Use the van der Waals equation and the ideal gas equation to calculate the volume of 1.000 mol of neon at a pressure of 500.0 atm and a temperature of 355.0 K. Explain why the two values are different. (Hint: One way to solve the van der Waals equation for V is to use successive approximations. Use the ideal gas law to get a preliminary estimate for V.)

Differences:

- The gas is at a very high pressure, which causes strong nonidealities.

- Attraction and repulsion actually phenomena exist among molecules, which is not considered by the ideal gas equation.

Explanation:

Hello,

In this case, the VdW equation takes the typical form:

Whereas and are referred to the attraction and repulsion effect, in such a way, for neon, such values are 0.208 bar*L²/mol² and 0.01672 L/mol respectively. However, with the given information, the polynomic form of the VdW equation is:

Which in terms of the molar volume becomes:

Thus, by solving via solver the roots, two are imaginary and the feasible molar volume is:

Now, the volume obtained from the ideal gas equation is:

In this case, the two values are different because:

- The gas is at a very high pressure, which causes strong nonidealities.

- Attraction and repulsion actually phenomena exist among molecules, which is not considered by the ideal gas equation.

Best regards.

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