Engineering, 14.02.2020 21:59, mikkelf6158
CaF2 and MgF2 are mutually insoluble in the solid state and form a simple binary eutectic system. Calculate the composition and temperature of the eutecdc melt assuming that the liquid solutions are Raoultian. The actual eutectic occurs at X CaF2 = 0.45 and T = 1243 K.
Answers: 1
![X_{CaF_2} = e^{[-\frac{\delta G_M(CaF_2)}{RT}]} \\\\X_{MgF_2} = e^{[-\frac{\delta G_M(MgF_2)}{RT}]} \\\\](/tpl/images/0511/8853/72c09.png)
![X_{CaF_2} = 1- e^{[-\frac{\delta G_M(MgF_2)}{RT}]} \\](/tpl/images/0511/8853/91598.png)
![e^{[-\frac{\delta H_m(_{CaF_2}) - T( \frac{\delta H_m}{T_m})(_{CaF_2})}{RT}]} = 1-e^{[-\frac{\delta H_m(_{MgF_2}) - T( \frac{\delta H_m}{T_m})(_{MgF_2})}{RT}]}](/tpl/images/0511/8853/da32f.png)
![e^{[-\frac{31200- T( \frac{31200}{1691})}{8.314T}]} = 1-e^{[-\frac{58160 - T( \frac{58160}{1563})}{8.314T}]}\\\\e[^{\frac{-3752.71}{T} + 2.219}] = 1 - e[^{\frac{-6995.429}{T} + 4.475}]](/tpl/images/0511/8853/ea2ec.png)
![[\frac{-3752.71}{T} +2.219] = -[\frac{-6995.429}{T} +4.475]\\\\\frac{-3752.71}{T} +2.219 = \frac{6995.429}{T} - 4.475\\\\\frac{6995.429}{T} +\frac{3752.71}{T} = 2.219 + 4.475\\\\\frac{10748.139}{T} = 6.694\\\\T = \frac{10748.139}{6.694} = 1605 K](/tpl/images/0511/8853/b90c0.png)
![X_{CaF_2} = e^{[-\frac{31200- 1605(\frac{31200}{1691})}{8.314*1605}]}\\\\= e[^-2.338 +2.219]\\\\= e^{(-0.119)}\\= 0.887](/tpl/images/0511/8853/dd625.png)
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CaF2 and MgF2 are mutually insoluble in the solid state and form a simple binary eutectic system. Ca...
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