Recap - Balloon at Launch

Weather balloons and the helium problem

Twice a day, at the same moment all over the world, about 900 weather stations let go of a balloon. Each one carries a small box of instruments, a radiosonde, that radios back the temperature, the pressure and the humidity of the air as it climbs. These numbers feed every weather forecast you read.

A weather balloon is made of thin rubber. At the ground it is filled with about 2,500 L of gas, a ball roughly 1.7 m across. As it rises, the air around it thins and the pressure outside falls, so the gas inside spreads out and the balloon swells. High up it is also very cold, which shrinks the gas a little, but the drop in pressure wins by far. About 30 km above the ground the balloon has grown to six or seven meters across, the rubber tears, and the radiosonde falls back to Earth under a small parachute.

The same helium, at the ground and high up: fewer collisions outside, so the balloon swells

The gas inside must be lighter than air. Hydrogen is the lightest gas of all and it is cheap: some stations make it on the spot by splitting water with electricity, 2H₂O → 2H₂ + O₂. But hydrogen burns, and a leak near a spark can start a fire. So most stations use helium, a noble gas that does not react at all.

Helium has a problem of its own. Earth's helium was made slowly, over millions of years, by the α decay of uranium and thorium in rocks, and it is collected from natural gas wells. Once it is let out into the air it rises, and it is so light that it slowly escapes to space. Hospitals need it to cool the magnets of MRI scanners, and in years of shortage its price has climbed steeply. Weather services in several countries have already moved some of their launches back to hydrogen, with automatic launchers that keep people away from the gas.

Calculate the mass of helium, $m$, in a balloon filled with 2,500 L of helium at room conditions (He, 4 g/mol). Assume that 1 mol of gas takes 25 L at room conditions.