Thermodynamics: An Engineering Approach 8th Edition

Published by McGraw-Hill Education
ISBN 10: 0-07339-817-9
ISBN 13: 978-0-07339-817-4

Chapter 16 - Chemical and Phase Equilibrium - Problems - Page 833: 16-78

Answer

$223.1\text{ kPa}$

Work Step by Step

According to Raoults's law, the partial pressures of ammonia and water are given by $$ \begin{aligned} & P_{\mathrm{g}, \mathrm{NH} 3}=y_{f, \mathrm{NH} 3} P_{\mathrm{sat}, \mathrm{NH} 3} \\ & P_{\mathrm{g}, \mathrm{H} 2 \mathrm{O}}=y_{f, \mathrm{H} 2 \mathrm{O}} P_{\mathrm{sat}, \mathrm{H} 2 \mathrm{O}}=\left(1-y_{f, \mathrm{NH} 3}\right) P_{\mathrm{sat}, \mathrm{H} 2 \mathrm{O}} \end{aligned} $$ Using Dalton's partial pressure model for ideal gas mixtures, the mole fraction of the ammonia in the vapor mixture is $$ \begin{aligned} y_{g, \mathrm{NH} 3} & =\frac{y_{f, \mathrm{NH} 3} P_{\text {sat }, \mathrm{NH} 3}}{y_{f, \mathrm{NH} 3} P_{\mathrm{sat}, \mathrm{NH} 3}+\left(1-y_{f, \mathrm{NH} 3} P_{\mathrm{sat}, \mathrm{H} 2 \mathrm{O}}\right)} \\ 0.96 & =\frac{430.6 y_{f, \mathrm{NH} 3}}{430.6 y_{f, \mathrm{NH} 3}+0.6112\left(1-y_{f, \mathrm{NH} 3}\right)} \longrightarrow y_{f, \mathrm{NH} 3}=\mathbf{0 . 0 3 2 9 4} \end{aligned} $$ Then, $$ \begin{aligned} P & =y_{f, \mathrm{NH} 3} P_{\text {sat }, \mathrm{NH} 3}+\left(1-y_{f, \mathrm{NH} 3}\right) P_{\text {sal }, \mathrm{H} 2 \mathrm{O}} \\ & =(0.03294)(430.6)+(1-0.03294)(0.6112)=14.78\text{ kPa} \end{aligned} $$ Performing the similar calculations for the regenerator, $$ \begin{aligned} & 0.96=\frac{1830.2 y_{f, \mathrm{NH} 3}}{1830.2 y_{f, \mathrm{NH} 3}+10.10\left(1-y_{f, \mathrm{NH} 3}\right)} \longrightarrow y_{f, \mathrm{NH} 3}=\mathbf{0 . 1 1 7 0} \\ & P=(0.1170)(1830.2)+(1-0.1170)(10.10)=\mathbf{2 2 3 . 1\ k P a} \end{aligned} $$
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