When kaolinite clay \(\left[\mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)(\mathrm{OH})_{4}\right]\) is heated to a sufficiently high temperature, chemical water is driven off. (a) Under these circumstances, what is the composition of the remaining product (in weight percent \(\mathrm{Al}_{2} \mathrm{O}_{3}\) )? (b) What are the liquidus and solidus temperatures of this material?

When kaolinite clay is heated, the chemical water is driven off, and the reaction can be represented as follows: \(\mathrm{Al}_{2}\left(\mathrm{Si}_{2}\mathrm{O}_{5}\right)(\mathrm{OH})_{4} \xrightarrow{heat} \mathrm{Al}_{2} \mathrm{O}_{3}+2\mathrm{SiO}_{2}+2\mathrm{H}_{2}\mathrm{O}\)

We need to find the molar mass of kaolinite clay (\(\mathrm{Al}_{2}(\mathrm{Si}_{2}\mathrm{O}_{5})(\mathrm{OH})_{4}\)), \(\mathrm{Al}_{2} \mathrm{O}_{3}\) and \(\mathrm{SiO}_{2}\). Molar Mass of Kaolinite clay: \(M_{\mathrm{Al}_{2}(\mathrm{Si}_{2}\mathrm{O}_{5})(\mathrm{OH})_{4}} = 2 M_{\mathrm{Al}} + 2 M_{\mathrm{Si}} + 9 M_{\mathrm{O}} + 4 M_{\mathrm{H}} = 2(26.98) + 2(28.09) + 9(16) + 4(1.01)= 258.16\,\mathrm{g/mol}\) Molar Mass of \(\mathrm{Al}_{2} \mathrm{O}_{3}\): \(M_{\mathrm{Al}_{2} \mathrm{O}_{3}} = 2M_{\mathrm{Al}} + 3M_{\mathrm{O}} = 2(26.98) + 3(16) = 101.96\,\mathrm{g/mol}\) Molar Mass of \(\mathrm{SiO}_{2}\): \(M_{\mathrm{SiO}_{2}} = M_{\mathrm{Si}} + 2M_{\mathrm{O}} = (28.09) + 2(16) = 60.09\,\mathrm{g/mol}\)

We can now calculate the weight percent of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) in the remaining product after the chemical water has been driven off, based on the stoichiometry of the reaction and the ratio of the number of moles of each compound: Weight percent of \(\mathrm{Al}_{2} \mathrm{O}_{3} = \frac{1\,mol\,\mathrm{Al}_{2} \mathrm{O}_{3} \cdot M_{\mathrm{Al}_{2} \mathrm{O}_{3}}}{1\,mol\,\mathrm{Al}_{2} \mathrm{O}_{3} \cdot M_{\mathrm{Al}_{2} \mathrm{O}_{3}}+ 2\,moles\,\mathrm{SiO}_{2} \cdot M_{\mathrm{SiO}_{2}}}\times 100 = \frac{101.96}{101.96 + 2(60.09)}\times 100 = 46.3\,\%\) (a) The composition of the remaining product is 46.3% \(\mathrm{Al}_{2} \mathrm{O}_{3}\) by weight.

We do not have enough information in the problem to determine the liquidus and solidus temperatures. One approach to finding these temperatures would be to consult phase diagrams for the \(\mathrm{Al}_{2} \mathrm{O}_{3}\)- \(\mathrm{SiO}_{2}\) system. However, this information has not been given in the problem. As a result, we cannot find the liquidus and solidus temperatures.