Question

How will you establish the relation between vapor density and molecular mass of a gas by applying Avogadro’s law?

Answer 1

Hint: Try to recall that vapor density is defined as the density of a gas relative to that of hydrogen. Also, vapor density of a gas is directly proportional to the molecular mass of that gas.

Complete step by step solution:
Vapor density is defined as “mass of a certain volume of a gas divided by the mass of the same volume of hydrogen”.
We already know about Avogadro’s law which states that “At same temperature and pressure, equal volume of all gases will have the same number of molecules”.
Deriving relation between vapor density and molecular mass of a gas:

From above definition, vapor density of a gas, V.D = $\dfrac{{{\text{mass of certain volume of gas or vapor}}}}{{{\text{mass of same volume of hydrogen gas}}}}$.

Now, by applying Avogadro’s law we can say that

V.D =$\dfrac{{{\text{mass of n molecules of gas or vapor}}}}{{{\text{mass of n molecules of hydrogen gas}}}}$.
         =$\dfrac{{{\text{mass of 1 molecule of gas or vapor}}}}{{{\text{mass of 1 molecule of hydrogen gas}}}}$
As we know that hydrogen gas is a molecule which consists of 2 hydrogen atoms
            So, V.D =$\dfrac{{{\text{mass of 1 molecule of gas or vapor}}}}{{{\text{2}} \times {\text{mass of 1 atom of hydrogen }}}}$
            Also, on the basis of old atomic mass unit scale we can say that
            Molecular mass of a gas= $\dfrac{{{\text{mass of 1 molecule of gas or
            vapor}}}}{{{\text{mass of 1 atom of hydrogen }}}}$
            Thus, from above definition of molecular mass,
Vapor density V. D= $\dfrac{{{\text{molecular mass of gas}}}}{2}$

Therefore, from above derivation we can now conclude that

 $ {\text{molecular mass of gas}} = 2 \times {\text{vapor density of gas}}$

Note: It should be noted that for a given mass of ideal gas, the volume and amount(moles) of the gas are directly proportional only if the temperature and pressure are kept constant.