tHERMAL O10

Solution for Question 10

Given:

• Two identical cylinders.
• Both cylinders weigh equally.
• Gas 1: Helium (He), Molar mass $M_{He} \approx 4$ g/mol.
• Gas 2: Nitrogen ($N_2$), Molar mass $M_{N2} \approx 28$ g/mol.

Reasoning:

Since the cylinders are identical and weigh equally, the mass of the gas inside must be equal:

$$m_{He} = m_{N2}$$

We know that moles $n = \frac{m}{M}$. Since Helium is much lighter ($M_{He} < M_{N2}$), the number of moles of Helium is much greater than Nitrogen:

$$n_{He} > n_{N2}$$

Assuming the gases are at the same temperature and occupy the same volume (identical cylinders), the Ideal Gas Law ($PV = nRT$) implies that Pressure is directly proportional to the number of moles:

$$P_{He} > P_{N2}$$

The rate at which a balloon inflates depends on the pressure gradient between the cylinder and the balloon. Since the Helium cylinder is at a significantly higher pressure, the gas will flow out much faster.