Chapter 6, Problem 6.51P

Interpretation Introduction

Interpretation:

For n-butane, the molar volume, enthalpy and entropy as a saturated vapor as well as saturated liquid at 370 K needs to be calculated.

Concept Introduction:

The equation used to calculate the molar volume of vapor is:

  $V_{vap}=\frac{ZRT}{P}$ .......(1)

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature of the system, and $R$ is the universal gas constant. $Z$ is the compressibility factor and is defined as:

  $Z=Z^0+\omega Z^1$ .......(2)

Here, $\omega$ is an acentric factor given in table B.1 and $Z^0\text{ and }{Z}^1$ are given in table D.1 and D.2.

The formula to calculate enthalpy of vapor $\left(H_{vap}\right)$ is:

  $H_{vap}=H_0^{ig}+{\displaystyle {\int }_{T_0}^T{C}_p^{ig}dT}+H^R$ .......(3)

Here, $H_0^{ig}$ is ideal-gas state enthalpy at initial temperature. Value of $C_p^{ig}$ is taken from table C.1. $H^R$ is defined as:

  $H^R={\left(H^R\right)}^0+\omega {\left(H^R\right)}^1$ .......(4)

Here, ${\left(H^R\right)}^0\text{ and }{\left(H^R\right)}^1$ are given in table D.5 and D.6.

The formula to calculate entropy of vapor $\left(S_{vap}\right)$ is:

  $S_{vap}=S_0^{ig}+{\displaystyle {\int }_{T_0}^T{C}_p^{ig}\frac{dT}{T}}-R\ln \frac{P}{P_0}+S^R$ .......(5)

Here, $S_0^{ig}$ is ideal-gas state entropy at initial temperature. Value of $C_p^{ig}$ is taken from table C.1. $S^R$ is defined as:

  $S^R={\left(S^R\right)}^0+\omega {\left(S^R\right)}^1$ .......(6)

Here, ${\left(S^R\right)}^0\text{ and }{\left(S^R\right)}^1$ are given in table D.9 and D.10.

To calculate molar volume of saturated liquid, the formula to be used is:

  $V_{liq}=V_c{Z}_c^{{\left(1-T_r\right)}^{2/7}}$ .......(7)

Equation to calculate enthalpy of liquid $\left(H_{liq}\right)$ is:

  $H_{liq}=H_{vap}-\Delta H$ .......(8)

Here, $\Delta H$ is heat of vaporization at the required temperature.

Equation by Reidel to calculate heat of vaporization at normal boiling point $\left(T_n\right)$ is:

  $\Delta H_n=R{T}_n\frac{1.092\left(\ln P_c-1.013\right)}{0.930-T_{rn}}$ .......(9)

Watson equation to calculate heat of vaporization at any temperature using known heat of vaporization at another temperature is:

  $\frac{\Delta H_2}{\Delta H_1}={\left(\frac{1-T_{r2}}{1-T_{r1}}\right)}^{0.38}$ .......(10)

Equation to calculate entropy of liquid $\left(S_{liq}\right)$ is:

  $S_{liq}=S_{vap}-\frac{\Delta H}{T}$ .......(11)