Question

Three balloons are filled with equal moles of hydrogen, nitrogen and helium. Which balloon will contract first, if the same size holes are made in all of them?
A. Balloon filled with hydrogen
B. Balloon filled with nitrogen
C. Balloon filled with helium
D. All will contract at the same time.

Answer 1

There is a relation between pressure rate and molar mass of the gases.
Pressure rate is inversely proportional to square root of the molar mass of the gases.
The above statement can be expressed as follows.
$\text{Pressure }Rate\propto \dfrac{1}{\sqrt{molar\text{ }mass}}$

Complete step by step answer:
- In the question it is given that there are three balloons filled with three different gases named as hydrogen, nitrogen and helium.
- We have to find which balloon will contract first if the same size holes are made in all of them.
- In the question it is also given that equal moles of the gases are present.
- We know that for one mole, the weight of the given gases is in order as follows.
${{H}_{2}}$ < He < ${{N}_{2}}$
- Means weight of hydrogen gas is low when compared to the remaining two given gases helium and nitrogen.
- Therefore the pressure rate is high in case of hydrogen.
$\text{Pressure }Rate\propto \dfrac{1}{\sqrt{molar\text{ }mass}}$
- Thus balloons containing hydrogen gas have more diffusion rate when compared to the remaining two balloons.

- So, the correct option is A.

Note: The molecular weight of hydrogen is two.
The molecular weight of Helium is four.
The molecular weight of Nitrogen is 14.
So, the balloon contains nitrogen gas contracts at last when compared to hydrogen and helium.