Molarity and Solution Dilution: M1V1 = M2V2, Grams Needed, and Percent Solutions
October 29, 2026
Molarity (M) is the number of moles of solute per liter of solution. Moles = grams ÷ molar mass. For sodium chloride (NaCl), the molar mass is 58.44 g/mol. Dissolving 5.844 g in enough water to make 1 liter gives 0.1 mol per liter, a 0.1 M solution.
To prepare a specific solution: grams needed = molarity × volume (L) × molar mass. For 250 mL of 0.2 M NaCl: 0.2 × 0.250 × 58.44 = 2.92 g. Dissolve in less water, then add water up to the 250 mL mark.
Skip the math and get your answer instantly:
Open the Scientific Calculator →Dilution: C₁V₁ = C₂V₂
The amount of solute doesn't change when you add solvent, so concentration × volume stays constant: M₁V₁ = M₂V₂. To make 500 mL of 0.5 M from a 6 M stock: V₁ = (0.5 × 500) ÷ 6 = 41.7 mL. Measure 41.7 mL of stock, then add water to a final volume of 500 mL (not 500 mL of water added). The same rule works for any concentration unit, as long as both sides use the same one. A 10× dilution takes 1 part stock plus 9 parts diluent; a 1:100 dilution takes 1 part plus 99.
| Goal | Calculation | Result |
|---|---|---|
| 0.1 M NaCl, 1 L | 0.1 x 1 x 58.44 | 5.844 g |
| 0.2 M NaCl, 250 mL | 0.2 x 0.25 x 58.44 | 2.922 g |
| 0.5 M from 6 M, 500 mL | 0.5 x 500 / 6 | 41.7 mL stock |
| 0.1 M from 1 M, 100 mL | 0.1 x 100 / 1 | 10 mL stock |
Percent Solutions
Weight/volume percent (w/v) is grams of solute per 100 mL of solution: a 0.9% saline solution has 0.9 g NaCl per 100 mL, or 9 g per liter, which is 0.154 M. Weight/weight percent (w/w) is grams of solute per 100 g of solution, as with a 5% brine. Volume/volume (v/v) is used for liquids, like 70% isopropyl alcohol. To dilute 91% isopropyl alcohol to 70%: V₁ = 70 × 100 ÷ 91 = 76.9 mL of 91% plus water to make 100 mL.
Serial Dilutions and Units
Serial dilutions repeat a fixed dilution factor; three 1:10 steps give a 1:1,000 dilution. Concentrations can also be given in mg/L (ppm for dilute aqueous solutions): 1 mg/L = 1 ppm, and 1 M NaCl is 58,440 mg/L. Convert units before calculating. Use volumetric flasks for accuracy, and add acid to water, never water to acid.
Safety
Wear gloves and eye protection when handling chemicals, and follow the lab's rules and safety data sheets. This article covers the math, not procedures for hazardous materials.
Frequently Asked Questions
What is molarity?
Moles of solute per liter of solution.
How do I find grams needed for a solution?
Molarity × volume in liters × molar mass.
What is the dilution formula?
M₁V₁ = M₂V₂.
What is w/v percent?
Grams of solute per 100 mL of solution.
Do I add the final volume of water?
No. Add water up to the final volume mark.