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

Explanation

Let us fix `1g` of oxygen with `Al = 52.9 g`
In `Al_(2)O_(3),47.1 g` of O are combined with `Al = 52.9 g`
`:. 1.0` g of O is combined with `Al=(52.9)/(47.1)g=1.123g`
In `CO_(2),72.73 g` of O are combined with `C = 27.27 g`
`:.` 1.0 g of O is combined with `C=(27.27)/(72.73)g=0.375g`
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 truem aluminium and carbon in aluminium carbide will combine either in the same ratio or in simple multiple ratio of their weights
`:.` Percentage of `Al` in `Al_(4)C_(3)=(1.123)/(1.123+0.375)xx100=(1.123)/(1.495)xx100=74.97%`.