How To Calculate Molarity

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Solutions are essential to life, chemistry, engineering and many other fields. The coffee you drink in the morning, many liquid medicines, ocean water, the air we breathe, and even the steel we use to build houses are all solutions.

These interesting entities are made of at least two different substances that mix homogeneously. The most abundant one is called the solvent, and the one that dissolves in it is called the solute. Solutions are mainly characterized by their volume, meaning how much space they occupy, and their concentration, meaning how much solute is to be found in each volume unit of solution.

One of many ways of measuring concentration —and one of the most common ones in chemistry labs— is molarity. This simple but powerful concept will let you prepare any solution with the specified concentration, or even determine how much solute is present in an existing sample. Keep reading to learn more about where molarity comes from and how to use it.

How to calculate molarity

A solution’s molarity is calculated by dividing the number of moles of solute that are dissolved in the solvent (n) by the total volume of the solution in liters (V), as indicated by the following equation. Its units are therefore mol/l, which is usually designated as M.


What is molarity?

Solutions are homogeneous mixtures of at least two different substances. By homogeneous we mean that, if we take a sample of any part of it and compare it to any other sample taken from another part of it, both will have the same composition and properties. 

Think of a glass of saline water. This solution is made of water and sodium chloride molecules that have been dissociated and which ions are homogeneously dispersed. The result is an even, transparent liquid. So, regardless of the place in which we take a 1 ml sample, we will find more or less the same amount of molecules and ions.

Solutions are mostly found as fluids, meaning in liquid or gaseous state, although solid solutions also exist. The most abundant substance in them, the solvent, acts as a matrix in which the atoms or molecules of the other substances, called the solutes, dissolve in.

Imagine you put a solid sample into a glass containing a liquid solvent. Depending on the substances involved, the sample might dissolve slower or faster, or it might not dissolve at all, in which case no solution is obtained. So, how do molecules dissolve in a solvent and form solutions? Let’s use our saline water example to try and understand this:

Water is a very common solvent, which forms solutions with many different types of substances, like salts and small organic compounds. This is mainly due to a very interesting property of the water molecule: its polarity. Due to the electron distribution within the molecule, the positively charged nuclei of both hydrogen atoms are partially exposed on one side, while the oxygen atom retains the greater part of the electronic cloud on the opposite side. This creates a type of electric dipole  —a spatial separation of charges— which can then interact with other electric charges in its surroundings. 

On the other hand, table salt is made of two atoms held together by an ionic bond. This means one of them, sodium, has lost one of its electrons to the other one, chlorine. The positively charged sodium cation (Na+) and the negatively charged chlorine anion (Cl-) then attract each other due to Coulomb forces, which strongly hold them together. Ionic bonds are therefore one of the strongest types of chemical bonds.

When a NaCl crystal is introduced in water, both molecules start to interact with each other. The negative side of water molecules attracts sodium cations, and their positive side attracts chlorine anions. The result is that both ions in table salt are separated and screened by water molecules in a process called solvation, which can be represented by the following image:

Electric charges generate electric fields between them. If all of the cations in a saline water solution were located on one side and all of the anions on the other side of the container, a net electric field would be produced, which would increase the total energy of the solution. Since a spontaneous energy increase is not possible, all dissolved ions will tend to distribute homogeneously in space, so that no net electric field is produced. This is why table salt forms a solution with water. 

In the case of solutions made with molecules which are not ionically bonded, such as organic compounds, the interaction between the solute and the solvent is different. The most common case is sugar dissolved in water. 

Sugar is an organic molecule in which atoms are bonded covalently, not ionically. This means electrons are shared and not entirely transferred from one atom to the other in each bond. Nevertheless, sugar is a polar molecule, since the electronic clouds in it are not homogeneously distributed throughout the entire molecule. This happens because of the presence of several hydroxy groups (-OH), which can act as a polar “branch” of the molecule:

When introduced in water, sugar molecules interact with water through hydrogen bonds or Van der Waals forces, which are weak interactions between sections of molecules. In this case, the sugar molecule does not break into ions, but it stays complete, and its polar ends are partially screened by the polar water molecules. Since no ionic bond breaking is necessary, sugar dissolves a lot easier in water than table salt. 

Now, if we add more salt to our saline water solution, more and more sodium and chlorine pairs will be dissolved. The process will continue until a point when there is so much salt in it that water molecules will not be able to solvate any more ions. The excess salt will then precipitate to the bottom of the container. 

This happens when the concentration of salt in water surpasses a specific value. But, how can we measure that concentration? In chemistry, there are several ways to refer to the amount of solute that is dissolved in a solution. One of those ways is through the solution’s molarity, also called its molar concentration, which indicates the amount of solute per unit volume of solution. 

In this case, the amount of solute that is effectively dissolved is measured in moles, which simply refers to multiples of 6,021023 atoms or molecules. Since chemical species are so small, and trillions of them can be present in just a few milliliters of solution, moles are a very useful unit to indicate the number of atoms or molecules dissolved in it. 

A solution’s molarity is then calculated by dividing the number of moles of solute by the volume of the solution in liters, as equation 1 shows. Its units are therefore moles per liter (mol/l), which is usually represented as M and called “molar”. So, when you hear you need to prepare a “1 molar” solution, you now know you must dissolve 1 mol of solute per liter of solution.

Keep in mind the definition of molarity requires the use of the volume of the entire solution! When dissolving any substance, the solvent’s initial volume might change, since its molecules have to make room for the solute’s species. The final volume of the solution is the quantity that needs to be used to calculate its molarity, and not the solvent volume prior to introducing the solute in it. To learn about a definition of concentration that is independent of volume, go ahead and read the section called Difference between molarity and molality.

How to measure the molarity of an already-prepared solution

If you want to prepare a solution with known amounts of solute and solvent, calculating the resulting molarity is pretty straight forward: you simply need to mix both, and then divide the moles of solvent you used by the resulting volume of the solution in liters. But what happens when you want to determine the molarity of a solution that has already been prepared? 

To do so, you need to measure its concentration using different methods that depend on the specific substances that make up the solution. Let’s assume you have a solution of any salt in water. Since salts have boiling points way above that of water, one easy method to determine the solution’s molarity is to first measure its volume, then put it in a pot, heat it up until all water has evaporated, and then measure the remaining amount of salt. 

Now, using the salt’s molar mass you can obtain the number of moles that were dissolved in the solution in the first place. If you are not sure about this procedure, go ahead and read our article on molar mass. Finally, you can use equation 1 to calculate the solution’s molarity. 

What happens when the solution was prepared using two liquid substances? In this case, distillation is the appropriate method to separate both components. This is possible thanks to differences in their boiling points. Once separated, you can determine the amount of solute in moles and divide it by the original volume of solution used to obtain it, which will yield the solution’s molarity. 

Difference between molarity and molality

One letter can change a lot of things! For example, if you are describing a friend who is bold and you call them bald instead, you might end up hurting their feelings. The same happens with molarity and molality

We now know molarity describes the number of moles per liter of solution. On the other hand, molality refers to the number of moles of solute per kilogram of solvent. This differs from the definition of molarity, because it is the mass of solvent which is taken into account, and not the solution’s final volume. 

So, if you have a solution of table salt and water with a molality of 0,5 mol/kg, it means you have 0,5 moles of salt dissolved in every kilogram of water.

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