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 $1g$ of oxygen as the fixed weight.
In $A{l}_2{O}_3,47.1g$ of $O$ combines with $=52.9gAl$
$\therefore 1g$ of $O$ will combine with $=\frac{52.9}{47.1}g$
$=1.123gAl$
In $C{O}_2,72.73g$ of $O$ combines with $=27.27gC$
$\therefore 1g$ of $O$ will combine with
$=\frac{27.27}{72.73}g=0.375gC$
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 $A{l}_4{C}_3$
$=\frac{1.123}{1.123+0.375}\times 100$
$=\frac{1.123}{1.498}\times 100=74.97\%$