Problem $2$

The molar enthalpy of a binary liquid mixture of species $1$ and $2$ is given by:

$H=a{x}_1+b{x}_2+c{x}_1{x}_2[\frac{?}{\text{m}\text{o}\text{l}}]$

where $a=275+75T,b=125+50T,c=750[\frac{J}{m}ol]$

where the temperature $T$ is in Kelvin.

a$.$ Derive the expression for the partial molar enthalpy of the species $1.$

b$.$ Using the result of a calculate the infinite dilution value for the partial molar enthalpy of the species $1$ at the temperature

$200C.$

c$.$ Calculate the enthalpy of mixing $($in J$)$ of a mixture with $2$ moles of species I and $3$ moles of species $2$ at $200C?$

d$.$ Consider the adiabatic mixing of a stream of pure $1$ flowing at $2mo\frac{l}{s}$ with a stream of pure $2,$ flowing at $3$ molls. Both

inlet streams are at $200$ C$.$ What is the exit temperature of the mixture?