Matter is anything that has mass and takes up space. So, in order to prove that air is matter, we need to prove that air has mass and takes up space. It's easier to prove that air takes up space, so let's do that part of the problem first.
Go and get a balloon. While you're at it, get two balloons. Go ahead and inflate the balloons with air. The balloons get larger as you put air into them. The only way that air could make them get larger is if air takes up space, so half of our proof is complete. Tie the balloons closed so that they stay inflated - we will need both balloons for the second half of this problem.
Although air has mass, a small volume of air, such as the air in the balloons, doesn't have too much. Air just isn't very dense. We can show that the air in the balloon has mass by building a balance. For this, you will need a meter stick, some tape, some string and a sharp needle. Take some of the string and tie one end to the middle of the meter stick. Take the other end of the string and tape it to the top of a table or a counter, just make certain that the meter stick is free to move around. Tie a section of string to each balloon. On one balloon, make an "X" with two pieces of tape (if you want to be fair, you can make a tape "X" on the second balloon as well, but we really only need one). Take the balloons and tie each one to the meter stick, one on each end of the meter stick. Balance the meter stick by repositioning the balloons, if necessary.
So, at the moment, you should have two balloons hanging from a meter stick, one from each end. If one of the balloons changes mass, we will be able to tell because the meter stick will 'tilt' towards the more massive object. So, all you need to do is to let the air out of one of the balloons. Take the needle and CAREFULLY poke a hole in the center of the "X". You don't want to pop the balloon - you just want to make a hole so that the air will leak out. Hopefully, the tape will keep the balloon together...
What happened? If all went well, one balloon lost its air in a very calm, controlled fashion without sending its balloon guts all over the room. The end of the meter stick with the deflated balloon should have risen into the air. It did this because there was less mass in the balloon after it deflated. The only way the balloon could have lost mass is if the air that was inside it has mass.
With this experiment you have shown that air takes up space and has mass, so you have proven that air is matter.
Matter is anything that has volume and weight. To prove that air occupies space. Simply blow a balloon to prove air occupies space. To prove air has weight Tie a inflated balloons to a ruler and burst one of them. The side of the ruler with an inflated balloon will move down. To prove that air has weight.
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