Question

Calculate the number of molecules in each of the following: i) 1 g N2 ii) 1 g CO2 (Given that NA is 6.022 x 1023, molecular mass of N2 = 28 and CO2 = 44)

Answer 1

i)molecular mass of N2 =28g
1g of N2 molecule = 6.022× 10^23
14g of N2 molecule = 6.022×10^23/14
28 g of N2 molecule = 6.022×10^23/14×28
=6.022×10^23×2
=12.044× 10^23molecul
ii)

Answer 2

Answer: i)  $0.22\times 10^{23}$

ii) $0.14\times 10^{23}$

Explanation:

According to avogadro's law, 1 mole of every substance occupies 22.4 Liters at STP and contains avogadro's number $6.023\times 10^{23}$ of particles.

To calculate the moles, we use the equation:

1. 1 g $N_2$:

$\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}$

$\text{Number of moles of }N_2=\frac{1 g}{28g}=0.036moles$  

Now 1 mole of $N_2$ molecule contains = $6.023\times 10^{23}$ of molecules

0.036 mole of $N_2$ molecule contains = $6.023\times 10^{23}}{1}\times 0.036=0.22\times 10^{23}$ molecules

Thus there are $0.22\times 10^{23}$ molecules of nitrogen in 1 g of $N_2$

1. 1 g $CO_2$:

$\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}$

$\text{Number of moles of }CO_2=\frac{1 g}{44g}=0.023moles$   (1L=1000ml)

Now 1 mole of $CO_2$ molecule contains = $6.023\times 10^{23}$ of molecules

0.023 mole of $CO_2$ molecule contains = $6.023\times 10^{23}}{1}\times 0.023=0.14\times 10^{23}$ molecules

Thus there are $0.14\times 10^{23}$ molecules of carbon dioxide in 1 g of $CO_2$.