Question

What is the purity of concentrated \[{H_2}S{O_4}\] solution (\[d = 1.8g/mol\] ) if \[5mL\] of these solution is neutralized by \[84.5mL\] of \[2N\]\[NaOH\]solution.
A. \[93\% \]
B. \[94.6\% \]
C. \[92.12\% \]
D. \[91.5\% \]

Answer 1

Hint: The purity of a solution is the percentage purity of a substance which is evaluated by ratio of the mass of the pure substance and the total mass of the sample considered multiplied by 100.

Complete step by step answer:
The given reaction is a neutralization reaction between an acid and a base. The acid used is sulfuric acid and the base used is sodium hydroxide. The corresponding balanced reaction is as follows:
${H_2}S{O_4} + 2NaOH \to N{a_2}S{O_4} + {H_2}O$
The volume of \[NaOH\] solution used in the neutralization process is \[84.5mL\]. The Normality of the solution used is \[2N\]. The moles of \[NaOH\] used is determined as
$ = \dfrac{{2 \times 84.5}}{{1000}} = 0.169moles$
Following the above equation it is clear that two equivalents of \[NaOH\] is used for consumption of \[1\] equivalent of \[{H_2}S{O_4}\]. Thus for two moles of \[NaOH\] solution, one mole of \[{H_2}S{O_4}\] is used for neutralization.
Hence for $0.169moles$ of \[NaOH\], moles of \[{H_2}S{O_4}\] used are = $\dfrac{{0.169}}{2} = 0.0845moles.$
A mole of substance is the ratio of the mass of the substance and the molar mass of the substance. Hence \[mole = \dfrac{{mass{\text{ }}of{\text{ }}subs\tan ce}}{{molar{\text{ }}mass{\text{ }}of{\text{ }}substance}}\]
Molar mass of \[{H_2}S{O_4}\] = \[2{\text{ }} \times \] atomic mass of \[H\] + atomic mass of \[S\] + \[4{\text{ }} \times \] atomic mass of \[O\]
\[ = 2 \times 1 + 32 + 4 \times 16 = 98g/mol\]
The mass of \[{H_2}S{O_4}\] in \[0.0845moles\] = moles of \[{H_2}S{O_4}\] \[ \times \] molar mass of \[{H_2}S{O_4}\].
\[ = 0.0845 \times 98 = 8.281g\]
The total mass of \[{H_2}S{O_4}\] which is used in the reaction is = density \[ \times \] volume \[ = 1.8 \times 5 = 9g\].
Hence the purity of the concentrated \[{H_2}S{O_4}\] solution
$ = \dfrac{{8.281}}{9} \times 100 = 92.01\% $
Thus option C is the correct answer.

Note: The purity or percentage of purity of a substance is determined using Quantitative chemistry calculations. The number of moles of the substance is the key to determine the purity of the substance.