# Number of Moles Formula

Mole is defined as the measure of the amount of substance. 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. 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. One mole of any substance equals Avogadro’s number, that is, 6.023 × 10^{23}. It is also used to express concentration units such as mole per litre or molecular weight. Let’s learn about the mole concept before learning how to calculate the number of moles formula.

The mole concept is very useful for measuring the products in any chemical reaction. Using the mole concept is essential because the traditional pattern of explaining a unit does not work at the molecular level. For example, measuring a molecule also means measuring the high amount of atoms present in the molecule. This is where the mole concept comes into play. Since the value of 1 mole is 6.023 × 10^{23 }atoms, we can say that a mol is a large unit. One mole is equal to Avogadro’s number. Let’s now learn how to find the number of moles.

**Number of Moles Formula**

The number of moles formula is written as:

The number of moles of a substance equals the ratio of its given mass in any type of 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. Symbolically, the number of moles formula is,

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.

## Uses of Mole Concept

Mole concept is the foundation of stoichiometry. While expressing the reactants and products in a chemical reaction, the mole concept is used to express the amount of the reactants and products. Therefore, all the chemical reactions can be represented in terms of moles. 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 byn = 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

## Solved Examples on Number of Moles Formula

**Example 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) = Mass of substance (m)/ Mass of one mole (M)

= 0.563/142

= 0.004 mol

**Example 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) = Mass of substance (m)/ Mass of one mole (M)

= 20/159.5

= 0.123 mol

**Example 3: Calculate the number of moles for 50g of potassium hydroxide.**

**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) = Mass of substance (m)/ Mass of one mole (M)

= 50/56

= 0.892 mol

**Example 4: 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

**Example 5: How many moles are present in 1.5 × 10 ^{23} molecules of H_{2}SO_{4}?**

**Solution:**

We know that,

1 mole of a substance = 6.023 × 10

^{23 }atomsTo find out the number of moles present in 1.5 × 10

^{23}molecules of H_{2}SO_{4}, the number of molecules should be divided by Avogadro’s number. Therefore,Number of moles = 1.5 × 10

^{23}/6.023 × 10^{23}moles= 0.25 moles

## FAQs on Number of Moles Formula

**Question 1: How do you calculate the number of moles formula?**

**Answer:**

In order to find the number of moles in a substance. The first step is to weigh the substance and then divide the measured weight by its molecular weight. This gives the values in the number of moles. To calculate the number of moles formula, the formula used is:

Number of moles formula = Mass of substance/Mass of one mole

**Question 2: What is Avogadro’s number?**

**Answer:**

The number of units in 1 mole of any substance is called Avogadro’s number. The value of Avogadro’s number is 6.023 × 10

^{23}.

**Question 3: How do you find moles from molarity?**

**Answer:**

To calculate the number of moles present in a solution, take the molarity of the solution and multiply it with the volume of the solution (in liters). This gives the number of moles present in the solution.

**Question 4: What is the formula for number of moles in a solution?**

**Answer:**

In order to find the number of moles in a solution, the molarity of the solution must be known. The formula for number of moles in a solution is:

Number of moles (Mol) = Molarity (M) × Volume (V)

**Question 5: How do you calculate number of moles formula using Avogadro?**

**Answer:**

In order to convert molecules into moles and vice-versa, Avogadro’s number is used. To convert moles into molecules, multiply the number of moles gives to 6.023 × 10

^{23}and to convert molecules into moles, divide the molecules given by 6.023 × 10^{23}.

**Question 6: What is the Formula for number of moles in a substance?**

**Answer:**

The formula for number of moles in a substance is given as:

Number of moles formula = Mass of substance/Mass of one mole

**Question 7: What is the formula for number of moles of compound?**

**Answer:**

In order to find the number of moles of a compound, simply find the weight of the compound and then divide it by the molecular weight of the compound. This shall give you the number of moles of compound.

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