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Explain Bayer's method for obtaining alumina from bauxite with equations?

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Hint- In order to deal with this question first we will discuss the Bayer's method then we will proceed further by understanding the process and steps that take place in obtaining alumina from bauxite and according to it we will write the equations.

Complete answer:
Bayer's method: In this method, bauxite powder is taken and concentrated (45%) and sodium hydroxide solution is added and then heated in a closed vessel at 433 K temperature and 5 to 6 bars of pressure, for 6 to 8 hours, so that aluminium oxide present in bauxite is converted into sodium aluminate which is soluble in water. In bauxite, in addition to aluminium oxide impurities like iron oxide and sand are also present. On refining bauxite by Bayer’s method, pure aluminium oxide is obtained which is also called alumina.
$A{l_2}{O_3}\left( s \right) + 2NaOH\left( {aq} \right) \to 2NaAl{O_2}\left( {aq} \right) + {H_2}O\left( l \right)$
Iron oxide does not dissolve in sodium hydroxide. Hence, it can be removed by filtration. Silica forms sodium silicate which is soluble in water. This sodium aluminate and sodium silicate are there in the filtrate. Excess of water is added to it and continuously stirred so that hydrolysis of sodium aluminate takes place and precipitates of aluminium hydroxide are obtained and the sodium silicate remains as an impurity in the solution. Some precipitates of aluminium hydroxide are added from outside in order to make the reaction simple and fast.
$NaAl{O_2}\left( {aq} \right) + 2{H_2}O\left( l \right) \to Al{\left( {OH} \right)_3}\left( s \right) + NaOH\left( {aq} \right)$
The precipitates are washed repeatedly with water, dried and on heating at 1473 K temperature pure aluminium oxide (alumina) is obtained.
\[2Al{\left( {OH} \right)_3}\left( s \right) \to \left[ {1473K} \right]A{l_2}{O_3}\left( s \right) + 3{H_2}O\left( g \right)\]

Thus, about 99.5 % pure alumina is obtained by Bayer’s method.

Note- Bauxite is a rock formed from a reddish clay substance called laterite soil, which is found most frequently in tropical or subtropical areas. Bauxite consists primarily of aluminum oxide (alumina), silica, iron oxides, and titanium dioxide compounds. It is the principal source of aluminum and gallium in the world. Aluminium is a lightweight, silvery-white metal. It is gentle and malevolent. Aluminum is used in a wide variety of items from canisters, foils, cooking utensils, window frames, beer kegs and aircraft parts.