Question

Aluminium oxide contains $52.9\%$ aluminium and carbon dioxide cantains $27.27\%$ carbon. Assuming that the law of reciprocal proportions is true, calculate the percentage of aluminium in aluminium carbide.

• A. 47.12%
• B. 59.33%
• C. 74.97%
• D. 61.10%

Answer 1

Answer: (C)

Let us take $1 \,g$ of oxygen as the fixed weight.
In $Al_2O_3, 47.1 \,g$ of $O$ combines with $= 52.9 \,g \,Al$
$\therefore 1\, g$ of $O$ will combine with $ = \frac{52.9}{47.1} g$
$ = 1.123\,g\,Al$
In $CO_2, 72.73 \,g$ of $O$ combines with $= 27.27 \,g \,C$
$\therefore 1\,g $ of $O$ will combine with
$ = \frac{27.27}{72.73} \,g = 0.375\,g\,C$
The ratio by weight of aluminium and carbon combining with a fixed weight of oxygen in the two oxides $= 1.123 : 0.375$.
Since the law of reciprocal proportions is true, aluminium and carbon are in the same ratio or in simple multiple ratio of their weights.
$\therefore $ Percentage of $Al$ in $Al_4C_3$
$ = \frac{1.123}{1.123 + 0.375} \times 100$
$ = \frac{1.123}{1.498} \times 100 = 74.97\%$