Which expression represents the van der Waals equation of state?

Which expression represents the van der Waals equation of state?

• A. P = RT/(V - b) - a/V^2
• B. k = A e^(-Ea/RT)
• C. ΔP = 8 μ L Q /(π r^4)
• D. P = RT/(V - b) - a/V^2

Answer: (D)

Real gases don’t behave like ideal gases because molecules have finite size and attract each other. The van der Waals equation introduces two corrections to capture that: a term that reduces the effective pressure due to attractions, and a term that reduces the available volume due to finite molecular size. The expression P = RT/(V - b) - a/V^2 uses V as molar volume (V_m) and includes these corrections: the denominator (V - b) accounts for the space the molecules cant occupy, while the subtractive a/V^2 term lowers the pressure because intermolecular attractions hold molecules together a bit, especially at higher densities. This form is the standard van der Waals equation of state for a real gas. The other options come from different topics (reaction kinetics and fluid flow) and do not describe a gas’s equation of state.

Real gases don’t behave like ideal gases because molecules have finite size and attract each other. The van der Waals equation introduces two corrections to capture that: a term that reduces the effective pressure due to attractions, and a term that reduces the available volume due to finite molecular size. The expression P = RT/(V - b) - a/V^2 uses V as molar volume (V_m) and includes these corrections: the denominator (V - b) accounts for the space the molecules cant occupy, while the subtractive a/V^2 term lowers the pressure because intermolecular attractions hold molecules together a bit, especially at higher densities. This form is the standard van der Waals equation of state for a real gas. The other options come from different topics (reaction kinetics and fluid flow) and do not describe a gas’s equation of state.