How to Calculate Molarity

If you like experimenting with chemicals in the lab, or aspire to be a chemist, then you need to be familiar with a few terms like solution, solvent, compound. etc. Here, we shall try to understand one such term called molarity, how is it calculated and its importance in chemical reactions.

Molarity is a measure of the concentration of a solution and is defined as the number of moles of solute per liter of solution.

Chemistry involves the study of the composition of substances and their reactions and properties. To study the reactions and chemical processes associated with the substances, they need to be used in a definite or measured quantity. Solutions of these substances make it easier for scientists to conduct experiments. Making proper solutions is fundamental to any laboratory, be it in research or industry. The concentration of a solution needs to be correct and up to the mark for results to be accurate. Let us try to know more about one such term that evaluates the strength of a solution - molarity. 

Understanding Molarity

Molarity is also known as molar concentration and measures the amount of substance or solute dissolved in a solution. For example, if you consider a sugar-water solution. Here, sugar is the solute and water, the solvent. Solute is the substance being dissolved. Solvent is the dissolving agent. Their homogenous mixture is called a solution. 

The addition of the solute in the solvent changes its volume. Therefore, the final volume of the solvent after dissolution is considered while calculating molarity. Hence, it is the volume of solution in liters while calculating molarity.

The formula to calculate molarity is :



where, mole = mass of solute / molar mass of the solute.

Number of moles:- Mole is the mass of the substance expressed in grams. It is the measure of the amount of substance that you have.
Molar mass:- Molar mass of any element/compound is defined as the atomic/molecular weight expressed in grams. It is important because if we take the molar mass of any substance, then it has 6.0221415×1023 (Avogadro's constant) number of atoms or molecules of that substance (which can be an element or a compound).

Here are a few examples that will clarify your doubts.

Take the example of Carbon, whose atomic number is 12. The molar mass of carbon is 12 g. So, this means that 12 g of carbon will have 6.0221415×1023 atoms of carbon.

Now, what about molar mass of a compound? An example, straight away, will clear up things. Consider Sodium Chloride (NaCl), whose molecular weight is 58.5 (23 for Na + 35.5 for Cl). So, in case of compounds, the molecular weight expressed in gm is the molar mass, which in this case is 58.5 grams. In other words, 58.5 grams of NaCl has 6.0221415×1023 molecules.

Thus, by substituting this in the above equation, the formula for molarity becomes:



Thus, the unit of molarity is moles/liter, symbolized as mol/L. 

Standard Formula

Given below are a few standard formulas for calculating molarity : 

1} Calculation of molarity when number of moles of solute and volume of a solution is known:



where, 
n = Number of moles of the substance
V = Volume of solution in Liters
N = Number of molecules present in the solution
NA = Avogadro's number 6.0221415×1023

2} The molarity of the diluted solution or its volume can also be calculated using the formula

M1V1 = M2 V2

where,
M1 = Molarity of the first solution
V1 = Its volume in liters.
M2 = Molarity of the second solution
V2 = Its volume in liters

3} If two solutions of the same solute are mixed then molarity (M) of resulting solution is calculated as follows. 



The SI unit of molarity is 'moles per cubic meter' denoted as mol/m3. The most commonly used unit is mol/L and the most proportionate unit is mol/dm3 that is moles per cubic decimeter.

Calculation of Molarity

Before you proceed, keep the periodic table handy for reference. It will give you the atomic masses of the required elements to calculate the molar mass of the solute. 

Here, are a few numerical illustrations that will help you understand the calculation of the molarity of a solution.

Problem 1: Calculate the molarity of a solution prepared by dissolving 25 g of common salt in 500 ml of water. (Given: Molar mass of NaCl is 58.44g/mol).

Solution: First, we calculate the number of moles of solute present:

Moles of NaCl = Total mass of NaCl/Molar mass = 25/58.44 = 0.43moles.

Volume in liters = 500 ml/1000 ml = 0.5 L.

From the above formula, we have,

Molarity = Number of moles of NaCl / Volume of water in liters.

= 0.43/0.5 

Molarity M = 0.86 mol/L

Problem 2: How much 0.50 M sugar solution will you need to make 250 ml of 0.2 M sugar solution?

Solution: According to the formula,
M1V1 = M2 V2 



= 250 × 0.2 
0.50

Sugar solution V1 = 100 ml

Similarly, you can try to find the molarity in the following examples, and cross-check them with the answers given:

✦ Calculate the molarity of a solution containing 1.724 moles of H2 as the solute in 2.50 L of solvent? (Answer: 0.69 mol/L)

✦ Find out the molarity of a solution made by dissolving 25.0 g of HCl in water to make 150.0 ml of solution? (Answer: 4.57 mol/L)

One of the basic characteristics of a solution is molarity. In any chemical experiment involving solutions, all the efforts will go in vain if the initial concentration of the solution is miscalculated. Hence calculation of molarity using the appropriate formula and steps is very important to obtain exact results.