Question

Briefly explain the significance of the constants \(a\) and \(b\) in the van der Waals equation.

Short answer

The constants \(a\) and \(b\) in the van der Waals equation are significant because they account for the deviations of real gases from the ideal gas law. The constant \(a\) represents the attractive forces between gas molecules, with a larger value indicating stronger forces. The constant \(b\) represents the volume occupied by each particle, accounting for the finite size of gas molecules. These constants improve the ideal gas law by considering molecular interactions and sizes, leading to a more accurate description of the behavior of real gases.

Step-by-step solution

Introduce the van der Waals equation.

The van der Waals equation is given by \[ \left(P + \frac{a}{V^2}\right) (V - b) = nRT, \] where \(P\) is the pressure, \(V\) is the molar volume, \(n\) is the amount of substance in moles, \(T\) is the temperature, \(R\) is the ideal gas constant, and \(a\) and \(b\) are constants specific to each gas.

Discuss the constant "a"

The constant \(a\) is called the van der Waals constant for attraction. It takes into account the attractive forces between gas molecules. A larger value of \(a\) means that the attractive forces between the molecules are stronger. The term \(\frac{a}{V^2}\) in the van der Waals equation thus represents the attractive forces between particles that are not considered in the ideal gas law.

Discuss the constant "b"

The constant \(b\) is called the van der Waals constant for repulsion or the excluded volume. It represents the volume occupied by each particle, i.e., the finite size of the gas molecules. In the ideal gas law, it is assumed that the gas molecules are point-like and have a zero volume. However, in reality, gas molecules have a finite volume, and this is represented by the constant \(b\). The term \((V - b)\) in the van der Waals equation accounts for the real volume available for the gas molecules to move around. In conclusion, the constants \(a\) and \(b\) in the van der Waals equation are significant as they improve the ideal gas law by accounting for the attractive forces between particles (\(a\)) and the finite size of the particles (\(b\)).