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# Mole Chemistry

Atoms and molecules are very, very tiny. We cannot count the individual particles of a molecule. Hence, there are measures such as atomic mass, atomic weight, molecular count to estimate the number of atoms or molecules. John Dalton and Thomson first determined atomic weights between 1803 and 1805. Atomic weight was originally defined relative to that of the lightest element hydrogen taken as 1.00. Dalton took 1/16th of the mass of an atom of oxygen as the unit of atomic mass.

Nowadays, the carbon-12 isotope is considered as the standard atomic mass unit as a reference for measuring atomic masses. One atomic mass unit can be defined as the mass unit that is equal to 1/12th of the mass of 1 atom of C-12. The unit of atomic mass or amu can be defined as the mass of 1 H-atom. Because the relative weights of hydrogen, carbon and nitrogen are 1.01, 12.01 and 14.01, we can also say that the weight of hydrogen is 1.01 amu per atom, the weight of carbon is 12.01 amu per atom and the weight of nitrogen is 14.01 amu per atom. Another way to represent atomic and molecular mass is "Mole concept".  Let’s discuss about mole concept and its application.

 Related Calculators conversion of grams to moles calculator convert moles to grams calculator Mole Fraction Calculator

## What is a Mole in Chemistry?

One mole of a chemical species contains the same number of particles as there are atoms in 12 grams of the isotope of Carbon – 12.
Thus,
1 mole of a substance = 1 gram molecular mass = GMW
= 1 gram molecule = 6.02 x 1023 molecules
= Atomicity x 6.023 x 1023 atoms
= Atomicity x 1 gm atom
= 22.4 liters of gaseous substance at S.T.P. (GMW)

Use the below widget to calculate the mole fraction.

## Mole Definition

The mole, in chemistry, is a measure of the amount of substance. It is defined according to the number of particles that the substance contains. In particular, we use the following definition.
A mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state. The number of atoms in 0.012 kilogram of carbon is known as Avogadro number, and is determined empirically. The currently accepted value is 6.0221415 x 1023 mol-1.
Explanation

Mole of oxygen = 16 + 16 = 32 grams of Oxygen.
= Weight of 6.02 x 1023 molecules of Oxygen
= Weight of 2 x 6.02 x 1023 atoms of Oxygen
= 2 x 1 gram atom of Oxygen
= Weight of 22.4 liters of Oxygen at S.T.P

6.023 x 1023 is called the Avogadro numberThe number of particles in a mole is called Avogadro's constant or Avogadro's number. This number may be used to measure any kind of particle, such as atoms, ions or molecules. The number of atoms in 12 grams of Carbon – 12 is approximately equal to 6.023 x 1023.

This is the number of particles per mole of Carbon -12 and it gives us our definition of Avogadro's number or Avogadro's constant.

So, 12.0 grams of Carbon contains 6.023 x 1023 atoms, therefore, 16.0 grams of oxygen will also contain 6.023 x 1023 atoms of oxygen. Similarly, one gram – atom of any other element will also contain 6.023 x 1023 atoms of that element and one molecule of any substance will contain 6.023 x 1023 molecules of that compound.

Molar mass and moles

Molar mass of an element is numerically equal to the element's atomic mass and has units grams per mole. Thus molar masses are conversion factors for moles and mass of a compound or an element.
Mass of one mole of particles is called Molar mass. In the case of atoms molar mass is equal to the atomic mass and in the case of molecules, molar mass is equal to the gram molar mass. So, Mass of 6.023 x 1023 molecules of any substance (element or compound) is equal to its gram molecular mass or one gram molecule.

Mole concept can be applied even to an ionic compound. One mole of an ionic compound represents one mole (6.023 x 1023) formula units of that compound.
1 mole of atoms or ions = 6.023 x 1023 atoms or ions.
1 mole of electrons = 6.023 x 1023 electrons

Moles and chemical equations:

A chemical equation is an extremely useful way of summarizing a lot of information. The equation should show the amount of each substance involved in the reaction and its state. Here is an example:

2H2(g) + O2(g) → H2O(l)

2 moles of hydrogen molecules react with 1 mole of oxygen molecules to form 2 moles of water, all in gaseous state.

## Mole Concept and Stoichiometry

Some Points about Mole Concept and Stoichiometry:
• Calculation of the mass of an atom of an element
= Gram atomic mass / Avogadro number
• Calculation of the mass of one molecule of a substance:
= Gram molecular mass / Avogadro number
• Calculation of the number of atoms in a given mass of an element:
= Mass of element in grams / gram atomic mass x N0
• Number of molecules in a given mass of the substance
= Mass of substance in grams / gram molecular mass x N0
• Calculation of the number of molecules present in V liters of gas at S.T.P
= Volume of the gas in liters / 22.4 liters x N0

## Mole Calculations

The formula used for all the mole calculations is :
Number of moles of a substance = Mass of the substance in grams / Molar mass of the substanceExample:

Moles of a compound

The formula for water says that 1 mole of water contains 2 moles of hydrogen and 1 mole of oxygen atoms. Similarly, the formula for ammonia which is NH3, tells us the molar composition of the gas:
1 mole of nitrogen atoms combines with 3 moles of hydrogen atoms to form ammonia.

Once we have established the number of moles of each element present in a covalent substance like water or ammonia, we can work out its molar mass.

M(H2O) = 2 x M(H) + 1 x M(O)
= 2 x 1 g/mol + 1 x 16 grams/mol
= 18 grams / mole
(Oxygen has an atomic mass of 16 and Hydrogen has an atomic mass of 1)

Therefore, say for example, we need to find the mass of 1 mole of water.
Mass of 1 mole of water = 18 grams/mol x 1 mol = 18 grams

## Chemistry Mole Problems

### Solved Examples

Question 1: A bottle contains 6 grams of Magnesium ribbon. How many moles of Mg are present?
Solution:

Number of moles of magnesium

= $\frac{Mass\ in\ grams\ of\ Magnesium} {Atomic\ mass\ of\ Mg}$

= $\frac{6 g}{24 g/ mol}$

= 0.25 mole of Mg.

Question 2: Calculate the number of moles in 25 g of Calcium Carbonate.
Solution:

Molecular mass of CaCO3 = 100
Number of moles of Calcium Carbonate
=$\frac{ Mass\ of\ Calcium\ carbonate\ in\ grams}{Molar\ mass\ of\ calcium\ carbonate}$

= $\frac{25 g}{100 g. mol^{-1}}$ = 0.25 mole of calcium carbonate.

Question 3: Calculate the number of moles in 11 grams of CO2 3.01 x 1023 molecules of CO2
Solution:

1. Molecular mass of CO2 = 44 grams/mole.

Moles of CO2
=$\frac{ Mass\ of\ Carbon\ dioxide }{ molar\ mass\ of\ carbon\ dioxide}$

= $\frac{11 grams}{44 grams .mol^{-1}}$

= 0.25 moles of carbon dioxide.

2. 6.02 x 1023 molecules of Carbon dioxide = 1 mole of CO2

3.01 x 1022 molecules of CO2

=$\frac{ 1 }{ 6.02 \times 1023 \times 3.01\times 1022 }$moles

= 0.05 moles of Carbon dioxide.

Question 4: Calculate the mass of half a mole of Nitrogen.
Solution:
1 mole of Nitrogen = 2 x 1gram atom of N2 = 2 x 14 = 28 grams.
(ATOMIC MASS OF N IS 14)
Therefore, half a mole of Nitrogen = 28 x ½ = 14 grams.

Question 5: How many atoms of oxygen are present in 300 grams of CaCO3?
Solution:

Gram molecular mass of CaCO3 = 100 g
Now, one mole of CaCO3 contains = 3 moles of Oxygen atoms.
Or, 100 grams of CaCO3 contains = 3 x 6.02 x 1023 oxygen atoms.

Therefore,
Oxygen atom in 300 grams of CaCO3

= $\frac{3 \times 6.02 \times 10^{23}}{100\times 300 }$= 54.207 x 1023 oxygen atoms.

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