# Question on Graham's law of diffusion

Identical balloons are connected through identical valves with two identical cylinders. One cylinder contains gaseous helium and the other gaseous nitrogen. Both the gases may be assumed ideal, and both the cylinders weigh equally. Which balloon will be inflated faster when the valves are opened, and why?

(a) The nitrogen balloon will be inflated faster because nitrogen is a heavier element, and so the molecules of nitrogen have greater momentum and thus force the balloon to expand at a greater rate.

(b) The helium balloon will be inflated faster, because helium is a lighter element and so its atoms move faster and can get into the balloon at a greater rate.

(c) The helium balloon will be inflated faster because the helium must be at higher pressure and hence the gas will be forced into the balloon at a greater rate.

(d) It will depend on whether the gases have to flow up or down to enter the balloon. Helium being lighter than air as compared to nitrogen will rise faster than nitrogen. Therefore, if the balloons are at the top of the cylinders, the helium balloon will be inflated faster; and if they are at the bottoms, the nitrogen balloon will be inflated faster.

The above question is from a well known book, the answer given there is option C. We know that diffusion rate is directly proportional to pressure and PV=nRT (n is number of moles), here in this case number of moles of 'He' will be greater than 'N', R is constant in both cases and volume is given constant but there is no information about temperature in the question, so how can we say that Pressure of 'He' would be greater than 'N'? Also, rate of diffusion is inversely proportional to root to mass, so how option B is wrong?

• As for temperature, since nothing is said, it is appropriate to assume it is constant for both tanks. Valves on a tank of gas hold back pressure. Diffusion is a slow process that is generally controlled (if at all) by porosity. You fill up a balloon in 10 seconds with significant pressure; then the balloon deflates over a week by diffusion. The inflated balloon B will DE-flate faster than inflated balloon A because He diffuses faster than N2 thru latex (mylar would take many weeks). Jan 2, 2022 at 21:21
• The key words are IDENTICAL HARDWARE and IDENTICAL WEIGHT. Since He is a lighter molecule there must be more He molecules in the tank and a higher pressure. But that doesn't mean it will flow faster. The chemistry is solved now we need a chemical engineer to work out Reynolds numbers viscosities, velocities, J-T effects, etc. It's a stupid question! simply ask : ''Which tank has more molecules and why?"1 Jan 3, 2022 at 0:50
• additional comment this has nothing to do with Graham's Law of diffusion. That is appropriate when there are no external forces and the motion is random not directed. Jan 3, 2022 at 0:59
• Be aware there are tricky tasks where not all info is there to help you. Some may be provided with intention to confuse or mislead you. Jan 3, 2022 at 12:48

## 1 Answer

It is overcomplicating the answer to assume it has anything to do with diffusion

Framing this as a "diffusion" problem is a distraction which is why it is hard to see the key features if you start with the assumption diffusion has anything to do with it.

The basic setup is simple. The starting position is two cylinders of gas with the same mass of gas. The key feature here is that, if the two sources have the same mass, there are about 7 times more moles of helium than of nitrogen (helium atoms being about 7 times less weighty than nitrogen molecules). This implies, given basic gas laws, that the pressure in the helium cylinder is far higher than the pressure in the nitrogen cylinder (same volume, but more moles of gas, pressure must be higher). So, if an identical valve is opened, the helium will flow much faster than the nitrogen. We don't even need to calculate how much faster as it is obvious that the flow will be much faster. Diffusion doesn't come into it at all as this is just basic gas law stuff.

The other provided answers are designed to distract from this basic idea with irrelevant complications. C is the correct answer.