Good question!
If you performed this experiment IN A VACUUM indeed the two balloons would fall at the same rate. Each would fall to the floor accelerating at 9.8 m/s². That is after one second of free fall both would be moving downwards at a velocity (speed) of 9.8 m/s , and after two seconds of free fall they would BOTH be moving down at 19.6 m/s , etc.

NOW IN AIR it is a different problem. Because in AIR we must consider the buoyancy of the balloon -gas system.

So if we put a light gas, say HELIUM that you can get at CVS in a balloon, then the balloon plus helium (He) systems actually weighs less than a balloon filled with air. So in this case the He filled balloon will actually MOVE UP! If you let it go. Meanwhile if you filled a balloon to the same volume size with CO₂, since CO₂ is denser than air the balloon will sink!

Carbon dioxide is denser than nitrogen and oxygen (i.e. air), so the balloon filled with carbon dioxide is heavier and sinks in the air faster than the balloon filled with normal air. It's the same reason that dropping a hammer will take longer to hit the ground than dropping a feather: the feather is impeded by air resistance more than the hammer.

This is a great way to see the effect of buoyancy. We've talked before about the fact that an object's weight will usually not change its falling speed read here please . Last time, I talked about one factor that affects falling speed, air resistance. Buoyancy is another effect that is only noticeable in specific cases, like balloons filled with different gases.

To get the complete story, we have to think about fluid pressure. Fluid pressure, in simple terms, is how hard a fluid like water or air pushes against any surface inside the fluid. Fluid pressure exists even when the fluid is not flowing, like the air in a closed room or the water in a quiet swimming pool. (Specifically, this type of fluid pressure is called hydrostatic pressure.) This is because the fluid is made up of molecules that are constantly bumping into each other. The direction that the fluid pushes is always perpendicular to the surface (directly into the surface), no matter how the surface is angled. The magnitude of this push (i.e. the pressure) depends on how deep we are in the fluid. This is because all of the fluid above us. So the deeper we are, the larger the pressure.

This means that the fluid pushes harder against the bottom of the balloon than against the top. So overall, fluid pressure will end up pushing the balloon upwards. (It turns out that the force from the fluid against the balloon's sides will cancel out, so the fluid doesn't make the balloon move sideways.) The combined force from the fluid pressure on the entire surface of an object is called buoyancy, and this force always directly opposes gravity.

Like for air resistance, the effect of buoyancy depends on the object's inertia (mass): objects with more mass are less affected by buoyancy. Carbon dioxide is heavier than air, so the balloon filled with carbon dioxide is slowed down less by buoyancy and lands first!

(Technical side note: in physics class, we often talk about forces instead of acceleration. Be careful when I say things like "the effect of buoyancy depends on mass": what I mean is the contribution of buoyancy to the acceleration depends on mass, while the contribution of gravity to the acceleration does not depend on mass. Instead, if we talk about forces instead of acceleration, the buoyant force does not depend on the mass, while the gravitational force does depend on the mass. These are both correct ways of thinking about the world, and they are connected through Newton's second law of motion.)

Your teacher was demonstrating the density (weight per volume) of various gases. Let’s compare some densities in the same units (so you can compare the numbers directly). Water has a density of 1000 kg/m³ and granite rock has an average density of 2600 kg/m³ – so granite will sink in water. Carbon dioxide has a density of 1.977 kg/m³, much less than either water or granite. But how does the density of carbon dioxide compare to air? Air is composed of mostly nitrogen gas (78%, 1.251 kg/m³) and oxygen (20%, 1.429 kg/m³) with an average density of 1.292 kg/m³. Carbon dioxide is denser than air so if the same volume of the two gasses is the same (one balloon), the carbon dioxide balloon will be heavier and will fall faster when dropped from the ceiling.

You may have confused this experiment with a famous one proposed by Galileo where he dropped two objects of equal weight off a tower. He (correctly) believed that the speed at which objects fell due to gravity was based on weight, not their size or shape. (He did not take into account air resistance, however, which can also affect how fast an object falls but is dependent on size and shape.)

Returning to your teacher’s experiment, what would happen if the balloons had the same weight and were dropped from the ceiling? If the balloons were each filled equal weights of carbon dioxide and air, could they have the same volume? (Highlight the section below to check your answers!:)

The balloons would fall at the same time. The air balloon would be bigger than the carbon dioxide balloon.