# Mole Concept

Mole concept is the method used to express the amount of substance. This has been experimentally proving that one gram atom of any element, as well as one gram molecule of any substance, contains the same amount of entities. The experimentally decided number is found to be 6.022137 × 10^{23}. After the discovery of the mole concept, the problem of finding absolute atomic masses of atoms was solved. It was so because the mole concept helps to count the number of atoms or molecules in a definite amount of the given substance. Let’s learn more about mole concept formulas and examples.

## What is a Mole Concept?

Mole concept is known as the method used to express the amount of substance. A mole is defined as the amount of substance containing the same number of different entities (such as atoms, ions, and molecules) as the number of atoms in a sample of pure 12C weighing precisely 12 g. Even a gram of any pure element contains a high amount of atoms. The mole connects a simple macroscopic feature (bulk mass) to a genuinely significant fundamental trait (number of atoms, molecules, etc.). One mole is also defined as the amount of a substance that contains as many entities as there are atoms in exactly 12 g of the ^{12}C isotope. It was found that the mass of one atom of carbon-12 element is equal to 1.992648 × 10^{-23} g as measured by the mass spectrometer. Since one mole of Carbon-12 atom weighs 12 g, therefore, the number of atoms in it equals 12 g mol^{-1} / 1.992648 × 10^{23} g atom^{-1} = 6.0221367 × 10^{23 }atoms mol^{-1}. The following formula may be used to calculate the number of moles of a chemical in a given pure sample:

n = N/N_{A}

Where n represents the number of moles of the chemical, N denotes the average number of fundamental units in the sample, and N_{A} represents the Avogadro constant.

### Avogadro’s Number (N_{A})

Avogadro’s number is 6.0221367 × 10^{23}. It is named Avogadro’s constant or number in honor of Amedeo Avogadro, a great pioneer in this field**.** It is denoted by **N _{A}**. We can also say that 1 mole is the collection of 6.0221367 × 10

^{23}units of a substance. Here, the substance is atoms, molecules, or ions. The number of units that make up a mole has been established empirically to be 6.0221367 × 10

^{23}. This is known as the fundamental constant, also known as Avogadro’s number (N

_{A}) or the Avogadro constant. This constant is appropriately stated in chemistry using an explicit unit termed per mole. No matter what the given substance may be, one mole of it is always equal to N

_{A}.

## Mole Concept Formulas

Mole concept is a method where we identify the mass of chemical substances as per requirement. The entire mole concept revolves around 12 g (0.012 kg) of the ^{12}C isotope. In the SI system, the unit of the fundamental quantity ‘the amount of substance’ is the mole. The symbol of the mole is “mol”. Below are the quantities related to the mole concept:

### Atomic Mass and Molecular Mass

Atomic mass of an element is the mass of its one atom. The unit of atomic mass is a.m.u. The atomic mass is roughly the sum of protons and neutrons present in the atom. One atomic mass unit (a.m.u.) is said to be exactly equal to one-twelfth the mass of one carbon-12 atom. Therefore, the value of one a.m.u. is 1 g / N_{A} = 1.66056 × 10^{-24} g. In the present era, the atomic mass unit is known as a unified mass unit. Hence, a.m.u. has been replaced by u.

For example, the atomic mass of carbon is 12.011 amu since carbon mostly contains carbon-12 isotope. Carbon-13 is 1.1%, and very few traces of carbon-13. The atomic mass of these isotopes is different.

Molecular Mass is the sum of the masses of the atoms present in a given molecule. The unit of molecular mass is a.m.u. However, if the molecular mass of a mole of a substance is asked, then the unit used is grams despite the fact that the SI unit is kilograms. The molecular mass of a molecule is defined as the relative mass of its molecule when compared to the mass of a ^{12}C atom divided into 12 units. In layman’s words, it denotes the number of times a molecule of the relevant material is heavier than an atom.

For example, the molecular mass of water (H

_{2}O) is 18.015 amu, the atomic mass of a hydrogen atom is 1.007 amu and the atomic mass of oxygen is 15.99 amu.

### What is Molar Mass?

Molar mass is defined as the total mass of one mole of the substance. It is frequently expressed in terms of ‘grams per mole’ (g/mol). The SI unit for this amount, however, is kg/mol. The following formula may be used to calculate molar mass:

Molar mass of a Substance = (Mass of the substance in grams)/(Number of Moles)

The molar mass of water, for example, is roughly 18.015 g/mol, which is the mass of N_{A} number of water molecules.

### Gram Atomic Mass and Gram Molecular Mass

Gram atomic mass is the mass of one mole of an atom. Gram molecular mass is the mass of one mole of a molecular substance expressed in grams. It is also known as molar mass. It is also defined as the mass of one mole of molecules. This is the difference between gram atomic and gram molecular mass. This amount of a substance is also called one gram molecule.

### How to Find Gram Molecular Mass?

A substance’s gram molecular mass is its molecular mass measured in grams. e.g., the molecular mass of O_{2} is 32 grams; this is the relative molecular mass given in grams. Remember that relative atomic mass is always expressed as a ratio and has no units.

### Gram Molecular Volume

The volume occupied by one gram mole of a substance in a vapor state or gaseous state at STP is called as gram molecular volume. The standard temperature to obtain GMV is 273K, and the standard pressure is 1 atm. The ideal gas equation is utilized to get gram molar volume (GMV = 22.4L).

### Relative Molecular Mass (RMM)

Relative molecular mass is the molecular weight of an element or molecule; it is expressed as RMM. It is the number of times a single molecule of a substance remains heavier than one-twelfth the mass of a carbon atom (^{12}C).

### Related Formulas

Following are the formulas for the number of moles, number of atoms and molecules, and the relationship between 1 amu and grams.

- Number of Moles = Mass of the Sample/Molar mass
- Number of atoms or molecules = Number of moles × (6.023 × 10
^{23})- 1 amu = 1 gram/(6.023 × 10
^{23}) = 1.66 × 10^{-24}grams

### Number of Electrons in a Mole of Hydrogen Molecule

One mole of H_{2 }contains 6.023 × 10^{23} molecules, and each molecule of hydrogen contains two electrons.

1 mole = 6.023 × 10^{23}

Hence, the total number of electrons in 1 mole of H_{2} is 12.046 × 10^{23}.

## Solved Examples on Mole Concept

**Example 1: Calculate the molecular mass of Ammonium Sulphate (NH _{4})_{2}SO_{4}. **

**Solution:**

Since, the relative atomic masses of N = 14, H = 1, S = 32, O =16

Therefore, the molecular mass of the given compound is,

= 2 (14 × 1 + 1 × 4) + 32 + 16 × 4

= 2(14 + 4) + 32 + 64

= 2 × 18 + 32 + 64

= 36 + 32 + 64

= 132 amu

**Example 2: The molecular mass of H _{2}SO_{4} is 98 a.m.u. What does it mean?**

**Solution:**

It means that one molecule of H

_{2}SO_{4}is 98 times as heavy as 1/12 the mass of a C-12 atom.

**Example 3: Calculate the number of atoms present in 18g of H _{2}O.**

**Solution:**

The 18 g of H

_{2}O ⇒ 1 mole of H_{2}O ⇒ N_{A}^{ }moleculesNow, 1 molecule of H

_{2}O contain 3 atoms⇒ 1 mole H

_{2}O will contain 3*N_{A}atoms = 3 × 6.022 × 10^{23}atoms = 1.8066 × 10^{24}atoms

**Example 4: How many moles are present in 200g of NaOH?**

**Solution:**

The mass of 1 mole of NaOH = 23 + 16 + 1= 40 g

Therefore, in 200g of NaOH the number of moles present = 200g / 40g mol

^{-1}= 5 mol

**Example 5: Calculate the mass of an atom of oxygen element.**

**Solution:**

Mass of 1 mole of oxygen = 16g

No. of atoms in 1 mole of oxygen = N

_{A}Therefore, mass of one atom of oxygen = 16g / N

_{A}= 16 / (6.022 × 10^{23}) = 2.657 × 10^{-23}g

**Example 6: Find the ratio of moles of oxygen atoms present in the compounds H _{2}SO_{4}, H_{2}SO_{3}, and SO_{2.}**

**Solution:**

1 mole of H

_{2}SO_{4}contains 4 × N_{A}atoms of oxygen1 mole of H

_{2}SO_{3}contains 3 × N_{A}atoms of oxygen1 mole SO

_{2}contains 2 × N_{A}atoms of oxygenTherefore the required ratio is 4 × N

_{A}: 3 × N_{A}: 2 × N_{A }= 4 : 3 : 2

**Example 7: How many moles of hydrogen and oxygen gas are required to produce 13 moles of water?**

**Solution:**

Chemical equation of water formation:

H

_{2}+ O_{2}⇢ H_{2}ONow the balanced equation is

2H

_{2}+ O_{2}⇢ 2H_{2}OThus we can deduce that 2 moles of hydrogen gas and 1 mole of oxygen gas combine together to form 2 moles of water. We can write the equation as :

H

_{2}(1 mole) + O_{2}(1/2 mole)⇢ H_{2}O (1 mole)Hence, for production of 13 moles of water the required chemical equation would be:

H

_{2}(13 moles) + O_{2}(13/2 moles) ⇢ H_{2}O (13 moles)Hence, for production of 13 moles of water we need 13 moles of hydrogen and 6.5 moles of oxygen gas.

**Example 8: Calculate moles of electrons present in 104 g of acetylene gas.**

**Solution:**

Now, formula for acetylene gas is C

_{2}H_{2}. It’s structure is H—C≡C—H. Therefore, number of electrons present in 1 molecule of acetylene are 14.Now, mass of 1 mole of acetylene is 26g ⇒ 104g of acetylene are 4 moles.

Now, 1 mole of acetylene = N

_{A}molecules⇒ N

_{A}molecules have 14 × N_{A}electrons⇒ 4 moles of acetylene have 4 × 14 × N

_{A}electrons = 56 × N_{A}electrons = 56 moles of electrons.

## FAQs on Mole Concept

**Question 1: What is the Mole concept?**

**Answer:**

Mole concept is a method where we identify the mass of chemical substances as per requirement. The entire mole concept revolves around 12 g (0.012 kg) of the

^{12}C isotope. In the SI system, the unit of the fundamental quantity ‘amount of substance’ is the mole.

**Question 2: What is one mole equal to?**

**Answer:**

One mole is the collection of 6.0221367 × 10

^{23}units of a substance. Here, the substance is atoms, molecules, or ions.

**Question 3: How do we use mole fraction?**

**Answer:**

Mole fraction is defined as the number of single component molecules divided by the total number of molecules. When two reactive elements are combined together, the ratio of the two elements is understood by the mole fraction.

**Question 4: What is the importance of the mole concept?**

**Answer:**

Mole concept provides a standard for measuring certain masses that are universally accepted. It provides a link between several masses and is an efficient way to measure macroscopic properties. For the study of chemistry, understanding mole concept is essential, and knowledge of how mole is applied to masses, number of substances, etc., is important.

**Question 5: Is mole fraction equal to partial fraction?**

**Answer:**

It can be said that the partial fraction of each gas is proportional to the mole fraction in a mixture.

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