Number of Moles Formula

The mole is a measure or the base unit for the amount of substance present in the given sample. 1 mole is a number that is equal to 6.022 x 10²³ particles, also known as the Avogadro’s constant. These particles can be any type of species, e.g atoms, molecules, electrons, protons, neutrons, etc. In fact, if we have a which contains approximately 6.022 x 10²³ almonds, it can be said that we have 1 mole of almonds in that particular box.

This number, 6.022 x 10²³ (Avogadro’s constant) is actually defined based on the number of atoms present in 12g of ¹²C isotope of Carbon. Where 12gm is the molar mass of ¹²C or in other words the mass of 1 mole or 6.022 x 10²³atoms of 12C isotope of Carbon. 

What is the Mole Concept: Understanding the Number of Moles 

The mole concept is a simpler method for expressing the amount of a substance in chemical substances. For this, we have two steps, the first is the numerical magnitude and the other is the units in which the magnitude is expressed.

Now, let us say that the mass of a bucket is 5 kilograms, here 5” is the magnitude and the unit is ‘kilogram’. However, while dealing with the particles at an atomic or molecular level, we do not find this traditional method suitable. Like even one gram of a pure element comprises a huge number of atoms, which is the reason we are using the mole concept.

Here, the mole concept mainly focuses on the unit ‘mole’. This concept pertains to the count of a very large number of particles. Here, one mole of any substance equals the Avogadro number. The Avogadro number has a value of 6.023×10²³. This value is very  useful for measuring the products in any chemical reaction.  Thus  6.023×10²³ of atoms, molecules or particles are 1 mol of atoms, molecules or particles.

Formula for the Number of Moles Calculation

Now, in order to calculate the number of moles of any substance present in the sample, we simply divide the given weight of the substance by its molar mass.

The number of moles formula is:

\[ n= \frac{\text{mass of substance}}{\text{mass of one mole}} \]

Mathematically,

\[ n = \frac{m}{M}\]

Here,

n = The number of moles,

m = The given mass, and

M = The molar mass

Solved Example on the Number of Moles of a Substance

Example 1: How many moles are in 25.0 grams of water?

Solution: 

In order to find the number of moles, we will have to use the following formula:

n = m/M

Molar Mass, M, of H₂O = 18.0 g/mol

Given mass, m, of H₂O = 25.0 gm

So, n = 25.0 (gm) / 18.0 (gm/mol)

Number of moles, n = 1.39 mol

Example 2: How many moles are in 3.4 x 10²³ molecules of H₂SO₄?

Options:

(a) 0.82 moles

(b) 0.01 moles

(c) 5.56 moles

(d) 0.56 moles

Answer: (d)

Solution:

1 mole of anything = 6.022x 10²³ of anything

In order to find the number of moles here, we will have to divide the given number of particles by Avogadro’s constant.

So, n = 3.4 x 10²³ / 6.022 x 10²³

Then number of moles, n = 0.56 moles