Question

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1:4. The ratio of the number of their molecules is …….
A. 1:4
B. 7:32
C. 1:8
D. 3:16

Answer 1

The number of molecules depend on the quantity called mole. It can be related to the avogadro’s number which is the number of molecules present in 1 mole. It is denoted by the symbol ${{N}_{A}}$

Complete step by step solution:
-Basically everything present in this universe is made up of atoms. The mass of an atom cannot be measured truly due to its very small size. So a relative term is used for it called relative atomic mass. Every atom has a mass which is related to hydrogen atom mass. Standard mass of hydrogen is 1 unit and to find the mass of any other atom, relative atomic mass is used.
$Relative\text{ }atomic\text{ }mass\text{ }=\text{ }\dfrac{mass\text{ of 1 atom of element}}{\text{mass of 1 hydrogen atom}}$
-Today a different unit is used which is based on the mass of 1 carbon-12 atom. It was adopted internationally in 1961 and according to it, relative atomic is given by
$Relative\text{ }atomic\text{ }mass\text{ }=\text{ }\dfrac{mass\text{ of 1 atom of element}}{\dfrac{1}{12}\text{x mass of 1 C-12 atom}}$
-Mole is the amount of substance that contains the atoms, molecules or other particles in an entity equal to the atoms present in 12 g of C-12 isotope. It is given as
Mole = $\dfrac{\text{wt}\text{. in grams}}{\text{molecular wt}\text{.}}$
-In the question we are given the ratio of the masses of the gases. If we assume that the mass of the whole mixture is 100 grams, then according to the ratios given we see that the mass of oxygen gas will be 20g and the mass of nitrogen gas will be 80g.
-We know that the nitrogen and oxygen gases do not occur in nature in free state as they do not have complete octets. They occur as molecules forming a covalent bond and occur as ${{N}_{2}}\text{ and }{{\text{O}}_{2}}$ respectively. So the masses of the gases will be the masses of their respective molecules and not their atoms.
-We know the atomic mass of nitrogen is around 14g and oxygen is around 16g. So the masses of these gases existing as a diatomic gas will be double of their atomic masses and will be 28g and 32g respectively.
-Now we can find the moles of these gases after knowing their molecular mass and their weight.
Moles for nitrogen will be $\dfrac{80}{28}$ and the moles of oxygen will be $\dfrac{20}{32}$
-The number of molecules are always determined by the moles of the substances and so their ratio will be given by the ratio of the moles of the gases. So, the ratio of the number of their molecules is given as
Ratio of molecules = ratio of moles
= $\dfrac{\dfrac{20}{32}}{\dfrac{80}{28}}$ =$\dfrac{7}{32}$

Therefore the correct option is B. 7:32

Note: Mole is not only related to mass but also to volume as any matter that has a certain mass will occupy a certain volume. 1 mole is the amount of molecules present in 22.4 litres of a gas calculated at standard temperature and pressure.