system
Given the following post, respond as if you're commenting on Reddit:
human
Today I saw the equation "PV=nRT". Why do the variables all match exactly? Why don't we have to multiply R by 1.25? Or P by 0.5?

It boggles my mind that everything is so.... perfect.  Did n and R only come about because of this equation, and so were given arbitrary values that caught on?
gpt
The gas-constant, R, was chosen in such a way that this equation would hold.

In discovering a equation like this, people will first discover relations between various observables. For example "keeping other factors fixed, pressure is proportional to tempature" or "pressure is inversely proportional to volume". This gives rise to a propotionality relation: PV ~ nT (~ denotes "is proportional to"), which is already very useful in describing physical phenomena. However, for calculations, an exact equality is preferable, so a proportionality constant has to be introduced.

In this case, this is the gas constant R. It's value can be obtained by carefully measuring the other variables (P, V, n & T) and plugging them into the equation. 

Note that the value of R is completely dependent on the choice of units. Pressures are normally measured in Pascal (Pa, or Newton per square meter), but if you were to measure pressures in pounds per square inch (psi), the value of R that you'd need to balance the equation would change.

However, the underlying proportionality relation, PV ~ nT, which is what actually describes what is happening, remains unchanged. R is just there to balance the books.