A mixture contained aluminium sulphate and sodium sulphate. A sample of the mixture weighing $3.36 g$ was dissolved in water and treated with ammonium hydroxide. The precipitate formed was incinerated to yield $0.5 g$ of anhydrous aluminium oxide. What is the percentage of aluminium sulphate in the mixture (rounding to neatest integer)
$(At wts : A l = 27, N a = 23, S = 32, O = 16, N = 14, H = 1)$

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Detailed Solution

$A l_{2} {(S O_{4})}_{3} + 6 N H_{4} O H \to 2 A l {(O H)}_{3} + 3 {(N H_{4})}_{2} S O_{4}$

The reaction for the incerenation of the precipitate is

$2 A l {(O H)}_{3} \overset{Δ}{\to} A l_{2} O_{3} + 3 H_{2} O ∴ \frac{0.5 \times 2}{102} = 0.0098 \approx 0.01 m o l A l$

Wt of aluminium sulphate in the mixture $0.01 m o l A l \times 342 A l_{2} {(S O_{4})}_{3}$
$2 m o l A l$ is present in $342 g o f A l_{2} {(S O_{4})}_{3}$
$∴ 0.01 m o l A l is present in \frac{0.01 \times 342}{2} = 1.676 \approx 1.68 g % o f A l_{2} {(S O_{4})}_{3} in the mixture = \frac{1.68}{3.36} \times 100 = 50 %$