Question

A football bladder contains equimolar proportions of ${{H}_{2}}$ and ${{O}_{2}}$. The composition by mass of the mixture effusion out of punctured football is in the ratio (${{H}_{2}}$:${{O}_{2}}$):

Answer 1

Hint: Understand the concentration of hydrogen and oxygen molecules in an equimolar concentration. The rate of effusion can be estimated using Graham's law of diffusion. It will help you give a relation between the rate of effusion and molecular mass of the gas effused. The ratio of the two effusion rates will help you arrive at the correct answer.

Complete step by step answer:
We will try to understand Graham's law of diffusion and then apply the formula to find the answer.
-Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.
$r\propto \dfrac{1}{M}$

-The complete explanation of the law was given by the kinetic theory of gases a few years later. Graham's law is used in isolating isotopes of an element as they have different rates of diffusion.
-Rate of diffusion (r) =$\dfrac{volume\_diffused}{time\_taken}$
The final formula thus becomes,
$\dfrac{{{r}_{1}}}{{{r}_{2}}}=\dfrac{\sqrt{{{M}_{2}}}}{\sqrt{{{M}_{1}}}}$
Where,
${{r}_{1}}$ is the rate of diffusion of first gas,
${{r}_{2}}$ is the rate of diffusion of second gas,
${{M}_{1}}$ is the molar mass of first gas,
${{M}_{2}}$ is the molar mass of second gas.
Since, the concentration of hydrogen and oxygen is equimolar,
Rate = \[\dfrac{W}{t}\]

Here, we will substitute the molar mass of oxygen and hydrogen as 32 and 2 g respectively.
$\dfrac{{{W}_{1}}}{{{W}_{2}}}=\dfrac{\sqrt{{{M}_{2}}}}{\sqrt{{{M}_{1}}}}$
$\dfrac{{{W}_{1}}}{{{W}_{2}}}=\dfrac{\sqrt{32}}{\sqrt{2}}$
$\dfrac{{{W}_{1}}}{{{W}_{2}}}=4$
Therefore, the ratio (${{H}_{2}}$:${{O}_{2}}$) is 4:1
So, the correct answer is “Option D”.

Note: The formula mentioned above is used when the diffusion of gases happens at the same conditions like temperature, pressure etc. Remember that the rate of diffusion is inversely proportional to molecular to avoid errors.