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$$$$NaOHsolution.
A. $93\%$
B. $94.6\%$
C. $92.12\%$
D. $91.5\%$

Answer 1

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.