Question #cc92d
1 Answer
Explanation:
The idea here is that you can use the molar solubility of calcium sulfate to calculate the number of grams of salt that can be dissolved in
So, you know that calcium sulfate is considered an insoluble salt, which implies that when you dissolve calcium sulfate in water, an equilibrium will be established between the undissolved solid and the dissolved ions.
#"CaSO"_ (4(s)) rightleftharpoons "Ca"_ ((aq))^(2+) + "SO"_ (4(aq))^(-2)#
By definition, the solubility product constant of calcium sulfate is equal to
#K_(sp) = ["Ca"^(2+)] * ["SO"_4^(2-)]#
Now, notice that every mole of calcium sulfate that dissociates produces
This means that if you take
#K_(sp) = s * s#
which, in your case, is equivalent to
#2.4 * 10^(-5) = s^2#
Solve for
#s = sqrt(2.4 * 10^(-5)) = 4.9 * 10^(-3)#
So, you know that you have
#color(blue)(ul(color(black)("molar solubility CaSO"_4 = 4.9 * 10^(-3)color(white)(.)"mol L"^(-1))))#
This means that you can only hope to dissolve
Convert the number of moles to grams by using the compound's molar mass
#4.9 * 10^(-3) color(red)(cancel(color(black)("moles CaSO"_4))) * "136.14 g"/(1color(red)(cancel(color(black)("mole CaSO"_4)))) = "0.667 g"#
Since this is how much calcium sulfate can be dissolved for every
#"1 L" = 10^3# #"mL"#
of solution, you can say that
#250 color(red)(cancel(color(black)("mL solution"))) * "0.667 g CaSO"_4/(10^3color(red)(cancel(color(black)("mL solution")))) = color(darkgreen)(ul(color(black)("0.17 g CaSO"_4)))#