When 0.4 mols of $A l_{2} O_{3}$ is heated with carbon, a brown solid X is formed along with evolution of a neutral gas which burns with blue flame.
What amount (in gm) of methane gas will be formed when X so formed is completely hydrolyzed with water?

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Solution

$2 A l_{2} O_{3} + 9 C ⟶ A l_{4} C_{3}_{(B r o w n s o l i d)} + 6 C O_{(g)}$
So, when 0.4 mol of $A l_{2} O_{3}$ is heated with carbon, 0.2 mols of $A l_{4} C_{3}$ will be formed.
$A l_{4} C_{3} + 12 H_{2} O ⟶ 4 A l (O H)_{3} + 3 C H_{4}_{(g)}$
0.2 mols of $A l_{4} C_{3}$ on complete hydrolysis will give $0.2 \times 3 = 0.6$ moles of $C H_{4}$ = 9.6 g of $C H_{4}$

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