Question

Aluminium oxide contains 52.9% aluminium and carbon dioxide 27.2% carbon. Assuming that the law of Reciprocal proportion is true, the percentage of aluminium in aluminium carbide will be
1. 1.123%
2. 0.375%
3. 74.97%
4. None of these

Answer 1

Correct Answer - Option 3 : 74.97%

Concept: 

• The law of reciprocal proportions was proposed by Jeremias Ritcher in 1792.
• It states that, "If two different elements combine separately with the same weight of a third element, the ratio of the masses in which they do so are either the same or a simple multiple of the mass ratio in which they combine."

Calculation:

Given: In Al₂O₃, % of Al = 52.9%, % of O = 100 -52.9 = 47.1%

In CO₂,

% of Carbon = 27.27%

% of Oxygen = 72.73%

In Al₂O₃

∵ 52.9 gm Al gives oxygen after reaction = 72.73 gm O₂

∴ 1 gm O₂ Obtained by = \(\frac{{52.9}}{{47.1}} = 1.21 \approx 1\)

So that in CO₂

∵ 27.27 gm Carbon gives 72.73 gm O₂ after reaction.

∴ 1 gm O₂ Obtained by = \(\frac{{27.27}}{{72.73}} = 0.37\)

So, 1 gm Oxygen reacts with Al & C

\(\frac{{1.12}}{{0.32}} = 3:01\)

∴  \({\rm{Quantity\;of\;Al\;}} = \frac{{Part\;of\;Al}}{{Total\;Part}} \times 100 = \frac{3}{4} \times 100 = 75\% \approx 74.97\% \)

So, 74.97% is correct.