Finding Molarity of a Unknown Solution

How to Calculate Molarity & Molarity Formula

November 27, 2021

Core Concepts

In this tutorial, you will learn the molarity formula, and how to calculate the molarity of a solution. If you enjoy this article, make sure to check out other resources linked below!

Topics Covered in Other Articles

Calculating Molar Mass
Mixtures vs. Compounds
Molecule vs. Compound

Vocabulary

Molarity (M): otherwise known as the molar concentration of a solution, molarity is the moles of solute per liters of solution. Molarity can be expressed as the abbreviations mol/L, or more popularly, M.
Molar mass: the sum of the atomic weights that make up a molecule. For an element, it is the same value as the atomic weight displayed in the periodic table.
Solute: the substance in a solution that is dissolved by the solvent. It is always the smaller component in the solution. In chemistry, the solute is the element or molecule in the solution.
Solvent: the substance that dissolves the solute. This is what makes up the majority of the solution, which is usually water or in some cases, an organic solvent.

What is molarity?

Molarity is the number of moles of solute per liter of solution. For example, if you dissolve table salt in water, salt is the solute, and water is the solution. One mole of sodium chloride weighs 58.44 grams. If you dissolve 58.44 grams of NaCl in one liter of water, you have a one molar solution, abbreviated as 1M. It is important to know, that the volume of solution is measured after the solute is dissolved, not before. Also, don't confuse molarity with molality, which is slightly different!

When you see "1M", you read that aloud as a "1 molar solution".

Molarity Formula

The formula for molarity is M = n /v

M = molar concentration of the solution, aka molarity
n = moles of solute
v = liters of solution

How do you calculate molarity?

Molarity is calculated, using the molarity formula above, by considering two components: volume and moles. In the case that moles of the compound are unknown, molar mass can be used to convert the compound from grams to moles. The periodic table provides the atomic masses that are used to calculate molar mass.

Step 1:

The first step to calculating molarity is identifying one of the two key factors that make up the solution: the volume of the solution and the amount of solute in grams or moles. First, we will start with volume in this tutorial. The volume of the solution can be measured by using a graduated cylinder. For molarity, volume must be in the unit of liters. If the starting volume is in milliliters, it must be converted to liters before calculating molarity. There are 1000 millimeters in a liter. So, with a simple calculation, any volume in milliliters can be converted to liters. For example, if the volume of the solution is 100 mL:

Step 2:

The second step is to determine the amount of solute present in the solution in moles. If the known amount of solute is in grams, it must be converted to moles using molar mass. If we say that the solute is 5.00 g of ammonia (NH₃), we can convert this to moles using ammonia's molar mass (17.04 g/mol):

Step 3:

The third and final step is to use the molarity formula and divide the number of moles of solute by the number liters of the solution to obtain the molarity in moles per liter. If we take the two values from the previous step, we see that the ammonia solution is 2.9 M. This means that every liter of this solution contains 2.9 moles of ammonia.

Another example of calculating molarity

Using a different compound, calcium chloride, we can calculate the molarity of a solution in the same way. Let's start with these values:

10.0 g CaCl₂
200 mL H₂O

Following the same process outlined above, we can determine the molarity of this calcium chloride solution in a few simple steps. First, the volume must be converted from milliliters to liters.

Next, we convert grams of calcium chloride into moles.

Finally, we divide the number of moles by the volume of the solution.

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