Question

$S{O_2}C{l_2}$(sulphuryl chloride) reacts with water to give a mixture of
${H_2}S{O_4}$ and $HCl$. What volume of $0.2\,M\,Ba{\left( {OH} \right)_2}$ is needed to
completely neutralize $25\,mL$ of $0.2\,M\,S{O_2}C{l_2}$ solution.
(A) $25\,mL$
(B) $50\,mL$
(C) $100\,mL$
(D) $200\,mL$

Answer 1

As we know that ${H_2}S{O_4}$ and $HCl$ both are strong acids, whereas $\,Ba{\left( {OH} \right)_2}$ is a strong base so this is a strong acid strong base titration. If we know the number of moles of ${H_2}S{O_4}$ and $HCl$ then we will easily find out the number of moles of $\,Ba{\left( {OH} \right)_2}$ and hence we can easily calculate the volume of $0.2\,M\,Ba{\left( {OH} \right)_2}$.

Complete step by step answer:
The reaction of sulfuryl chloride reacts with water occurs as
$S{O_2}C{l_2} + 2{H_2}O \to {H_2}S{O_4} + 2HCl$
Now we will calculate the number of moles of $25\,mL$ of $0.2\,M\,S{O_2}C{l_2}$ by the
formula
$concentration(C) = \dfrac{{number\,of\,moles(n)}}{{volume\,(V)}} - - - - (i)$
Rearranging the above formula, we get as
$n = V\,\times\,C$
Putting the values $C = 0.2\,M,V = 25mL$

$$\Rightarrow n = 25\,mL\,\times\,0.2\,\,M\\\ \Rightarrow n = 5\,mmol = 5\,\times{10^{ - 3}}mole$$

$\Rightarrow\,S{O_2}C{l_2}\:\:+\:\:2{H_2}O\:\to\:{H_2}S{O_4}\:\:+\:\:2HCl$

$5\times{10^{ -3}}moles$	0	0
0	$5\times\,{10^{ -3}}moles$	$10\times{10^{-3}}moles$

Therefore, the number of moles of $\,Ba{\left( {OH} \right)_2}$to neutralize {H_2}S{O_4}$$$$\, = 5\times\,{10^{ - 3}}
And the number of moles of $\,Ba{\left( {OH} \right)_2}$ to neutralize HCl$$$$\, = 5\times\,{10^{ - 3}}
So, the total number of moles of $\,Ba{\left( {OH} \right)_2}$ to neutralize both acids
$\,=\,10\times\,{10^{ - 3}}$
From the equation$(i)$we can easily find the volume of $\,Ba{\left( {OH} \right)_2}$ as

$$\Rightarrow V = \dfrac{n}{C}\\\ \Rightarrow V = \dfrac{{10\,\times\,{{10}^{ - 3}}mole}}{{0.2\,M}}\\\ \Rightarrow V = 50\,\times\,{10^{ - 3}}L\\\ \therefore V = 50\,mL$$

Note: The volume of $\,Ba{\left( {OH} \right)_2}$ is $50\,mL$. In acid base titration, the
number of moles of hydroxyl ions must be equal to the number of moles of hydrogen ions for
the complete neutralization.