# Number of Moles Formula

Mole is the most basic method for describing the amounts of reactants and products consumed and generated during any chemical reaction. It is the foundation of stoichiometry and is defined as the mass of a material made up of the same number of fundamental units. Depending on the material, the fundamental units might be molecules, atoms, or formula units. One mole of any substance equals Avogadro’s number, that is, 6.023 x 10^{23}. It is also used to express in concentration units such as mole per litre or molecular weight.

**Number of Moles Formula**

The number of moles of a substance equals the ratio of its given mass in a chemical reaction to the mass of one mole of that substance. It can be interpreted as the number of moles possible for that given mass of the substance. It is denoted by the symbol n and its unit of measurement is mol. The mass of one mole of a substance is equal to its molecular mass which is evaluated by finding the number of atoms of each element present in the compound and then multiplying the atomic weight of each element with it.

n = m/Mwhere,

n is the number of moles,

m is the mass of substance,

M is the mass of one mole of that substance.

For example,

Consider the reaction of carbonic acid with potassium hydroxide to give potassium carbonate and water.

H

_{2}CO_{3}+ 2KOH → K_{2}CO_{3}+ 2H_{2}OIt means 1 mole of H

_{2}CO_{3}and 2 moles of KOH give 1 mole of K_{2}CO_{3}and 2 moles of H_{2}O.Suppose for this reaction, we have 200 g of the reactant KOH and 100 g of the product K

_{2}CO_{3}.We know, the molecular mass of KOH is 56g. So, the number of moles is given by,

n = Given mass/Molar mass

= 200/56

= 3.57 mol

We know, the molecular mass of KOH is 62g. So, the number of moles is given by,

n = 100/62

= 1.61 mol

**Sample Problems**

**Problem 1. Calculate the number of moles for 0.563g of Na _{2}SO_{4}.**

**Solution:**

We have the compound Na

_{2}SO_{4 }and m = 0.563 g.Calculate the molecular weight of the compound.

2 atoms of sodium = 2 × 23 = 46g

1 atom of sulphur = 1 × 32 = 32g

4 atoms of oxygen = 4 × 16 = 64g

Mass of one mole (M) = Molecular weight

= 46 + 32 + 64

= 142g

Using the formula we get,

Number of moles (n) = m/M

= 0.563/142

= 0.004 mol

**Problem 2. Calculate the number of moles for 20g of CuSO _{4}.**

**Solution:**

We have the compound CuSO

_{4}and m = 20g.Calculate the molecular weight of the compound.

1 atom of copper = 1 × 63.5 = 63.5g

1 atom of sulphur = 1 × 32 = 32g

4 atoms of oxygen = 4 × 16 = 64g

Mass of one mole (M) = Molecular weight

= 63.5 + 32 + 64

= 159.5g

Using the formula we get,

Number of moles (n) = m/M

= 20/159.5

= 0.123 mol

**Problem 3. Calculate the number of moles for 50g of KOH.**

**Solution:**

We have the compound KOH and m = 50g.

Calculate the molecular weight of the compound.

1 atom of potassium = 1 × 39 = 39g

1 atom of oxygen = 1 × 16 = 16g

1 atom of hydrogen = 1 × 1 = 1g

Mass of one mole (M) = Molecular weight

= 39 + 16 + 1

= 56g

Using the formula we get,

Number of moles (n) = m/M

= 50/56

= 0.892 mol

**Problem 4. Calculate the number of moles for 70g of AlCl _{3}.**

**Solution:**

We have the compound AlCl

_{3}and m = 70g.Calculate the molecular weight of the compound.

1 atom of aluminium = 1 × 27 = 27g

3 atoms of chlorine = 3 × 35.5 = 106.5g

Mass of one mole (M) = Molecular weight

= 27 + 106.5

= 133.5 g

Using the formula we get,

Number of moles (n) = m/M

= 70/133.5

= 0.52 mol

**Problem 5. Calculate the number of moles for 200g of H _{2}SO_{4}.**

**Solution:**

We have the compound H

_{2}SO_{4}and m = 200g.Calculate the molecular weight of the compound.

2 atoms of hydrogen = 2 × 1 = 2g

1 atom of sulphur = 1 × 32 = 32g

4 atoms of oxygen = 4 × 16 = 64g

Mass of one mole (M) = Molecular weight

= 2 + 32 + 64

= 98 g

Using the formula we get,

Number of moles (n) = m/M

= 200/98

= 2.04 mol

**Problem 6. Calculate the number of moles for 400g of CaCO _{3}.**

**Solution:**

We have the compound CaCO

_{3}and m = 400g.Calculate the molecular weight of the compound.

1 atom of calcium = 1 × 40 = 40g

1 atom of carbon = 1 × 12 = 12g

3 atoms of oxygen = 3 × 16 = 48g

Mass of one mole (M) = Molecular weight

= 40 + 12 + 48

= 100 g

Using the formula we get,

Number of moles (n) = m/M

= 400/100

= 4 mol

**Problem 7. Calculate the number of moles for 360g of MgSO _{4}.**

**Solution:**

We have the compound MgSO

_{4}and m = 360g.Calculate the molecular weight of the compound.

1 atom of magnesium = 1 × 24 = 24g

1 atom of sulphur = 1 × 32 = 32g

4 atoms of oxygen = 4 × 16 = 64g

Mass of one mole (M) = Molecular weight

= 24 + 32 + 64

= 120 g

Using the formula we get,

Number of moles (n) = m/M

= 360/120

= 3 mol