Question

Which one of the following pairs of gases contains the same number of molecules?
(A) 16 g of O₂ and 14 g of N₂
(B) 8 g of O₂ and 22 g of CO₂
(C) 28 g of N₂ and 22 g of CO₂
(D) 32 g of O₂ and 32 g of N₂

Answer 1

Answer:

A) 16g of O2 and 14g of N2

Explanation:

16g of O2

mole=16÷32

= 0.5

14g of N2

mole =14÷28

=0.5

so, A) is ans.

Answer 2

Answer:

16 g of O₂ and 14 g of N₂ has equal  number of molecules.

Explanation:

The number of molecules in a substance is given by the ratio of specific mass to the molecular mass.

$Number \ of \ molecules =\frac{specific\ mass}{molecular\ mass}$

(A) 16 g of O₂ and 14 g of N₂

     Atomic number of oxygen is 8 and its mass is 16.

      Hence, mass of O₂ is $2\times 16=32$

     Therefore, number of molecules in 16 g of O₂ is $\frac{16}{32} = \underline {0.5}$

    Atomic number of Nitrogen is 7 and its mass is 14.

     Hence, mass of N₂ is $2\times 14=28$

    Therefore, number of molecules  in 14 g of N₂ is $\frac{14}{28} =\underline {0.5}$

(B) 8 g of O₂ and 22 g of CO₂

    Number of molecules in 8 g of O₂ is $\frac{8}{32} =0.25$

    Atomic number of carbon is 6 and its mass is 12.

    Hence, mass of CO₂ is $12+2\times 16=44$

    Therefore, number of molecules 22 g of CO₂ is $\frac{22}{44} =0.5$

(C) 28 g of N₂ and 22 g of CO₂

     number of molecules  in 28 g of N₂ is $\frac{28}{28} =1$

     number of molecules 22 g of CO₂ is $\frac{22}{44} =0.5$

(D) 32 g of O₂ and 32 g of N₂

    number of molecules in 32 g of O₂ is $\frac{32}{32} =1$

    number of molecules  in 32 g of N₂ is $\frac{32}{28} =0.14$

From all the given pairs of gases, only 16 g of O₂ and 14 g of N₂ has equal  number of molecules.

So, option A is the correct answer.