CHEM 3070 Problem Set 10 Due on Friday, 4/1/2016 1. At fixed pressure p, a perfectly ideal solution of two miscible liquids is defined by the...

Will someone help me with 2 c, d, and f please?  

Just as a slight warning, this is an advanced thermodynamics question. I've had other tutors try to help with similar questions, but they used general chemistry reasoning and the answers turned out to be wrong. 

I have attached the complete problem set, which may make the questions more clear. 

2. This problem also concerns the boiling of an ideal mixture of miscible liquids. Whereas the previ-ous problem developed a phase diagram in the plane of temperature and composition (with pressureheld fixed), here you will construct a phase diagram in the plane of pressure and composition (withtemperature held fixed).First consider the liquid and vapor phases of a pure substance. As in the previous problem, we denotethe chemical potential of the pure liquid µ∗(T, p). The chemical potential of the dilute vapor has anideal form:µ(v)(T, p) = µ(0) + kBT ln(p/p∗),(3)where p∗ is the pressure at which liquid and vapor coexist. (p∗ is often referred to as the "vaporpressure" of the liquid. It depends on temperature, but since T is fixed we will not burden ourselveswith writing this dependence explicitly. For the purposes of this problem, p∗ is just a constant thatdefines a standard state.)

(c)For pressures not too different from p∗, we may approximate the pressure dependence of µ∗(T, p)by Taylor expansion,

µ∗(T, p) = µ∗(T, p∗) + (something) × (p − p∗).

Perform this Taylor expansion.

(d)For the rest of this problem, we will neglect the pressure dependence of µ∗(T, p) that you calculatedin part (c).In other words we will take

µ∗(T, p) ≈ µ∗(T, p∗).

Explain why this approximation is reasonable.To support your argument, you might calculate avalue for [µ∗(T, p) − µ∗(T, p∗)]/(kBT) for the case of a liquid (such as water) at p = p∗ + 10atm.

(f)Using Raoult's Law, together with the constraints x

(l)1 + x

(l)2 = 1 and p1 + p2 = p, determine the

mole fraction x

(l)1 (p) of species 1 in the liquid phase when it coexists with vapor at total pressure

p.

(f) Using Raoult's Law, together with the constraints x

(l)1 + x

(l)2 = 1 and p1 + p2 = p, determine the

mole fraction x

(l)1 (p) of species 1 in the liquid phase when it coexists with vapor at total pressure

p.