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Suppose we know the Van Der Waals coefficients $a$ and $b$ for a set of gases in the real gas equation, then which is the correct method to predict which gas shows most ideal behavior at STP ?

Our professor said that we must check the critical temperature using the formula $$T_c=\frac{8a}{27Rb}$$ Then he said: "The gas for which $$|T_c-273|$$ is minimum will show the most ideal behaviour".

I sort of don't agree with this logic. Let us have a look at Andrew's curves:

enter image description here

We notice that greater is the temperature compared to critical temperature more is the ideal behaviour. So the correct method should be checking $(273-T_c)$. The gas which has maximum value of $(273-T_c)$ should show maximum ideal behaviour at $273 K$. Is my logic correct or not ? Why?

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  • $\begingroup$ Its not clear why since a $T_c$ of $173$ and $373$ gives the same result. Presumably he means the one with the lowest $T_c$ in degrees Kelvin. $\endgroup$ – porphyrin Mar 7 '17 at 13:22
  • $\begingroup$ @porphyrin Yeah that is one problem. But the bigger problem is he said that difference between Tc and 273 should be minimum for ideal behavior. Shouldn't it be maximum for ideal behavior ? $\endgroup$ – user38977 Mar 7 '17 at 14:49
  • $\begingroup$ Its just a conversion. Helium seem to have the lowest critical temp, $-268$ C or$ 5$ K, (hydrogen $33$ K, nitrogen $126$ K). Values seem to be mainly listed in centigrade not Kelvin, hence the $273$ is to convert. Can't see what $273$ has to do with it otherwise. Lowest temp (in K) should exhibit most ideal behaviour. $\endgroup$ – porphyrin Mar 7 '17 at 18:51
  • $\begingroup$ "Lowest temp (in K) should exhibit most ideal behaviour." <--- You mean the gas having lowest critical temperature shows most ideal behaviour at 273 K ? @porphyrin $\endgroup$ – user38977 Mar 8 '17 at 1:57

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