Non-Ideal Gases and Redlich-Kwong Equation of State

Question

(A) One good way to treat nonideal gases is the Redlich-Kwong equation of state,  

P = RT /(V-b) - a/√T(V(V+b))

where a and b are constants that depend the identity of the gas (i.e., they can be found from critical constants similar to what is done for the van der Waals equation of state, but the formulas are different).  Determine the formula for the following partial derivative of the Redlich-Kwong equation of state,

(∂P/∂Vm)T  

(B) Five moles of methane are confined to a container with volume 20 L at 300K. Estimate the pressure using the ideal gas equation of state. Give your answer in atm.

(C) Estimate the pressure in B using the van der Waals equation of state. Give your answer in atm.

(D) Estimate the pressure in B using the Redlich-Kwong equation of state given the Redlich-Kwong constants for methane are a = 3.2 Pa m⁶ mol² K^½ and b = 2.96 × 10^-5 m³ mol^-1. Give your answer in atm.

Summary

The question belongs to Chemical Engineering and it is about Redlich-Kwong equation state where given a and b are constants. The formula for the partial derivative of Redlich-Kwong needs to be derived. The other questions are about calculating the pressure of ideal gas for five moles of methane.

Note: The solution is in handwritten format.