WHAT IS A MOLE?
Take an example of the reaction of hydrogen and oxygen to form water:
2H2 + O2 \(\rightarrow\) 2H2 O
The above reaction indicates that
i. two molecules of hydrogen combine with one molecule of oxygen to form two molecules of water, or
ii. 4 u of hydrogen molecules combine with 32 u of oxygen molecules to form 36 u of water molecules.
We can infer from the above equation that the quantity of a substance can be characterised by its mass or the number of molecules. But, a chemical reaction equation indicates directly the number of atoms or molecules taking part in the reaction. Therefore, it is more convenient to refer to the quantity of a substance in terms of the number of its molecules or atoms, rather than their masses. So, a new unit “mole” was introduced. The mole, symbol mol, is the SI unit of amount of substance.
Source: This topic is taken from NCERT TEXTBOOK
RELATIONSHIP BETWEEN MOLE, AVOGADRO NUMBER AND ATOMIC NUMBER AND ATOMIC MASS
Mole
One mole contains exactly 6.02214076\(\times\)1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol–1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. The mole is the amount of substance of a system that contains 6.02214076\(\times\)1023 specified elementary entities.
1 mole (of anything) = 6.022 \(\times\)1023 in number, as, 1 dozen = 12 nos.
1 gross = 144 nos.
Besides being related to a number, a mole has one more advantage over a dozen or a gross. This advantage is that mass of 1 mole of a particular substance is also fixed.
Gram atomic mass
The mass of 1 mole of a substance is equal to its relative atomic or molecular mass in grams. The atomic mass of an element gives us the mass of one atom of that element in atomic mass units (u). To get the mass of 1 mole of the atom of that element, that is, molar mass, we have to take the same numerical value but change the units from ‘u’ to ‘g’. Molar mass of atoms is also known as gram atomic mass. For example, the atomic mass of hydrogen=1u. So, the gram atomic mass of hydrogen = 1 g.
1 u hydrogen has only 1 atom of hydrogen 1 g hydrogen has 1-mole atoms, that is, 6.022 \(\times\) 1023 atoms of hydrogen. Similarly, 16 u oxygen has only 1 atom of oxygen, 16 g oxygen has 1-mole atoms, that is, 6.022 \(\times\) 1023 atoms of oxygen.
Gram molecular mass
To find the gram molecular mass or molar mass of a molecule, we keep the numerical value the same as the molecular mass, but simply change units as above from u to g. For example, as we have already calculated, the molecular mass of water (H2O) is 18 u. From here we understand that 18 u water has only 1 molecule of water, 18 g water has 1-mole molecules of water, that is, 6.022 \(\times\) 1023 molecules of water.
Chemists need the number of atoms and molecules while carrying out reactions, and for this, they need to relate the mass in grams to the number. It is done as follows:
1 mole = 6.022 \(\times\) 1023 number = Relative mass in grams.
Thus, a mole is the chemist’s counting unit. The word “mole” was introduced around 1896 by Wilhelm Ostwald who derived the term from the Latin word moles meaning a ‘heap’ or ‘pile’. A substance may be considered as a heap of atoms or molecules. The unit mole was accepted in 1967 to provide a simple way of reporting a large number– the massive heap of atoms and molecules in a sample.
Figure 3.5: Relationship between mole, Avogadro number, and mass
Source: This topic is taken from NCERT TEXTBOOK
Illustration 3.3:
Calculate the number of moles for the following:
i. 52 g of He (finding mole from mass)
ii. 12.044 \(\times\) 1023 number of He atoms (finding mole from the number of particles).
Sol:
No. of moles = n
Given mass = m
Molar mass = M
Given the number of particles = N
Avogadro number of particles = NA
i. Atomic mass of He = 4u
Molar mass of He = 4g
Thus, the number of moles = \(\frac{given \,\, mass}{molar\,\, mass}\)
n = \(\frac{m}{M}=\frac{52}{4}=13\)
ii. we know,
1 mole = 6.022 \(\times\) 1023
The number of moles = \(\frac{given \,\, no.\,of\,\,particles}{Avogadro\,\, number}\)
n = \(\frac{N}{N_A}=\frac{12.044\times10^{23}}{6.022\times10^{23}}=2\)
Illustration 3.4:
Calculate the mass of the following:
i. 0.5 mole of N2 gas (mass from a mole of the molecule)
ii. 0.5 mole of N atoms (mass from a mole of an atom)
iii. 3.011 \(\times\) 1023 number of N atoms (mass from number)
iv. 6.022 \(\times\) 1023 number of N molecules (mass from number)
Sol:
i. mass = molar mass\(\times\) number of moles
m = M \(\times\) n = 28 \(\times\) 0.5 =14 g
ii. mass = molar mass \(\times\) number of moles
m = M \(\times\) n = 14 \(\times\) 0.5 = 7 g
iii. The number of moles, n = \(\frac{given \,\, no.\,of\,\,particles}{Avogadro\,\, number}\) = \(\frac{N}{N_A}=\frac{3.011\times10^{23}}{6.022\times10^{23}}\)
m = M \(\times\) n = 14 \(\times\) \(\frac{3.011\times10^{23}}{6.022\times10^{23}}\) =14 \(\times\) 0.5 = 7g
iv. The number of moles, n = \(\frac{given \,\, no.\,of\,\,particles}{Avogadro\,\, number}\) = \(\frac{N}{N_A}=\frac{6.022\times10^{23}}{6.022\times10^{23}}\)
m = M \(\times\) n = 28 \(\times\) \(\frac{6.022\times10^{23}}{6.022\times10^{23}}\) = 28 \(\times\) 1 = 28g
Illustration 3.5:
Calculate the number of particles in each of the following:
i. 46 g of Na atoms (number from mass)
ii. 8 g O2 molecules (number of molecules from mass)
iii. 0.1 mole of carbon atoms (number from given moles)
Sol:
i. The number of atoms n =
\(\frac{given \,\, mass}{molar\,\, mass}\times\,\,avogadro \,\,number\\ =\frac{m}{M}\times\,\,N_A\\ =\frac{46}{23}\times\,\,6.022\times10^{23}\\ =12.044\times10^{23}\)
ii. The number of molecules =
\(\frac{given \,\, mass}{molar\,\, mass}\times\,\,avogadro \,\,number\\ =\frac{m}{M}\times\,\,N_A \)
Atomic mass of oxygen= 16u
molar mass of O2 molecules= 16 \(\times\) 2 = 32g
\( n=\frac{m}{M}\times\,\,N_A\\ =\frac{8}{32}\times\,\,6.022\times10^{23}\\ =1.5055\times10^{23}\\ =1.51\times10^{23}\)
iii. The number of particles (atom) = number of moles of particles \(\times\) Avogadro number
N = n \(\times\) N = 0.1 x 6.022 \(\times\) 1023 = 6.022 \(\times\) 1022
Note:
* Avogadro Constant or Avogadro Number was named in honor of Italian scientist, Amedeo Avogadro.
Source: This topic is taken from NCERT TEXTBOOK