Molarity is moles of solute divided by liters of solution
Molarity measures how many moles of a dissolved substance (the solute) are in one liter of total solution. The formula is straightforward: molarity = moles of solute ÷ liters of solution. If you dissolve 1 mole of table salt in water and add more water until the total volume reaches 1 liter, you have made a 1 molar (1 M) solution.
Chemists use molarity because it tells you the concentration of a substance in a way that matters for reactions. Two solutions with the same molarity will behave the same way in a chemical reaction, even if they started with different amounts of solute or solvent. This makes molarity more useful than straightforward measuring grams per liter.
Key Takeaways
- Molarity = moles of solute ÷ liters of solution; the unit is written as M or mol/L.
- To find moles, divide the mass of your solute in grams by its molar mass (found on the periodic table).
- The volume must be the total volume of the final solution, not just the volume of solvent you added.
- Rearranging the molarity formula lets you solve for moles, mass, or volume if you know the other values.
Finding the moles of solute
Before you can calculate molarity, you need to know how many moles of solute you have. Start with the mass of the solute in grams—this is usually what you measure or are given in a problem. Then look up the molar mass of the substance, which is the mass of one mole measured in grams per mole (g/mol).
The molar mass is the sum of the atomic masses of all atoms in the molecule. For sodium chloride (NaCl), sodium has an atomic mass of about 23 and chlorine about 35.5, so the molar mass is 58.5 g/mol. You can find atomic masses on any periodic table. Once you have the molar mass, divide the mass of your sample by the molar mass: moles = mass in grams ÷ molar mass in g/mol.
For example, if you have 11.7 grams of NaCl and the molar mass is 58.5 g/mol, then moles = 11.7 ÷ 58.5 = 0.2 moles.
Measuring the volume of the solution
The volume in the molarity formula is the total volume of the final solution, not the volume of solvent you started with. This is a common source of error. When you dissolve a solute in a solvent, the volumes do not always add together perfectly—the final volume may be slightly different from what you would expect.
To measure the volume correctly, dissolve your solute in a small amount of solvent first, then transfer the mixture to a volumetric flask—a flask with a narrow neck and a mark showing the exact volume it holds (1 L, 500 mL, 250 mL, and so on are common sizes). Add more solvent until the liquid level reaches the mark on the flask. This ensures your total volume is exact.
If you are working from a problem rather than making a solution in the lab, the volume will be given to you. Make sure it is in liters; if it is in milliliters, divide by 1,000 to convert.
Putting the formula together
Once you have the moles of solute and the liters of solution, the calculation is straightforward multiplication and division. Use the formula molarity = moles ÷ liters.
Continuing the NaCl example: you have 0.2 moles of NaCl and a total solution volume of 1 liter. Molarity = 0.2 moles ÷ 1 liter = 0.2 M. If your solution volume were 500 mL (0.5 liters), the molarity would be 0.2 ÷ 0.5 = 0.4 M. The smaller the volume, the higher the molarity for the same amount of solute.
Using molarity to find moles or mass
The molarity formula can be rearranged to solve for different unknowns. If you know the molarity and volume, you can find the moles: moles = molarity × liters. If you know the molarity and volume and need the mass, first find moles using the formula above, then multiply by the molar mass: mass = moles × molar mass.
For instance, if you have a 0.5 M solution of NaCl and you want to know how many moles are in 2 liters, calculate moles = 0.5 M × 2 L = 1 mole. To find the mass, multiply 1 mole × 58.5 g/mol = 58.5 grams of NaCl.
Common mistakes to avoid
Forgetting to convert milliliters to liters is the most frequent error. If a problem gives you 250 mL, divide by 1,000 to get 0.25 liters before you divide into the moles. Using the volume of solvent instead of the total solution volume will also throw off your answer—always use the final volume after mixing.
Another mistake is confusing molar mass with molecular weight or atomic mass. Molar mass is always in grams per mole and is what you need for this calculation. If a problem gives you mass in units other than grams (such as milligrams), convert to grams first by dividing by 1,000.
Working through a complete example
Suppose you dissolve 5 grams of glucose (C₆H₁₂O₆) in water and dilute to a final volume of 250 mL. The molar mass of glucose is 180 g/mol (6 × 12 + 12 × 1 + 6 × 16). First, find moles: 5 grams ÷ 180 g/mol = 0.0278 moles. Next, convert the volume: 250 mL ÷ 1,000 = 0.25 liters. Finally, calculate molarity: 0.0278 moles ÷ 0.25 liters = 0.111 M.
You can round this to 0.11 M depending on how many significant figures your measurements support. If you measured the 5 grams on a scale that reads to the nearest 0.1 gram, your answer should reflect that precision.
Frequently Asked Questions
What is the difference between molarity and molality?
Molarity uses the volume of the final solution in liters, while molality uses the mass of the solvent in kilograms. Molarity changes slightly with temperature because volume changes, but molality does not. For most chemistry work at room temperature, molarity is the standard.
Can I calculate molarity if I only know the percentage concentration?
Yes, but you need the density of the solution. Percentage concentration tells you the mass of solute per 100 grams of solution. Multiply by the density to get grams per milliliter, then convert to moles and liters using the methods above.
What if my solute is a solid that does not dissolve completely?
Molarity assumes all the solute dissolves. If the solute does not fully dissolve, you have a saturated solution, and the molarity is limited by how much can actually dissolve at that temperature. Only the dissolved portion counts toward molarity.
How do I know how many significant figures to use in my answer?
Your answer should have the same number of significant figures as the measurement with the fewest significant figures. If you measured 5 grams (one significant figure) and 250 mL (two or three, depending on the glassware), your molarity should have one significant figure.