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Question: In a saturated solution \[A{g_2}S{O_4}\] , silver ion concentration is \[3 \times {10^{ - 2}}M\] . I...

In a saturated solution Ag2SO4A{g_2}S{O_4} , silver ion concentration is 3×10−2M3 \times {10^{ - 2}}M . Its solubility product is. Assume no reaction of cation/ anion.
A. 1.35×1051.35 \times {10^5}
B. 1.08×10−41.08 \times {10^{ - 4}}
C. 2.7×10−62.7 \times {10^{ - 6}}
D. 4.5×10−44.5 \times {10^{ - 4}}

Explanation

Solution

As we know Silver sulphate,Ag2SO4A{g_2}S{O_4} is considered as insoluble in aqueous solution, which implies that a dissociation equilibrium between the dissociated ions and the undissolved solid is established when you dissolve the salt in water.

Complete step by step answer:
Now we can use silver sulphate solubility product constants to determine what concentration of sulphate ions would cause the solid to precipitate out of solution.
Ag2SO4(s)⇌2Ag+(aq)+SO2−4(aq)A{g_2}S{O_{4(s)}} \rightleftharpoons 2A{g^ + }_{(aq)} + S{O^{2 - }}_{4(aq)}
Now, when we dissolve the salt in pure water, the initial concentration of the dissolved ions will be equal to zero. By the definition, the solubility product constant Ksp{K_{sp}} is equal to,
Ksp=[Ag+]2[SO42−]{K_{sp}} = {[A{g^ + }]^2}[S{O_4}^{2 - }]
In this case, this will be equal to
Ksp=(2s)2.s=4s3{K_{sp}} = {(2s)^2}.s = 4{s^3}
Where, s indicates the silver sulphate which dissolves in saturated solution expressed in moles per unit.
Now here we’ve value of Concentration of [Ag+]=3×10−2[A{g^ + }] = 3 \times {10^{ - 2}}
Ksp=4×[3×10−2]2{K_{sp}} = 4 \times {[3 \times {10^{ - 2}}]^2}
On simplification we get,
=36×10−436 \times {10^{ - 4}}
If there is no reaction cation or anion then the concentration of [Ag+][A{g^ + }] will be separated.
Then the reaction will be as,
{K_{sp}} = $$$$\dfrac{{{{[A{g^ + }]}^2}}}{3}
On substituting the value we get,
Ksp=3.24×10−43{K_{sp}} = \dfrac{{3.24 \times {{10}^{ - 4}}}}{3}
On simplification
Ksp=1.08×10−4{K_{sp}} = 1.08 \times {10^{ - 4}}

So, the correct answer is Option B.

Additional information:
A solution which can’t dissolve the further amount of solute at a particular temperature is called saturation solution. For example, when you keep adding sugar to the water, time will reach when no more sugar will dissolve in the water and sugar will settle down at the bottom. A saturated solution is a solution that contains the utmost amount of solute that is capable of being dissolved.

Note: We must remember when a chemical compound in a solid state is in chemical equilibrium with a solution then which exists dynamic equilibrium. This means that in a saturated solution of silver sulphate, the concentration of the salt that will dissolve to produce ions is equal to that of concentration.