Ans: The chemical equation is given below-
$\text{BaS}{{\text{O}}_{\text{4}}}\left( \text{s} \right)\to \text{B}{{\text{a}}^{\text{2+}}}\left( \text{aq} \right)\text{ + S}{{\text{O}}_{\text{4}}}^{\text{2-}}\left( \text{aq} \right)$
At t = 0 1 0 0
At equilibrium
in water 1-S S S
At equilibrium in
the presence 1-S S (S+0.01)
of sulphuric acid
${{\text{K}}_{\text{sp}}}\text{ for BaS}{{\text{O}}_{\text{4}}}\text{ in water = }\!\![\!\!\text{ B}{{\text{a}}^{\text{2+}}}\text{ }\!\!]\!\!\text{ }\!\![\!\!\text{ S}{{\text{O}}_{\text{2}}}^{\text{4-}}\text{ }\!\!]\!\!\text{ = }\left( \text{S} \right)\text{ }\left( \text{S} \right)\text{ = }{{\text{S}}^{\text{2}}}$
But S = 8 x $\text{1}{{\text{0}}^{\text{-4}}}\text{ mol d}{{\text{m}}^{\text{-3}}}$
${{\text{K}}_{\text{sp}}}\text{ = }{{\left( \text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}} \right)}^{\text{2}}}\text{ = 64 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}\text{ }$... (1)
The expression for ${{\text{K}}_{\text{sp}}}$ in the presence of sulphuric acid will be as follows:
${{\text{K}}_{\text{sp}}}$ = (S) (5 + 0.01) ... (2)
Since value of ${{\text{K}}_{\text{sp}}}$will not change in the presence of sulphuric acid, therefore from (1) and (2)
(S) (S + 0.01) = $\text{64 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}$
${{\text{S}}^{\text{2}}}$ + 0.01 S = $\text{64 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}$
${{\text{S}}^{\text{2}}}$ + 0.01 S - $\text{64 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}$= 0
$\text{S=}\frac{\text{-0}\text{.01 }\!\!\pm\!\!\text{ }\sqrt{{{\text{(0}\text{.01)}}^{\text{2}}}\text{+(}}\text{4 }\!\!\times\!\!\text{ 64 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}\text{)}}{\text{2}}$
When we solve the above equation, we will get the value of
S is= $\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{ mo}{{\text{l}}^{\text{-1}}}\text{ d}{{\text{m}}^{\text{-3}}}$