Molarity is the number of moles of solute per liter of solution: M = mol ÷ L. Dissolve 5.85 grams of sodium chloride (0.100 mol) in enough water to make 250 mL of solution, and the concentration is 0.100 mol ÷ 0.250 L = 0.400 M, read as “0.400 molar.” To use the formula from grams, first convert grams to moles with the molar mass.
IUPAC calls this quantity the amount concentration, with units of mol/L (also written mol dm⁻³). The symbol M is the long-standing shorthand.
The molarity formula
| Symbol | Meaning | Unit |
|---|---|---|
| M | Molarity | mol/L |
| n | Amount of solute | mol |
| V | Volume of solution | L |
| m | Mass of solute | g |
| MW | Molar mass of solute | g/mol |
Combining the two gives a single working formula: M = m ÷ (MW × V).
Calculating molarity from grams
5.85 g of NaCl dissolved to make 250 mL of solution
Molar mass of NaCl = 22.990 + 35.45 = 58.44 g/mol
Moles = 5.85 ÷ 58.44 = 0.100 mol
Volume = 250 mL = 0.250 L
M = 0.100 ÷ 0.250 = 0.400 M
The most common error is leaving the volume in milliliters. Divide by 1,000 first, or the answer comes out 1,000 times too small. Molar masses come from the periodic table; see how to calculate molar mass or use the molar mass calculator.
How much solute do I need?
Rearrange to find the mass needed for a target concentration:
Make 250 mL of 0.150 M glucose (C₆H₁₂O₆, 180.156 g/mol)
Moles = 0.150 mol/L × 0.250 L = 0.0375 mol
Mass = 0.0375 × 180.156 = 6.76 g
Making the solution
- Weigh 6.76 g of glucose.
- Transfer it to a 250 mL volumetric flask.
- Add distilled water to about two-thirds full and swirl until dissolved.
- Add water until the bottom of the meniscus sits on the calibration line.
- Stopper and invert several times to mix.
Adding the solid to exactly 250 mL of water would give slightly more than 250 mL of solution and a slightly lower concentration. The volumetric flask avoids that error. If you start from a hydrated salt, such as copper sulfate pentahydrate, use the molar mass of the hydrate including its water. The molarity calculator solves for any one of molarity, mass, volume or molar mass.
Diluting a stock solution
When you add solvent, the moles of solute stay the same, so concentration × volume is constant:
Make 500 mL of 1.00 M HCl from 12.0 M stock
V₁ = (1.00 × 500) ÷ 12.0 = 41.7 mL of stock, diluted to 500 mL total
Volumes can stay in milliliters here, as long as both sides use the same unit. For concentrated acids, put most of the water in the flask first and add the acid slowly to the water; adding water to acid can boil and spatter. The dilution calculator solves for any of the four values.
Serial dilutions
For very low concentrations, a single dilution would require measuring an impractically small volume of stock. Instead, dilute in steps. In a tenfold serial dilution, mix 1.0 mL of solution with 9.0 mL of solvent, then take 1.0 mL of that mixture into another 9.0 mL, and so on. Each step divides the concentration by 10:
1.0 M → 0.10 M → 0.010 M → 0.0010 M (1.0 mM) after three steps
Microbiology and biochemistry labs use serial dilutions to make standard curves and to count bacteria. Small pipetting errors multiply across steps, so use calibrated pipettes and mix thoroughly at every stage.
Temperature and molarity
Because molarity is based on volume, and liquids expand when warmed, a solution’s molarity drops slightly as temperature rises. For most aqueous work the change is a fraction of a percent per few degrees, but precise analytical work specifies the temperature at which a volumetric flask is calibrated, usually 20°C. When temperature independence matters, chemists use molality instead.
Converting other concentration units to molarity
Commercial reagents are often labeled by mass percent. Convert using the solution’s density:
Concentrated hydrochloric acid: 37% HCl by mass, density 1.19 g/mL, MW 36.46 g/mol
M = (1.19 × 1,000 × 0.37) ÷ 36.46 ≈ 12.1 M
That is why concentrated HCl is commonly treated as about 12 M. Other units you will meet:
| Unit | Meaning | Relation to molarity |
|---|---|---|
| mM (millimolar) | 10⁻³ mol/L | 0.400 M = 400 mM |
| µM (micromolar) | 10⁻⁶ mol/L | 1 µM = 0.001 mM |
| Molality (m) | mol per kg of solvent | Close to M for dilute aqueous solutions |
| % w/v | g per 100 mL | 0.9% NaCl saline = 9 g/L ≈ 0.154 M |
| ppm (aqueous) | about mg per L | Divide by molar mass in mg/mol |
The solution concentration calculator converts between these.
Ions in solution
For ionic compounds, the concentration of each ion depends on the formula. Calcium chloride, CaCl₂, splits into one Ca²⁺ and two Cl⁻ ions:
0.10 M CaCl₂ → [Ca²⁺] = 0.10 M, [Cl⁻] = 0.20 M, total ions = 0.30 M
Square brackets mean “molar concentration of.” Total ion concentration matters for colligative properties such as freezing-point depression.
Molarity in titrations
In a titration, a solution of known molarity reveals the molarity of another. If 18.4 mL of 0.100 M NaOH neutralizes 25.0 mL of HCl (a 1:1 reaction):
Moles NaOH = 0.100 × 0.0184 = 0.00184 mol = moles HCl
[HCl] = 0.00184 ÷ 0.0250 = 0.0736 M
For reactions that are not 1:1, multiply by the mole ratio from the balanced equation. The titration calculator handles both cases, and the resulting concentration feeds directly into how to calculate pH.
Common mistakes
- Using milliliters instead of liters in M = n ÷ V.
- Using the solvent volume instead of the final solution volume.
- Ignoring water of hydration in the molar mass.
- Forgetting stoichiometry for ion concentrations and titrations.
- Rounding the molar mass too far. Keep at least four significant figures; the grams to moles calculator uses full precision.
Frequently asked questions
What is the formula for molarity?
Molarity (M) = moles of solute ÷ liters of solution. If 0.100 mol of sodium chloride is dissolved to make 0.250 L of solution, the molarity is 0.100 ÷ 0.250 = 0.400 M.
How do I calculate molarity from grams?
Convert grams to moles by dividing by the molar mass, then divide by the solution volume in liters. For 5.85 g of NaCl (58.44 g/mol) in 250 mL: 5.85 ÷ 58.44 = 0.100 mol, and 0.100 ÷ 0.250 L = 0.400 M.
What is the difference between molarity and molality?
Molarity is moles per liter of solution; molality is moles per kilogram of solvent. Molality does not change with temperature because it uses mass, so it is preferred for freezing-point and boiling-point calculations. For dilute water solutions the two values are close.
How do you dilute a solution to a specific molarity?
Use C₁V₁ = C₂V₂. To make 500 mL of 1.00 M HCl from 12.0 M stock, you need V₁ = (1.00 × 500) ÷ 12.0 = 41.7 mL of stock, diluted with water to a final volume of 500 mL. Always add acid to water, not water to acid.
Why is molarity based on volume of solution and not volume of water?
Dissolving a solute changes the total volume, so adding 250 mL of water to a solid does not give exactly 250 mL of solution. That is why solutions are made in a volumetric flask: dissolve the solute, then add solvent up to the calibration mark.