Chapter 4, Problem 4.13P

Interpretation Introduction

Interpretation:

To find $\Delta V$ from the vapor pressure equation and $\Delta H$ from the equations and comparing with the value of table.

Concept Introduction:

We calculate the liquid volume and vapor volume for Acetone using the below equations’

  $Z=1+B_0\times \frac{P_r}{T_r}+\omega B_1\times \frac{P_r}{T_r}$

  $B_0=0.083-\frac{0.422}{T_r^{1.6}}$

  $B_1=0.139-\frac{0.172}{T_r^{4.2}}$

  $T_r=\frac{T_n}{T_c}$ and $P_r=\frac{P}{P_c}$

  $T_n$ =Normal boiling point = 329.4 K

  $T_c$ = Critical Temperature

  $P_c$ = Critical Pressure

  $P_{sat}$ = Saturated Pressure

Z = Compressibility Factor

  $\Delta H_n$ = Latent heat of vaporization = 29.1 kJ/mol

  $\Delta H_{calc}$ = Calculated Latent heat of vaporization

R = Universal Gas constant

  $V_{sat}=V_c\times Z_c{}^{\left(1-T_r\right)\frac{2}{7}}$

  $V_{sat}$ = Saturated Volume

  $V_c$ = Critical Volume

Z_C = Compressibility Factor at critical conditions

Antoine equation is as below

  $P_{sat}=e^{A-\frac{B}{T+C}}$

A, B, C are constants of Antoine equation

  $P_{sat}$ = Saturated Pressure

Clapeyron equation is as below

  $\Delta H_{calc}=T\times \Delta V\times \frac{d{P}_{sat}}{dT}$

where,

  $\Delta V=V-V_{sat}$ = Change in volume

  $\Delta H_{calc}$ = Calculated change of enthalpy