Question

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.

Answer 1

To answer this question we must have the knowledge of the law of reciprocal proportion. These both elements combine with oxygen and then with each other, so the ratio of their mass will remain the same.

Complete step by step solution:
Let us first look at the definition of law of reciprocal proportion:
If element A combines with element B and also with element C, then, if B and C combine together, the proportion by weight in which they do so will be related to the weights of B and C which separately combine with a constant weight of A.
In our question element A is oxygen that combines with both element B and C that is aluminium and carbon respectively to form aluminium oxide and carbon dioxide. Then element B and C combine together to form aluminium carbide. So this fits well will the statement of law and hence the ratio in which they combine will be the same as they combine with A.
let us for the amount of oxygen 1 g. Percentage of aluminium in aluminium oxide is $52.9\%$, hence the percentage of oxygen will be $100 - 52.9\% = 47.1\%$. That means,
$47.1{\text{ g}}$ of oxygen combined with $52.9{\text{ g}}$ of aluminium.
1 g of oxygen will combine with $\dfrac{{52.9}}{{47.1}}{\text{ g }} = 1.123{\text{ g}}$ of aluminium
Percentage of carbon in carbon dioxide is $27.27\%$, hence the percentage of oxygen will be $100 - 27.27\% = 72.73\%$. That means,
${\text{72}}{\text{.73 g}}$ of oxygen combined with $27.27{\text{ g}}$ of carbon.
1 g of oxygen will combine with $\dfrac{{27.27}}{{72.73}}{\text{ g }} = 0.375{\text{ g}}$ of carbon.
Hence the ratio of aluminium : carbon will be $1.123:0.375$ and it will be same in aluminium carbide as well,
${\text{percentage of Al in aluminium carbide}} = \dfrac{{1.123}}{{1.123 + 0.375}} \times 100$
Solving this we get:
${\text{percentage of Al in aluminium carbide}} = \dfrac{{1.123}}{{1.498}} \times 100 = 75\%$
Hence, the answer is $75\%$ .

Note: The law of reciprocal proportion was designed by Jeremias Richter. He used this law for the neutralization of the ratio of metal with acid. As we have calculated the percentage of aluminium we can calculate the percentage of carbon by subtracting the percentage of aluminium from 100.