Example 1: Calculate the number of moles for the following:

(i) 52 g of He (finding mole from mass)

(ii) 12.044 × $$10^{23}$$ number of He atoms (finding mole from a number of particles).

Sol:

No. of moles = n

Given mass = m

Molar mass = M

Given a number of particles = N

Avogadro number of particles = $$N_0$$

(i) The atomic mass of He = 4 u

Molar mass of He = 4 g

Thus, the number of moles =  $$\frac{given\:mass} {molar\:mass}$$

n = $$\frac{m}{M}$$ = $$\frac{52}{4}$$

(ii) we know, 1 mole = 6.022 × $$10^{23}$$

The number of moles = $$\frac{given\:a\:number\:of\:particles }{Avogadro\:number}$$ 

n = $$\frac{N}{N_0}$$ = $$\frac{12.044\times 10^{23}}{6.022\times 10^{23}}$$ = 2.

Example 2: Calculate the mass of the following:

(i) 0.5 mole of $$N_2$$ 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 × $$10^{23}$$ number of N atoms (mass from number)

(iv) 6.022 × $$10^{23}$$ number of $$N_2$$ molecules (mass from number)

Sol:

(i) mass = molar mass × number of moles 

m =  M $$\times$$ n =  28 $$\times$$ 0.5 = 14 g

(ii) mass = molar mass × number of moles ⇒ m = M × n = 14 × 0.5 = 7 g

(iii) The number of moles, n = $$\frac{given\: number\: of\: particles}{Avogadro\: number}$$

n = $$\frac{N}{N_0}$$

n = $$\frac{3.011\times 10^{23}}{6.022\times 10^{23}}$$

14 ×0.5 = 7 g

(iv) n = $$\frac{N}{N_0}$$

m = M × n = M × $$\frac{N}{N_0}$$

m = 28 × $$\frac{6.022\times 10^{23}}{6.022\times 10^{23}}$$

m = 28 × 1 = 28 g