# Mole Concept – What is a Mole, Molar Mass, Solved Examples

Chemistry is the study of how atoms and molecules interact with one another at the atomic level. Chemists require a simple method for determining the number of molecules in a beaker. The mole idea, which we shall explain here, bridges this gap by connecting the mass of a single atom or molecule in a.m.u. to the mass of a huge collection of similar molecules in grams. Atomic mass refers to a single atom, whereas molecular mass refers to a collection of atoms. If you choose to pursue this topic, you must first obtain a thorough understanding of molecular mass and the mole concept. Let us get started!

**Atomic Mass:**Atomic mass of an element is the mass of its one atom. The unit of atomic mass is**a.m.u.**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**In the present era, the atomic mass unit is known as a unified mass unit. Hence,_{A}= 1.66056 × 10^{-24}g.**a.m.u.**has been replaced by**u.****Molecular Mass:**It is the sum of masses of the atoms present in the given molecule.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.**Relative Molecular Mass (RMM):**The molecular weight of an element or molecule 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).**Gram Molecular Mass:**It 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 amount of a substance is also called one gram molecule. 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.

**Mole Concept**

It is critical to remember that a substance’s identity includes not only the kind of atoms but also the amount of each atom type. We now have access to powerful tools that allow us to directly measure tiny characteristics. However, the same characteristics were previously determined through the examination of macroscopic features with very basic methods. Such an experimental method did need the development of a new unit for quantifying the number of chemicals, known as the mole. It’s worth noting that this unit is still necessary for current chemical science. What exactly is a mole? It is a numerical unit that is similar to conventional units such as a pair, gross, dozen, and so on.

The 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. The symbol of the mole is “mol”.

After the discovery of the mole concept the problem of not being able to find absolute atomic masses of atoms was solved. It was so because the mole concept provided the luxury of being able to count the number of atoms or molecules in a definite amount of the given 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}.

**What is a Mole?**

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. 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 out 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}): **The number 6.0221367 × 10

^{23}is known as the Avogadro constant or number in honor of Amedeo Avagadro, a great pioneer in this field

**.**It is denoted by

**N**. We can also say that 1 mole is the collection of 6.0221367 × 10

_{A}^{23}entities. Here, the entities are 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 maybe, one mole of it is always equal to N

_{A}.

**Mole of Atoms:**A mole of an element’s atoms has the same mass as the element’s gram atomic mass. e.g.:- 1 mole of Hydrogen (H) atom equals 1 gram.
- Since an element’s symbol symbolizes one mole of that element’s atoms.
- Therefore, 1 mole of Hydrogen atoms is represented by H.
- 2H denotes two moles of Hydrogen atoms.

**Mole of Molecules:**One mole of a substance’s molecules has the same mass as the substance’s grams molecular mass. e.g.:- The gram molecular mass of oxygen is 32 grams.
- 1 mole of oxygen is represented by O
_{2}. - Then, 2O
_{2}denotes the two moles of the Oxygen molecule.

### Molar Mass

A molecule’s 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 NA number of water molecules.

### Sample Problems

**Problem 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

**Problem 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.

**Problem 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

**Problem 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

**Problem 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

**Problem 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

**Problem 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}+ O_{2}⇢ H_{2}O1 mole 1/2 mole 1 mole

Hence, for production of 13 moles of water the required chemical equation would be:

H

_{2}+ O_{2}⇢ H_{2}O13 moles 13/2 moles 13 moles

Hence, for production of 13 moles of water we need 13 moles of hydrogen and 6.5 moles of oxygen gas.

**Problem 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.

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