Question

If we plot `P` vs. `1//V`, then do we get a straight line?

Answer 1

We don't, unless the temperature is fixed. For simplicity, this is certainly true for ideal gases. The ideal gas law is:

`PV = nRT`

Solving for pressure we get:

`P = (nRT)*1/V`

Since mols `n`, the universal gas constant `R`, and `T` are held fixed intentionally, if we chose to make a graph of `P` vs. `1/V`, it is linear. That's a mathematical result of forcing `nRT` to be a constant.

It is of the form `y = mx + b` where `x = 1/V`, `b = 0`, and `m = nRT`. Mind you, if you chose to plot `P` vs. `V` you would not see a straight line. What would you see instead?