# Hydrogen in soap bubble

I read somewhere that if hydrogen gas is passed through soap solution bubbles containing hydrogen are formed. My question is how these bubbles are stable! Hydrogen has much less density and mass than air. So how can the bubble form anyway. If i take temperature inside and outside the bubble to be same then by $$p = (rho)*R*T/M$$ we get pressure inside is lower. Then why not the bubble crushes in?

You can write the ideal gas equation of state in different ways. You have written:

$$P = \rho \frac{RT}{M}$$

where $$\rho$$ is the density and $$M$$ is the molar mass. Suppose we note that the density is mass divided by volume, $$\rho = m/V$$, then we can substitute this into the equation to get:

$$P = \frac{m}{M} \frac{RT}{V}$$

and the mass divided by the molar mass, $$m/M$$, is equal to the number of moles, which we usually write as $$n$$. So we can rearrange the equation to:

$$PV = nRT$$

which I think is the most common way to write it.

Now suppose we have two bubbles of the same size, one containing hydrogen and one containing air. The volume is the same because they are the same size, and the pressure and temperature are the same because they are both in equilibrium with the atmosphere around them. And if $$P$$, $$V$$ and $$T$$ are the same the number of moles $$n$$ must be the same as well. Our two bubbles are identical!

The only difference is that $$n$$ moles of hydrogen weigh less than $$n$$ moles of air i.e. the bubble containing hydrogen will be lighter.

Room-temperature hydrogen obeys the ideal gas law, $$p\propto\rho T$$, for pressure $$p$$, density $$\rho$$, temperature $$T$$. While the pressure outside the bubble is less than the pressure inside the bubble, the bubble will shrink. When the wall of the bubble reaches equilibrium, the pressure inside is just slightly higher than the pressure outside, because of surface tension in the curved bubble. For hydrogen bubbles in air, the density at equilibrium is substantially less dense than air, so the bubbles float.

You could ask exactly the same question about helium-filled Mylar balloons, which do slowly “crush” as the helium leaks out in the weeks after your birthday party.

• Tell me if im getting it wrong.. Shrinking in makes inside air denser till the pressure of inside air increases upto a certain amount which surface tension can balance? Commented Jul 8, 2022 at 3:32
• Just like that, yes.
– rob
Commented Jul 8, 2022 at 3:38
• Is it possible that temperature inside also increases to help increasing pressure? Commented Jul 8, 2022 at 3:44
• In “adiabatic” compression or expansion, the gas doesn’t exchange heat with its environment, so its temperature changes. In a soap bubble, the temperature follows the environmental temperature.
– rob
Commented Jul 8, 2022 at 4:06