M
Calculate molarity (M), moles of solute, or volume of solution. Enter any two known values and solve for the third. Also includes a dilution calculator.
Use C₁V₁ = C₂V₂. Enter three values to solve for the fourth (leave one blank).
| Quantity | Formula | Result |
|---|
Molarity (M) is the most common unit of concentration in chemistry. It measures the number of moles of solute dissolved in one liter of solution. The formula is simple: M = n ÷ V, where n is the number of moles of solute and V is the volume of the solution in liters. Molarity is used in labs worldwide to prepare chemical solutions, perform titrations, and carry out quantitative analysis.
| Find | Formula | Units |
|---|---|---|
| Molarity (M) | M = n ÷ V | mol/L |
| Moles (n) | n = M × V | mol |
| Volume (V) | V = n ÷ M | L |
| Dilution | C₁V₁ = C₂V₂ | M · mL = M · mL |
| Unit | Symbol | Definition |
|---|---|---|
| Molarity | M | moles of solute per liter of solution |
| Molality | m | moles of solute per kilogram of solvent |
| Normality | N | equivalents of solute per liter of solution |
| Mass percent | % w/w | grams of solute per 100 g of solution |
| Parts per million | ppm | mg of solute per liter of solution |
A mole is a unit of measurement equal to 6.022 × 10²³ particles (Avogadro's number). It's the bridge between the atomic scale and the everyday scale — it lets chemists count atoms and molecules by weighing them. 1 mole of any substance contains the same number of particles.
1 M (1 molar) means 1 mole of solute is dissolved in enough solvent to make exactly 1 liter of solution. For example, a 1 M NaCl solution contains 58.44 grams of sodium chloride (the molar mass of NaCl) dissolved to make 1 liter of solution.
The dilution formula is C₁V₁ = C₂V₂, where C₁ is the initial concentration, V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. It states that the number of moles of solute stays the same before and after dilution — you're just adding more solvent.
To make a 0.1 M solution of a substance, calculate the required mass using: mass = molarity × volume × molar mass. For example, for 500 mL of 0.1 M NaCl: mass = 0.1 × 0.5 × 58.44 = 2.922 g. Dissolve 2.922 g of NaCl in a 500 mL volumetric flask and fill to the mark with distilled water.
Molarity (M) is moles per liter of solution, while molality (m) is moles per kilogram of solvent. Molarity changes with temperature (since volume changes), while molality does not. Molality is preferred in experiments involving boiling point elevation and freezing point depression.
A stock solution is a concentrated solution prepared in advance and diluted as needed. For example, a lab might prepare a 10 M HCl stock solution, then dilute it to 0.1 M when needed using the dilution formula C₁V₁ = C₂V₂. This saves time and reduces errors from repeated weighing.