Molarity is moles of solute divided by liters of solution

Molarity measures how many moles of a dissolved substance (the solute) exist in one liter of total solution. The formula is straightforward: molarity = moles of solute ÷ liters of solution. If you know any two of these three values, you can find the third. Most chemistry problems give you the mass of the solute and the volume of the solution, so you will usually need to convert mass to moles first, then divide by volume.

The unit for molarity is M, which means moles per liter. A 1 M solution contains 1 mole of solute dissolved in enough solvent to make 1 liter of total solution. A 2 M solution is twice as concentrated — it holds 2 moles in that same 1 liter.

Key Takeaways

  • Molarity = moles of solute ÷ liters of solution; the answer is always in units of M (moles per liter).
  • To find moles from mass, divide the mass in grams by the molar mass of the substance in grams per mole.
  • Volume must be in liters; if you have milliliters, divide by 1000 to convert.
  • The total volume of the solution is what matters, not the volume of solvent alone — if you dissolve 10 grams of salt in 500 mL of water, the final solution volume may be slightly different.

Convert mass to moles using molar mass

Before you can use the molarity formula, you need to know how many moles of solute you have. If the problem gives you mass in grams, use the molar mass of the substance to convert. Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). You can find it by adding up the atomic masses of all the atoms in the chemical formula.

The conversion is: moles = mass in grams ÷ molar mass in g/mol. For example, if you have 58.5 grams of sodium chloride (NaCl) and the molar mass of NaCl is 58.5 g/mol, then you have 58.5 ÷ 58.5 = 1 mole of NaCl. If you had 117 grams of NaCl, you would have 117 ÷ 58.5 = 2 moles.

To find molar mass, look up the atomic mass of each element on the periodic table and add them together. For NaCl: sodium is about 23 g/mol and chlorine is about 35.5 g/mol, so the total is 23 + 35.5 = 58.5 g/mol. For a compound with multiple atoms of the same element, multiply first. For example, H₂O has two hydrogen atoms (2 × 1 = 2) plus one oxygen atom (16), for a total of 18 g/mol.

Convert volume to liters

Molarity is always expressed as moles per liter, so your volume must be in liters before you divide. If the problem gives volume in milliliters, divide by 1000. If it gives liters, use that number directly. For example, 500 mL = 500 ÷ 1000 = 0.5 L, and 2.5 L is already in the correct unit.

Pay attention to what volume the problem is asking about. Some problems give you the volume of solvent (the liquid you are dissolving the solute in), but molarity uses the total volume of the final solution. If you dissolve 10 grams of sugar in 100 mL of water, the final solution volume is not exactly 100 mL — the sugar takes up space too. For most school-level problems, this difference is small enough to ignore, but in a real lab you would dissolve the solute in some solvent, then add more solvent until the total volume reaches your target (usually marked on a volumetric flask).

Divide moles by liters to find molarity

Once you have moles of solute and liters of solution, the final step is straightforward division. Molarity = moles ÷ liters. If you have 2 moles of solute in 4 liters of solution, the molarity is 2 ÷ 4 = 0.5 M. If you have 0.5 moles in 0.25 liters, the molarity is 0.5 ÷ 0.25 = 2 M.

Always include the unit M in your answer. The number alone does not tell someone whether you are talking about moles per liter or some other concentration measure. Writing "0.5 M" is clear; writing "0.5" is not.

Work through a complete example

Suppose you need to find the molarity of a solution made by dissolving 10 grams of calcium chloride (CaCl₂) in enough water to make 500 mL of total solution.

Step 1: Find the molar mass of CaCl₂. Calcium is 40 g/mol, and chlorine is 35.5 g/mol. Since there are two chlorine atoms, the molar mass is 40 + (2 × 35.5) = 40 + 71 = 111 g/mol.

Step 2: Convert grams to moles. Moles = 10 g ÷ 111 g/mol = 0.0901 moles (or about 0.09 moles).

Step 3: Convert volume to liters. 500 mL = 500 ÷ 1000 = 0.5 L.

Step 4: Divide moles by liters. Molarity = 0.0901 moles ÷ 0.5 L = 0.180 M (or about 0.18 M).

Rearrange the formula to find moles or volume

The molarity formula can be rearranged if you know molarity and need to find moles or volume instead. If you know molarity and volume and need moles, use: moles = molarity × liters. If you know molarity and moles and need volume, use: liters = moles ÷ molarity.

For example, if you have a 2 M solution and you want to know how many moles are in 0.25 liters, multiply: 2 M × 0.25 L = 0.5 moles. If you have 1.5 moles of solute and you want to make a 3 M solution, divide: 1.5 moles ÷ 3 M = 0.5 liters. These rearrangements are useful when you are preparing a solution of a specific concentration or when you are diluting an existing solution.

Frequently Asked Questions

What is the difference between molarity and molality?

Molarity uses liters of total solution as the denominator, while molality uses kilograms of solvent. Molarity changes with temperature because volume changes, but molality does not. For most introductory chemistry, you will use molarity. Molality appears more often in advanced chemistry and when temperature varies significantly.

Do I need to know the molar mass of every element?

No. You can look up molar masses on the periodic table or in a chemistry reference. The periodic table shows the atomic mass of each element, and you add them together based on the chemical formula. Your textbook or teacher will tell you which resources you can use during an exam.

What if the problem gives me the number of particles instead of mass?

If you have a number of atoms or molecules, convert to moles using Avogadro's number: 6.022 × 10²³ particles = 1 mole. Divide the number of particles by 6.022 × 10²³ to get moles, then proceed with the molarity formula as usual.

Can molarity be less than 1?

Yes. A solution can have a molarity of 0.5 M, 0.1 M, or even 0.001 M. These are called dilute solutions. A molarity greater than 1 M is called concentrated. The terms are relative and depend on the substance and the context.