Chapter 5, Problem 5B.7AE

(i)

Interpretation Introduction

Interpretation: The proportions of hexane and heptane that should be mixed by mole fraction in order to achieve the highest entropy have to be calculated.

Concept introduction: Mole fraction is the ratio of the number of moles of a component and the total moles of the solution.  It has no units.  The formula to calculate the mole fraction is,

    $x_{\text{A}}=\frac{n_{\text{A}}}{n_{\text{A}}+n_{\text{B}}}$

Where,

• $n_{\text{A}}$ is the number of moles of A.
• $n_{\text{B}}$ is the number of moles of B.

(ii)

Interpretation Introduction

Interpretation: The proportions of hexane and heptane that should be mixed by mass in order to achieve the highest entropy have to be calculated.

Concept introduction: The increase in entropy when, two individual systems are mixed without a chemical reaction is called entropy of mixing.  The formula to calculate the entropy of mixing is,

    ${\Delta }_{\text{mix}}S=-nR\left(x_{\text{A}}\ln x_{\text{A}}+x_{\text{B}}\ln x_{\text{B}}\right)$

Where,

• $n$ is the total moles.
• $R$ is the gas constant.
• $x_{\text{A}}$ and $x_{\text{B}}$ are the mole fractions of component $\text{A}\text{and}\text{B}$, respectively.