Question

What is the minimum concentration of $S{O_4}^{2 - }$ required to precipitate $BaS{O_4}$ in a solution containing $1 \times {10^{ - 4}}$ mole of $B{a^{ + 2}}$ and ${K_{sp}}$ of $BaS{O_4} = 4 \times {10^{ - 10}}$ ?

Answer 1

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

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

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 \[{K_{sp}}\] . 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.