What is a mole? In everyday life, we buy things in terms of numbers such as dozen (for 12), score (for 20) or gross (for 144), or weight such as kilogram or quintal, etc. For example, we buy eggs in dozen, bananas in dozen, and wheat in kilogram but atoms and molecules are too small.
They cannot be seen even under a microscope. So, how can we count or weigh atoms? Wilhelm Ostwald introduced a bigger unit for expressing a definite amount of a chemical substance i.e. mole.
Mole Concept
One mole of a substance is defined as that amount of substance that contains the same number of particles (atoms, ions, or molecules) as there are present in 12 gm of the c-12 atom.
Experimentally it has been found that 0.012kg of carbon-12 contains 6.023 * 1023 atoms. This number is known as Avogadro�s Number. It is represented by N0.
Avogadro�s Number = N0 = 6.023 *1023
So one mole of a substance is the amount of the substance which contains 6.023 *1023 particles
1 mole of C- atoms = 6.023 *1023 C- atoms
1 mole of O- atoms = 6.023 *1023 O- atoms
1 mole of O2 molecules = 6.023 *1023 molecules of Oxygen
1 mole of H2O molecules = 6.023 *1023 molecules of H2O
1 mole of CO2 molecules = 6.023 *1023 molecules of CO2
1 mole of Na+ ions = 6.023 *1023 ions of Na+
As 1 dozen = 12 articles. 1 mole (of anything) = 6.023 * 10 23 particles (atoms, molecules, or ions). The advantage of a mole over a dozen or a gross is that the mass of 1 mole of a particular substance is always fixed.
Now, you must want to know what the mass of one mole of a substance is. The mass of 1 mole of a substance is equal to its relative atomic mass or molecular mass in grams. This is also known as the molar mass of that substance. For an element, the atomic mass of an atom is the mass of one atom, and molar mass is the mass of 1 mole of the element.
In fact, the molar mass of a substance is the mass of 6.023 * 10 23 particles of that substance. If the substance is an element, the molar mass is equal to its gram atomic mass i.e. atomic mass in grams. This means to write the molar mass of an element, we will take the same numerical value as that of the atomic mass but units are changed from �AMU� to grams.
If the substance is a molecule, the molar mass is equal to its gram molecular mass. The mass of one mole of an ionic compound is numerically equal to the molecular mass but units have to be changed from �AMU� to grams.
Calculation of the number of moles in a given mass.
To calculate the number of moles in 100grams of water (H2O)
Formula:- No. of moles (n) = given mass in grams (m) / molar mass in grams (M)
We know that atomic mass of Hydrogen = 1AMU
And atomic mass of Oxygen = 16 AMU
Therefore molecular mass of water (H2O) = 2 * 1 + 1 * 16 = 18 AMU
So, M= molar mass of water = 18grams/mole
Also, m = given mass of H2O = 100 grams
Using the formula:-
n= m/M
We have number of moles = (100/18) moles
= 5.56 moles
To calculate the mass of 0.5 moles of water (H2O).
Formula:- Mass in grams (m) = no. of moles (n) * molar mass (M) i.e. m= n * M
We know that molar mass of water = 18 g/mol
Also No. of moles (n) = 0.5
Using the formula:-
m= n * M
m = (0.5 * 18) grams
This implies m= 9 grams
Note: -N0 means N Zero
Calculation of number of atoms or molecules
To calculate the number of molecules of water in a drop of water weighing 0.05g.
Formula:- Number of moles (n) = given mass in grams/molar mass (M). That means n = m/M and we know that number of molecules (N) = No. of moles (n) * Avogadro No. (N0)
This means N = n * N0
Substituting the values of n we get
N/N0 = m/M
Which implies N = (m/M) * No.
We know that the atomic mass of Hydrogen = 1 AMU
And the atomic mass of Oxygen = 16 AMU
Therefore, the Molecular mass of water = 2 * 1 + 1 * 16 = 18 AMU
So, we have M = Molar mass of water = 18 g /mol
Also we know that N0 = Avogadro number = 6.022 * 1023
And m = given mass of water = .05g
From above, Number of molecules = (given mass of water/Molar mass) * (Avogadro number)
Which implies N = (.05/18) * 6.022 * 1023
Which implies N= 1.6072 * 1021 molecules
To calculate the mass of 1020 molecules of water.
Formula:- Mass = (no. of molecules (N)/Avogadro number (N0) * molar mass (M)
We know that Atomic mass of Hydrogen = 1AMU
And atomic mass of Oxygen = 16 AMU
Therefore we have, Molecular mass of water (H2O) = 2 * 1 + 1 * 16 = 18 AMU
Molar mass of water = 18g/mol
Number of molecules given (N) = 1020 molecules
Avogadro number (No.) = 6.022 * 1023
Therefore we have, m = (N/N0) * M
Which implies m= (1020 / (6.022 * 1023)) *18 grams
= 1.66 * 10-4 grams
Calculation of actual mass of a single atom or molecules
To calculate the mass of a molecule of water.
Formula:- The actual mass of a single atom or molecule = molar mass (M)/Avogadro Number (N0)
The molar mass of water = 18g/mol
N0 = Avogadro number = 6.022 * 1023
Substituting the value in the formula
Actual mass of a single molecules of water = 18 g/Avogardro number = 18/(6.023 * 1023) g
= 2.989 * 10-23 g
Note: - N0 means N Zero.
Solve This MCQ
One mole of�CO2�contains?
(A).�6.02�10236.02�1023�atoms of oxygen
(B).�6.02�10236.02�1023�atoms of carbon
(C).�18.10�102318.10�1023�molecules of�CO2
(D)�33g atoms of�CO2
Answer:
One mole is defined as the amount of a substance that includes the same number of particles or entities as there are in 12 g of 12C isotope. One mole of any element (or one 1 g atom) =�6.02�1023 atoms. There are two oxygen atoms and one carbon atom in the given compound CO2 in the question. One mole of CO2, therefore, contains one mole of carbon and two moles of oxygen.
Therefore, one mole of CO2 contains one mole of carbon and two moles of oxygen.
1 mole of CO2 = 1 mole of Carbon = 6.02�1023 atoms of carbon.
1 mole of CO2 = 2 moles of Oxygen = 2�6.02�1023 = 12.04�1023 atoms of oxygen.
However, according to the definition of a mole,
1 mole of CO2 = 6.02�1023 molecules of CO2
Therefore, option (b) is the correct answer.
Note:�6.02�1023�is Avogadro's number and represents the number of atoms/molecules present in one mole of a substance.
Read More: Atoms and Molecules: Ions - Explanation | Science Class 9
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