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Question: What is the minimum concentration of \(S{O_4}^{2 - }\) required to precipitate \(BaS{O_4}\) in a sol...

What is the minimum concentration of SO42−S{O_4}^{2 - } required to precipitate BaSO4BaS{O_4} in a solution containing 1×10−41 \times {10^{ - 4}} mole of Ba+2B{a^{ + 2}} and Ksp{K_{sp}} of BaSO4=4×10−10BaS{O_4} = 4 \times {10^{ - 10}} ?

Explanation

Solution

Write down the equation for the reaction of precipitation of BaSO4BaS{O_4} and then from this formula, calculate the formula for Ksp{K_{sp}} with the concentrations of Ba+2B{a^{ + 2}} and SO42−S{O_4}^{2 - } . The concentration of Ba+2B{a^{ + 2}} is already given so the concentration of SO42−S{O_4}^{2 - } can be calculated accordingly.

Complete answer:
We can write the precipitation reaction of BaSO4BaS{O_4} as follows
BaSO4→Ba2++SO42−BaS{O_4} \to B{a^{2 + }} + S{O_4}^{2 - }
Now we calculate the equation for Ksp{K_{sp}} from this equation
Ksp=[Ba2+][SO42−]{K_{sp}} = \left[ {B{a^{2 + }}} \right]\left[ {S{O_4}^{2 - }} \right]
The concentration of Ba2+B{a^{2 + }} and the value of Ksp{K_{sp}} is already given to us. By substituting these values in the above equation, we get
4×10−10=1×10−4×[SO42−]4 \times {10^{ - 10}} = 1 \times {10^{ - 4}} \times \left[ {S{O_4}^{2 - }} \right]
We solve this to get the value of concentration of SO42−S{O_4}^{2 - }
[SO42−]=4×10−101×10−4\left[ {S{O_4}^{2 - }} \right] = \dfrac{{4 \times {{10}^{ - 10}}}}{{1 \times {{10}^{ - 4}}}}
By solving, [SO42−]=4×10−6\left[ {S{O_4}^{2 - }} \right] = 4 \times {10^{ - 6}}
Therefore, the concentration of SO42−S{O_4}^{2 - } required to precipitate BaSO4BaS{O_4} is 4×10−64 \times {10^{ - 6}}

Additional information: When two solutions containing certain soluble salts are combined together, sometimes an insoluble salt is formed which is called a precipitate. This process of formation of a precipitate is known as Precipitation reaction. These reactions are mainly double displacement reactions and they help us in determining the presence of different salts in a solution. These reactions can be used to determine the presence of minerals as they are water-insoluble.

Note: One must always balance a reaction before deriving the formula for Ksp{K_{sp}} . This holds significance since the number of molecules of a substance becomes the power of the concentration in the derived formula. Since the above reaction contains only one molecule of products and reactants, the power on the concentration remains one.