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Which is more basic \[A{l_2}{O_3}\]or\[MgO\]?

Answer
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Hint: Keep in mind the periodic table while answering this question. Mg belongs to the s block whereas Al belongs to the p block. Thus we can say that Mg is left to Al in terms of a period.
Also consider that \[A{l_2}{O_3}\] is an amphoteric oxide. Metal oxides which react with both acids as well as bases to produce salts and water are known as amphoteric oxides. As a rule all the metal oxides will be basic and all the non-metal oxides are acidic.

Complete answer:
There are many things that point out to the fact that \[MgO\] is more basic than \[A{l_2}{O_3}\].
We observe that metals are mostly present on the left side of the periodic table and nonmetals towards the right side of a period. Since the oxides of non-metals are acidic and that of metals are basic we say that along a period from left to right basic character decreases.
Observing the periodic table and the positions of Mg and Al we can conclude that \[MgO\]is more basic than \[A{l_2}{O_3}\].
Another point that confirms the answer is that \[A{l_2}{O_3}\] is an amphoteric oxide whereas \[MgO\] is a basic metal oxide. Which gives us more confirmation that \[MgO\] is more basic than\[A{l_2}{O_3}\]

Note:
\[{K_2}O\]\[MgO\]\[A{l_2}{O_3}\]\[Si{O_2}\]\[C{O_2}\]
Strongly Basic BasicAmphotericWeakly AcidicAcidic

Also as we go down a group the basicity of oxides increases with increases. For example in group V, \[N{O_2}\]and \[{P_4}{O_8}\] are acidic, \[A{s_2}{O_4}\]and \[S{b_2}{O_3}\] are amphoteric, \[B{i_2}{O_3}\] is basic.
Even when we consider the oxides of the second group elements basicity increase in the following order
\[BeO{\text{ }} < {\text{ }}MgO{\text{ }} < {\text{ }}CaO{\text{ }} < {\text{ }}SrO{\text{ }} < {\text{ }}BaO\]