What is the molar solubility of calcium sulfate in pure water?

Ksp=2.4x10-5 for calcium sulfate.
A. What is the molar solubility of calcium sulfate in pure water?

B. What is the mass solubility of calcium sulfate in pure water, expressed in g/L?

1 Answer
Nov 14, 2016

Answer:

We assess the following equilibrium:

#CaSO_4(s) rightleftharpoons Ca^(2+) + SO_4^(2-)#

Explanation:

And #K_(sp)=([Ca^(2+)][SO_4^(2-)])/[[CaSO_4(s)]#

But since #[CaSO_4(s)]#, the concentration of a solid, is a meaningless concept, the equilibrium is governed solely by the ion product, i.e.

#K_(sp)=[Ca^(2+)][SO_4^(2-)]=2.4xx10^-5#.

If we say the solubility of #CaSO_4=S#, then,

#K_(sp)=[Ca^(2+)][SO_4^(2-)]=SxxS=S^2=2.4xx10^-5#

And thus #S=sqrt{2.4xx10^-5}# #=# #4.90xx10^-3*mol*L^-1#

Given that #CaSO_4# has a molar mass of #136.14*g*mol^-1#,

#S=136.14*g*cancel(mol^-1)xx4.90xx10^-3*cancel(mol)*L^-1~=0.7*g*L^-1#

Note that this problem assumes standard conditions of #298*K# and #1*atm# pressure. Under non-standard conditions, say at #398*K#, how do you think the solubility would evolve?