolved in — and a handful of formulas that relate them.
Molarity: concentration as moles per liter
Molarity (M) is moles of solute divided by liters of solution: M = mol/L. Dissolve 0.5 moles of a compound into 2 liters of solution and you get 0.5/2 = 0.25 M — a quarter-molar solution. This is the concentration unit used throughout chemistry precisely because it directly relates to the number of reacting molecules, not just their mass.
Dilution: C1V1 = C2V2
Diluting a stock solution to a lower concentration follows a beautifully simple conservation law: the moles of solute don't change, only the volume they're dissolved in does. That gives C1V1 = C2V2, where C1V1 is the stock's concentration and volume, and C2V2 is the target. To dilute a 10M stock down to 1M in a final volume of 500mL, solve for V1: V1 = (C2×V2)/C1 = (1×500)/10 = 50mL of stock solution, topped up with 450mL of diluent to reach the full 500mL.
The ideal gas law: four variables, one equation
PV = nRT ties together pressure, volume, moles, and temperature, with R as the gas constant (0.0821 L·atm/(mol·K) in these units). Given 1 mole of gas at 298K in a 24.5L container, pressure works out to P = nRT/V = (1 × 0.0821 × 298) / 24.5 ≈ 1.0 atm — which is exactly why 1 mole of gas at room temperature and standard pressure occupies close to 24.5 liters, a useful number to remember.
Percent yield: theory vs. reality
Real reactions rarely produce exactly the theoretical maximum amount of product. Percent yield = (actual yield / theoretical yield) × 100 quantifies the gap. Producing 45g when the stoichiometry predicted 50g gives (45/50) × 100 = 90% yield — the missing 10% typically lost to side reactions, incomplete conversion, or purification losses.
Run your own numbers
- The molarity calculator and dilution calculator handle solution prep math directly
- The ideal gas law calculator solves for pressure given moles, temperature, and volume
- The percent yield calculator and pH to pOH calculator cover two more common lab calculations