Question

Salt cake$N{{a}_{2}}S{{O}_{4}}$ is prepared as follows:
\[2NaCl+{{H}_{2}}S{{O}_{4}}\,\,\to \,\,N{{a}_{2}}S{{O}_{4}}+2HCL\]
How much \[80%\] pure salt cake could be produced from \[100.0\text{ }g\] of \[90%\] pure salt in the above reaction?
A. \[43.92\text{ }g\]
B. \[68.62\text{ }g\]
C. \[87.84\text{ }g\]
D. \[136.25\text{ }g\]

Answer 1

Hint: Firstly, students must know what salt cake is in order to solve the question.Salt cake is a crude form obtained by reaction of sulphuric acid on common salt \[\left( NaCl \right)\]. 2 moles of pure salt are forming 1 mole of $N{{a}_{2}}S{{O}_{4}}$ (salt cake). We need to find the number of molar masses of \[NaCl\] and then equate it in an equation form to obtain the answer.

Complete step by step answer:
First, we find the molar masses of \[NaCl\] and $N{{a}_{2}}S{{O}_{4}}$
Molar mass of \[NaCl=\text{ }23+35.5\]
\[\Rightarrow 58.5\text{ }g/mol\]
Next the molar mass of $N{{a}_{2}}S{{o}_{4}}\,=\,23\times 2+32+4\times 16$
\[\Rightarrow 142\text{ }g/mol\]
Now,
\[100g\] of \[90%\] pure \[NaCl\] corresponds to \[\left( 90/100 \right)\times 100\times 58.5=1.54\] moles. So, the number of moles of $N{{a}_{2}}S{{O}_{4}}$ formed from 1.54 moles of \[NaCl\] (common salt) is \[\dfrac{1.54}{2}=0.77\] moles.
Since 2 moles of \[NaCl\] gives 1 mole of $N{{a}_{2}}S{{O}_{4}}$. So,
1 mole of \[NaCl\] gives $\dfrac{1}{2}$ moles of $N{{a}_{2}}S{{O}_{4}}$.
Therefore, 1.54 moles of \[NaCl\] gives 0.77 moles of $N{{a}_{2}}S{{O}_{4}}$.
The mass of $N{{a}_{2}}S{{O}_{4}}$ obtained is\[0.77\times 142=\text{ }109.8\text{ }g\]
But as you can see, it is given in the question that the salt cake is\[80%\] pure. Hence, the mass of the salt cake that can be obtained is given by:
\[\left( 109.8/80 \right)\times 100=\text{ }136.25\text{ }g\]
Thus, we get the amount of \[80%\]pure salt cake produced to be\[136.25g\].

Thus, Option A is correct.

Note:
As stated earlier salt cake is impure sodium sulphate, especially obtained by the interaction of sulphuric acid and common salt in the synthesis of hydrochloric acid; which is chiefly used in the manufacture of glasses, ceramic glazes, soaps, etc. Students must check if the reaction is balanced or not so that the number of moles can be correctly found out.