Chapter 9.8, Problem 27P

Interpretation Introduction

Interpretation:

The change in entropy and enthalpy of the system of the system has to be determined.

Concept introduction:

The number of moles of nitrogen $\left(N_{nitrogen}\right)$ is expressed as,

$N_{nitrogen}=\frac{m_{nitrogen}}{M{W}_{nitrogen}}$

Here, mass of nitrogen is $m_{nitrogen}$, and molecular weight of water is $M{W}_{nitrogen}$.

The molecular weight of nitrogen $\left({\text{N}}_{\text{2}}\right)$ as $\text{28}\text{g}/\text{mole}$.

The mole fraction of nitrogen gas $\left(y_{nitrogen}\right)$.

$y_{nitrogen}=\frac{N_{nitrogen}}{N_{nitrogen}+N_{argon}}$

Here, number of moles of argon is $N_{argon}$.

The mole fraction of argon gas $\left(y_{argon}\right)$ is expressed as,

$y_{argon}=\frac{N_{argon}}{N_{argon}+N_{nitrogen}}$

The change in entropy $\left(\Delta S\right)$ of the system is expressed as,

$\begin{array}{c}\Delta S=N\left(-R{y}_{nitrogen}\ln y_{nitrogen}-R{y}_{argon}\ln y_{argon}\right)\\ \Delta S=\left(N_{nitrogen}+N_{argon}\right)\left(-R{y}_{nitrogen}\ln y_{nitrogen}-R{y}_{argon}\ln y_{argon}\right)\end{array}$

Here, gas constant is $R$.

The value of gas constant as $\text{8}\text{.314}\text{J}/\text{mol}\cdot \text{K}$.