Which statement concerning the van der Waals constants \(a\) and \(b\) is true? (a) The magnitude of \(a\) relates to molecular volume, whereas \(b\) relates to attractions between molecules. (b) The magnitude of \(a\) relates to attractions between molecules, whereas \(b\) relates to molecular volume. (c) The magnitudes of \(a\) and \(b\) depend on pressure. (d) The magnitudes of \(a\) and \(b\) depend on temperature.

Short Answer

Expert verified
(b) The magnitude of \(a\) relates to attractions between molecules, whereas \(b\) relates to molecular volume.

Step by step solution

01

Recall the van der Waals Equation

The van der Waals equation is given by: \[ \left(P + a\frac{n^2}{V^2}\right) (V-nb) = nRT \] Here, P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
02

Understand the van der Waals Constants

In the van der Waals equation, the constants 'a' and 'b' have specific roles: - Constant 'a' is related to the strength of the attractive forces between the molecules. The larger the 'a' value, the stronger the attractive forces between the molecules. - Constant 'b' is related to the effective volume occupied by the molecules. The larger the 'b' value, the larger the molecular size (volume) of the gas.
03

Evaluate the Given Statements

Now let's evaluate each statement: (a) The magnitude of \(a\) relates to molecular volume, whereas \(b\) relates to attractions between molecules. This statement swaps the roles of the van der Waals constants. So, it is incorrect. (b) The magnitude of \(a\) relates to attractions between molecules, whereas \(b\) relates to molecular volume. This statement correctly represents the roles of constants 'a' and 'b' in the van der Waals equation. So, this statement is true. (c) The magnitudes of \(a\) and \(b\) depend on pressure. The values of 'a' and 'b' are determined by the nature of the gas molecules, not by the pressure. So, this statement is incorrect. (d) The magnitudes of \(a\) and \(b\) depend on temperature. The values of 'a' and 'b' are determined by the nature of the gas molecules, not by the temperature. So, this statement is incorrect.
04

Conclusion

Based on our understanding of the van der Waals constants and evaluating the given statements, the correct answer is: (b) The magnitude of \(a\) relates to attractions between molecules, whereas \(b\) relates to molecular volume.

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