A natural gas stream 90 mol % CH₄ (component 1) contaminated with 10 mol % CO₂ (component 2). In order to calculate pumping requirements you are asked to perform calculations of properties of the gas mixture at 300 K and 10 bar.  To a reasonable first approximation this gas mixture can be represented by the van der Waals equation of state with the van der Waals mixing rules. Pure component constants for the van der Waals equation of state are a=0.2303Pa m⁶/mol², b=4.306 × 10⁻⁵m³/mol for CH₄ and a=0.3658Pa m⁶/mol², b=4.286 × 10⁻⁵m³/mol for CO₂. [The binary interaction parameter k_ij may be taken to be 0.]

a. Calculate the molar volume of the mixture at 300 K and 10 bar. 

b. Calculate the difference between the real and ideal gas molar enthalpies of this mixture at 300 K and 15 bar. 

c. Calculate the difference between the real and ideal gas molar entropies of this mixture at 300 K and 15 bar.