# How to Calculate Molarity? Formulae with Examples

A solution is a homogeneous mixture of two or more substances whose concentration can be varied within in certain limit. For example, x amount of sugar can be dissolved maximum in one liter of water. If we want to mix further sugar in the same quantity of water, we have to raise the temperature of water. After adding some more, a time will come when no more sugar will be dissolved in that water because the water becomes saturated.

A solution with two components is known as binary solution. In a binary solution, the component present in lower proportion is called ‘solute’ (the substance that is dissolved) while the other one present in higher percentage is called ‘solvent’ (which does the dissolving). “Mole” is an important concept to understand the calculations on the concentration of solution. The Latin term ‘mole’ was first used by scientist Oswald in 1896. In Latin ‘mole’ means heap or pile. A ‘mole’ is defined as the number of atoms in 12 gram of carbon-12 isotopes (One of two or more atoms having the same atomic number but different mass numbers). The number of atoms in 12 gram of carbon-12 has been experimentally found to be 6.022 x 1023. This number is also known as Avogadro’s number, named in the honor of Amedeo Avogadro. Thus, a mole contains 6.022 x 1023 units which can be anything like molecules, atoms, electrons, ions, etc. For example, 1 mole of Hydrogen molecules means hydrogen 6.022 x 1023 molecules or similarly 1 mole of Hydrogen atom or 1 mole of potassium ions means 6.022 x 1023 of Hydrogen atoms or 6.022 x 1023 of potassium ions respectively. The weight of one mole depends on the nature of particles (units).The mass of one mole atoms of any element is exactly equal to the atomic mass in grams (gram atom or gram atomic mass).

“Molarity” measures the strength or concentration or amount-of-substance concentration by the number of moles of solute per liter of solution. In simple term, it is a measurement of the concentration of a solution. It has been defined as the number of moles of the solute present in 1 liter or 1000 milliliter of the solution. To calculate molarity we use the equation:

Molarity = Moles of Solute / Volumes of solution in liters

Or, Molarity = Mass of Solute (in gram) / (Molar Mass of solute X Volume of Solution in liter)

Therefore, the units of molarity are moles per liter (mol L-1 or mole/ L) or moles per cubic decimeter (mol dm3). Thus, to calculate molarity, we have to follow the following steps:

1. Find the number of moles of solute present in solution.
2. Find the volume or number of liters of solution present.
3. Divide the number of moles of solute by number of liters of solution

## Example Problem on Concentration and Molarity

We will work out a problem where 20 gm of Sodium hydroxide (NaOH) has been dissolved in sufficient water to yield a 482 cm3 solution. To work out this problem, we have to find out the number of moles of Sodium hydroxide or NaOH and convert the cubic centimeters into liters.

Step 1:

First, to determine the number of moles in 20 gm of NaOH, we have to find out the respective atomic masses of the constituents of NaOH. The constituents of NaOH are: Na (Sodium), O (Oxygen) and H (Hydrogen). From the Periodic Table, we can find the atomic masses of these constituents, they are—

Na =23, O=16 and H= 1

Putting these value— Na + O + H = 23 + 16 + 1 = 40                                                                                                         Therefore, 1 mol NaOH weighs 23.0 g + 16.0 g + 1.0 g = 40.0 g                                                                                                          So, the number of moles in 20.0 g is: moles NaOH = 20.0 g × 1 mol/40.0 g = 0.500 mol [By Unitary Method]

Step 2:

Find out the volume of solution in liters.                                                                                                                                        1 Liter = 1000 cm3                                                                                                                                      Therefore, the solution of 482 cm3 becomes, 482 cm3 × 1 liter/1000 cm3 = 0.482 liter

Step 3

Finding out the molarity of the solution, simply divide the number of moles by the volume of solution to get the molarity:                   Molarity = 0.500 mol / 0.482 liter
Or, Molarity = 1.04 mol/liter = 1.04 M

Result: The molarity of the solution made by dissolving 20.0 g of NaOH to make a 482 cm3 solution is 1.04 M