Deviation of a gas from ideal gas behaviour

[RightFresh]

Hi all, I have a question from a tutorial sheet that I'm stuck with. The question is

Estimate the pressure at which a gas of argon atoms, at a temperature of 300 K, will begin to show deviations from the ideal gas behaviour due to the finite size of the atoms. Answer: Of order 10^9 Pa.

So I tried taylor expanding the hard sphere gas equation: P'(V-b)=NkT, to get P'=P(1+b/V) to first order, where P is the ideal gas pressure. However, I don't know if this is the right approach or just what to do next really. Could someone point me in the right direction please?

 

[Bystander]

begin to show deviations from the ideal gas behaviour

What magnitude of deviations?

Answer: Of order 10^9 Pa.

Please check this number --- it's somewhat beyond ridiculous.

 

[RightFresh]

It just says deviations & that's the answer given

 

[RightFresh]

What magnitude of deviations?

Please check this number --- it's somewhat beyond ridiculous.

It just says deviations & that's the answer given

 

[Bystander]

Without some specification of magnitude of departure, there's no way to answer the question. You could make an assumption of 0.1% (or 0.3 to perhaps 1 % for ordinary measurement accuracies), and at the fixed temperature calculate a pressure at which the excluded volume reached that value, but you're never going to see 10⁹ Pa for such a calculation.