I saw the graph of compressibility factor against pressure I was confused to see that all the gases are started by 1 unit of conpressibility factor when pressure is zero. So why do we take the compressibility factor equal to one when the graph is being plotted?


I think that at $p = 0$ the compressibility factor ($Z = pV_m/RT$) itself is not particularly well-defined since $p = 0$, $V_m = \infty$ and $T = 0$. Zero pressure is not a state that we can reach.

However, if you use any equation of state and take the limit as $p \to 0$ (or $V_m \to \infty$, which is equivalent), you will find that $Z \to 1$. Try it with the virial equation of state:

$$pV_m = RT\left( 1 + \frac{B}{V_m} + \frac{C}{V_m^2} + \cdots \right)$$

This happens with all gases because the individual gases are identified by their virial coefficients $B, C, \ldots$ and the terms involving these constants vanish as $V_m \to \infty$.

A simple qualitative explanation is that in the limit of $p = 0$ all gases behave ideally; for an ideal gas, $Z$ is of course equal to $1$ because of the ideal gas law $pV_m = RT$.


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