Question

Copper sulphate crystal contains 25.45% $Cu$ and 36.07% \[H_2O\]. If the law of constant proportion is true, calculating the weight of Cu requires obtaining \[40{\text{ }}gram\] crystalline copper sulphate.

Answer 1

Hint: In this question we have to find the weight of copper required obtaining \[40{\text{ }}gram\] crystalline copper sulphate if the law of constant proportion is true. We have to physically apply the law that particular elements that compose a chemical compound are always present into a permanently fixed ratio in terms of their mass.

Complete step by step solution: No, not for all forms of substances, the law of constant proportion is not valid. The law of constant proportion is also known as the law of definite proportion. It is stated that the particular elements that compose a chemical compound are always present into a permanently fixed ratio in terms of their mass and this ratio does not depend on the surface of the chemical compound or the method through which it was prepared.
In other words, the law of constant proportion says that every pure substance always contains the same number of elements combined in the same proportions by weight. For example- pure form of water will always include hydrogen and oxygen in a predetermined mass ratio that cannot be changed.
Thus in this case the law of constant proportion is true.
So, From the given values
Crystalline Copper sulphate ($CuS{O_4}$ ) requires–
$100gram$ of crystal of sulphate \[\left( {S{O_4}} \right)\] needs \[25.45\] gram of Copper ($Cu$ )
So, $100gram$$CuS{O_4}.5{H_2}O \to 25.45gram\;Cu$
Therefore, $40\;gram$ $CuS{O_4}.5{H_2}O \to \dfrac{{25.45 \times 40}}{{100}} = 10.18 gram\;Cu$
Hence, \[10.18\] gram of copper is required in obtaining \[\;40\] gram crystalline copper sulphate.

Note: The law of constant proportion was firstly given by The French chemist namely Joseph-Louis Proust as he was the first person who has gather the convincing evidence for, the law of constant proportion in a series of all his researches on the composition of various substances.