It is easy to understand that chemical reactions can reduce the pressure of the air inside a closed volume. For instance, we can burn white phosphorous in a closed container and the air pressure of the container will reduce about 20%.
However, it is not a good enough idea to apply into practice. Because not all the components in the air can participate burning reaction and burning is very dangerous. Maybe white phosphorous is very expensive.
In our practice, we usually use physical reaction instead of chemical reaction to make vacuum. There are two kinds of vacuum pump to make vacuum. The definition 'vacuum' is 'relative vacuum' or 'approximate vacuum'. Actually, the complete vacuum is impossible.
Positive displacement pumps. It is one of the mechanism that can achieve the goal.(make by wikipedia.org)
The first kind is positive displacement pumps. They repeatedly expand the volume of the container, attract gases into the chamber and exhaust the extra gases. If the process goes many times, the air pressure will go down greatly.
The second kind is the Entrapment pumps. The use some material ,like activated carbon, to absorb the molecules. This kind of material work efficiently and cost more.
Of course, there are other kinds of vacuum pumps.
So it sounds easy to make a vacuum pumps by yourself?
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