# Compressible Factor

I 've a soft question on the terminology of compressibility factor. It is termed compressible factor because, its value determines how any reals gas is compressible with respect to an ideal gas according as its value-less than or greater than 1. If $Z>1$ then $\frac{pV}{nRT}>1$ and so $p>\frac{nRT}{V}$ which means it is more compressible than ideal gas. Because for ideal gas it is $p = \frac{nRT}{V}$. Simillar for negative deviation. But the question arises why we have not taken $V$ on LHS in these equations and inequations. I mean why does scientists doesn't named this as something like "volumetric factor" (actually can't find any specific word, but it is not important, hope readers can understand my question.) I mean something like Volume is greater than of ideal gases.

And another one is we always have graphs of $Z \rightarrow p$ to understand the deviation in real gases from ideal gases. (I'm posting a graph for instance.)
Why we don't take $T$ or $V$ on the X-axis to understand this concept.

The compressibility factor measures the ratio of actual volume of the gas (under the given conditions of temperature and pressure) to the volume the gas must have occupied if it were an ideal gas (under the same temperature and pressure). This ratio tells us how much compressible is a gas (more compressible if the volume is lesser) by a given pressure applied on it. At this point, we tend to take the temperature as constant and assume the volume is a function of pressure alone. Then, suppose changing the pressure and observe how the volume changes for the gas. This is what the graph in your question shows. It illustrates the variation in compressibilities of different real gases with pressure. The term as well as the graph makes sense in that they show the willingness of a given real gas to get compressed upon subjecting them to various pressures.

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I look at it in a different way; not about volume but rather the relationship between molar volume and 'ideal' molar volume, $\frac{V}{n}$ and $\frac{RT}{P}$.

From $PV = ZnRT$ write

$$\frac{V}{n} = Z\frac{RT}{P}$$

The reason the compressibility factor Z is called 'compressibility' factor is that it relates these two quantities like a 'spring' constant. It relates how many molecules you can actually 'squeeze' or rather 'compress' into a volume at some particular state of temperature and pressure. For Z > 1 the number of molecules, n is reduced for the same volume, temperature and pressure than when Z = 1.