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Problems on mole concept | part- 1

 

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