Question

Four flasks of ${\text{1}}$ litre capacity each are separately filled with gases ${H_2},He,{O_2}$​ and ${O_3}$​. At the same temperature and pressure the ratio of the number of atoms of these gases present in different flasks would be:
A) ${\text{1:1:1:1}}$
B) ${\text{2:1:2:3}}$
C) ${\text{1:2:1:3}}$
D) ${\text{3:2:2:1}}$

Answer 1

Hint: The conditions of constant temperature and pressure have been given for all gases which means one can apply these concepts in terms of the ideal gas equation. One can find out the ration for the number of moles which can give the correct choice of option.

Complete step by step answer:

1) First of all let's analyze the given question data where four gases of equal quantity of one litre have been filled up at the same temperature and pressure.
2) The ideal gas law equation is as following which all the four gases follow,
$PV = nRT$
3) As per the given data in question we can say that the volume of all the four flasks is constant which is equal to one litre. The values of pressure and temperature of all four gases are also constant. As all other values are constant we can say that the value of the number of moles for all four gases is also constant. The value $R$ is always the same as it is the value of the universal gas constant.
4) Therefore, we can say that the molar ratio of all the four gases hydrogen, helium, oxygen, and ozone is ${\text{1:1:1:1}}$.
5) Now that the value of molar ratio is equal to each other the number of atoms ratio will depend on the presence of the number of atoms of each individual atom. Hence, we can say that the ratio of the number of atoms of these gases present in different flasks would be ${\text{2:1:2:3}}$

which shows option B as a correct choice.

Note:
One should remember that in the above question all the given gases are filled in the different flask and not in the same flask as a mixture. At the constant temperature and pressure, all the gases filled in different flasks behave ideally.