Question

A \[1800g\] mixture of anhydrous \[CuS{O_4}\] and its hydrated for \[\left( {CuS{O_4}.5{H_2}O} \right)\]undergoes \[20\% \] loss in mass on heating. Mole fraction of \[CuS{O_4}\] in mixture is (atomic mass of $Cu$ is $64$)
A.\[\dfrac{3}{{40}}\]
B.\[\dfrac{4}{9}\]
C.\[\dfrac{5}{9}\]
D.\[\dfrac{1}{2}\]

Answer 1

Hint: We need to know that the anhydrous copper sulphate is a chemical compound having the formula \[CuS{O_4}.5{H_2}O\] which is white in colour. And if the water is added to the copper sulphate, it will hydrate and it is converted into blue in colour. Here, the copper ions trap the individual water molecules into the ionic lattice. A reaction between water and copper sulphate can be used for the test of water.

Complete answer:
The mole fraction of the mixture present in the water is not equal to \[\dfrac{3}{{40}}\]. Hence, option (A) is incorrect.
The mole fraction of copper sulphate which is present in the mixture after the heating of mixture is not equal to \[\dfrac{4}{9}\]. Hence, the option (B) is incorrect.
According to the question, the reaction of heating anhydrous copper sulphate can be written as,
\[CuS{O_4}.5{H_2}O \to CuS{O_4} + 5{H_2}O\]
Given, the amount of anhydrous copper sulphate mixture is equal to\[1800g\] and loss of water in % is equal to \[20\].
Therefore, loss of water in mass \[ = \dfrac{{20}}{{100}} \times 1800\]
                                                          \[ = 360g\]
Number of moles of water \[ = \dfrac{{360}}{{18}} = 20moles\]
Moles of copper sulphate eliminated from anhydrous form \[ = \dfrac{{20}}{5} = 4moles\]
And the molar mass of copper sulphate \[ = 96 + 64 = 160g\]
Mass of copper sulphate \[ = 4 \times 160 = 640g\]
Mass of anhydrous copper sulphate initially\[ = 640 + 360 = 1000g\]
Hence, mass of copper sulphate at initial time \[ = 1800 - 1000 = 800g\]
Thus, moles of copper sulphate \[ = \dfrac{{800}}{{160}} = 5moles\]
And the total moles of copper sulphate\[5 + 4 = 9moles\]
Therefore, mole fraction of \[CuS{O_4}\]\[,{\chi _{CuS{O_4}}} = \dfrac{5}{{5 + 4}} = \dfrac{5}{9}\]
Hence, option (C) is correct.
The mole fraction of copper sulphate in the mixture will not equal \[\dfrac{1}{2}\]. Hence, the option (D) is incorrect.

Hence, option (C) is correct.

Note:
We need to know that the mole fraction is the unit of the amount of constituent which is denoted as, \[{n_i}\]and it is divided with the total amount of the constituents which is present in a mixture. When adding water into the copper sulphate, there is a formation of copper sulphate pentahydrate and the water molecule will be lost by the dehydration of copper sulphate and there is a formation of copper sulphate monohydrate.