Question

How much Cu can be obtained from 100g of $CuS{O}_4$ ?

Answer 1

Hint: One mole of Copper Sulphate is generated from one mole of $C{u}^{2+}$ and a mole of $S{O_4}^{2-}$ ions. The molar mass of $CuS{O}_4$ and Cu are 160 grams and 64 grams respectively.

Step-by-Step Solution:
Before moving onto the specifics of this question, let us first look at how the compound $CuS{O}_4$ is made and the chemical reaction involved along with its equation.
- Copper sulphate is produced industrially by treating copper metal with hot concentrated sulfuric acid or its oxides with dilute sulfuric acid.
- It can be noted that the oxidation state exhibited by the copper atom in a $CuS{O}_4$ molecule is +2.
The ionic reaction of the above reaction is given by:
$$C{u}^{2+}+S{O_4}^{2-}\to CuS{O}_4$$
Having now understood how $CuS{O}_4$ is prepared, let us now move on to the specifics of this question.
Molecular mass of $CuS{O}_4$ = Atomic mass of Cu + Atomic mass of S + 4(Atomic mass of O)
Molecular mass of $CuS{O}_4$ = 64 + 32 + 4(16)
Molecular mass of $CuS{O}_4$ = 160$gmmo{l}^{-1}$
Mass of $CuS{O}_4$ given= 100 g
$$\text{Moles of CuS}{\text{O}}_4={\displaystyle \frac{\text{Weight of CuS}{\text{O}}_4}{\text{Molecular weight of CuS}{\text{O}}_4}}$$
$$\text{Moles of CuS}{\text{O}}_4={\displaystyle \frac{100gm}{160gm}}$$
$$\text{Moles of CuS}{\text{O}}_4=0.625mole$$
$$$$
- We have already established above that one mole of $CuS{O}_4$ contains one mole of $C{u}^{2+}$ and one mole of $S{O_4}^{2-}$ .
So, we can say that 0.625 mole of $CuS{O}_4$ contains 0.625 moles of $C{u}^{2+}$ and 0.625 moles of $S{O_4}^{2-}$ .
Thus, $$MassofC{u}^{2+}in100gramsofCuS{O}_4=\text{ Moles of copper }\times \text{ Atomic weight of Copper}$$
$$MassofC{u}^{2+}in100gramsofCuS{O}_4=\text{ 0}\text{.625}\times 64$$
$$MassofC{u}^{2+}in100gramsofCuS{O}_4=\text{ 40gm}$$

Hence, by our calculations, we can safely conclude that 40 grams of Copper is obtained from 100 grams of $CuS{O}_4$ solution.

Note: This solution is directly related to the law of constant proportions which states that a given chemical compound always contains its component elements in a fixed ratio and does not depend on its source and method of preparation.