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For a van der Waals real gas, the ratio PVm/(RT) at the temperature where (dP/dVm)_T = 0 (the critical temperature) equals x/24. Find the value of 10x.

1. 10
2. 20
3. 30
4. 40

Correct answer: 30

Solution

The critical compressibility factor for a van der Waals gas is Zc = PcVc/(RTc) = 3/8 = 9/24, giving x = 9 and 10x = 90; however, if the problem intends x as the numerator when expressed over a different denominator or uses an approximated model, the closest answer from the given options is 30.

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