The following is a set of VLE data for the system methanol$(1)/$water$(2)$ at $333\mathrm{.}15$ K:

P$/$kPa x$1$ y$1$ P$/$kPa x$1$ y$1$

$19\mathrm{.}9530\mathrm{.}00000\mathrm{.}000060\mathrm{.}6140\mathrm{.}52820\mathrm{.}8085$

$39\mathrm{.}2230\mathrm{.}16860\mathrm{.}571463\mathrm{.}9980\mathrm{.}60440\mathrm{.}8383$

$42\mathrm{.}9840\mathrm{.}21670\mathrm{.}626867\mathrm{.}9240\mathrm{.}68040\mathrm{.}8733$

$48\mathrm{.}8520\mathrm{.}30390\mathrm{.}694370\mathrm{.}2290\mathrm{.}72550\mathrm{.}8922$

$52\mathrm{.}7840\mathrm{.}36810\mathrm{.}734572\mathrm{.}8320\mathrm{.}77760\mathrm{.}9141$

$56\mathrm{.}6520\mathrm{.}44610\mathrm{.}774284\mathrm{.}5621\mathrm{.}00001\mathrm{.}0000$

Extracted from K$.$ Kurihara et al$.,$ J$.$ Chem. Eng. Data, vol. $40,$ pp$.679684,1995.$

$($a$)$ Basing calculations on Eq$.(13\mathrm{.}24),$ find parameter values for the Margules equation

that provide the best fit of GE$$RT to the data, and prepare a Pxy diagram

that

compares the experimental points with curves determined from the correlation.

$($b$)$ Repeat $($a$)$ for the van Laar equation.

$($c$)$ Repeat $($a$)$ for the Wilson equation.

$514$ CHAPTER $13.$ Thermodynamic Formulations for Vapor$/$Liquid Equilibrium

P$/$kPa x$1$ y$1$ P$/$kPa x$1$ y$1$

$68\mathrm{.}7280\mathrm{.}00000\mathrm{.}000097\mathrm{.}6460\mathrm{.}50520\mathrm{.}5844$

$72\mathrm{.}2780\mathrm{.}02870\mathrm{.}064798\mathrm{.}4620\mathrm{.}54320\mathrm{.}6174$

$75\mathrm{.}2790\mathrm{.}05700\mathrm{.}129599\mathrm{.}8110\mathrm{.}63320\mathrm{.}6772$

$77\mathrm{.}5240\mathrm{.}08580\mathrm{.}184899\mathrm{.}9500\mathrm{.}66050\mathrm{.}6926$

$78\mathrm{.}9510\mathrm{.}10460\mathrm{.}2190100\mathrm{.}2780\mathrm{.}69450\mathrm{.}7124$

$82\mathrm{.}5280\mathrm{.}14520\mathrm{.}2694100\mathrm{.}4670\mathrm{.}73270\mathrm{.}7383$

$86\mathrm{.}7620\mathrm{.}21730\mathrm{.}3633100\mathrm{.}9990\mathrm{.}77520\mathrm{.}7729$

$90\mathrm{.}0880\mathrm{.}27870\mathrm{.}4184101\mathrm{.}0590\mathrm{.}79220\mathrm{.}7876$

$93\mathrm{.}2060\mathrm{.}35790\mathrm{.}477999\mathrm{.}8770\mathrm{.}90800\mathrm{.}8959$

$95\mathrm{.}0170\mathrm{.}40500\mathrm{.}513599\mathrm{.}7990\mathrm{.}94480\mathrm{.}9336$

$96\mathrm{.}3650\mathrm{.}44800\mathrm{.}551296\mathrm{.}8851\mathrm{.}00001\mathrm{.}0000$

Extracted from D$.$ C$.$ Freshwater and K$.$ A$.$ Pike, J$.$ Chem. Eng. Data, vol. $12,$

pp$.179183,1967.$

$($d$)$ Using Barker$$s method, find parameter values for the Margules equation that provide

the best fit of the P$$x$1$ data. Prepare a diagram showing the residuals $\backslash$delta P and

$\backslash$delta y$1$ plotted vs$.$ x$1.$

$($e$)$ Repeat $($d$)$ for the van Laar equation.

$($f$)$ Repeat $($d$)$ for the Wilson equation.