15.0 moles of gas are in a 8.00 L tank at 22.3 ∘C∘C . Calculate the difference in pressure between methane and an ideal gas under these conditions. The van der Waals constants for methane are a=2.300L2⋅atm/mol2 a=2.300L2⋅atm/mol2 and b=0.0430L/molb=0.0430L/mol.

Explanation:

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In this case, since the ideal gas equation is used under the assumption of no interaction between molecules and perfectly sphere-shaped molecules but the van der Waals equation actually includes those effects, we can compute each pressure as shown below, considering the temperature in kelvins (22.3+273.15=295.45K):

Next, since the VdW equation requires the molar volume, we proceed as shown below:

Now, we use its definition:

Thus, by plugging in we obtain:

Thus, the pressure difference is:

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