The Foundations of Chemistry

we find the concentration of each ion in the newsolution. Now we ask the question “Couldany

combination of the ions in this solution form a slightly soluble compound?” The answer is

“Yes, Ba^2 
and SO 42 couldform BaSO 4 ,” so we calculate Qspand compare it with Ksp.

Solution

We find the amountof each solute at the instant of mixing.

__? mmol Na 2 SO 4 100. mL0.075 mmol Na 2 SO 4

__? mmol BaCl 2 50. mL0.75 mmol BaCl 2

When diluteaqueous solutions are mixed, their volumes can be added to give the volume of

the resulting solution.

volume of mixed solution100. mL
50. mL150. mL

Then we find the molarity of each solute at the instant of mixing.

MNa 2 SO 4 0.00050 MNa 2 SO 4

MBaCl 2 0.0050 MBaCl 2

Now we find the concentration of each ionin the new solution.

100%

Na 2 SO 4 (s)8888n 2Na
(aq) 
 SO 42 (aq) (to completion)

0.00050 M ::::::F 0 0.0010 M 00 0.00050 M 0

100%

BaCl 2 (s) 8888n Ba^2 
(aq) 
 2Cl(aq) (to completion)

0.0050 M ::::::F 0 0.0050 M 00 0.010 M 0

We consider the kinds of compounds mixed and determine whether a reaction could occur.

Both Na 2 SO 4 and BaCl 2 are soluble ionic salts. At the moment of mixing, the new solution

contains a mixture of Na
, SO 42 , Ba^2 
, and Clions. We must consider the possibility of

forming two new compounds, NaCl and BaSO 4. Sodium chloride is a soluble ionic compound

so Na
and Cldo not combine in dilute aqueous solutions. BaSO 4 , however, is only very

slightly soluble, and solid BaSO 4 will precipitate from the solution if QspKspfor BaSO 4. Ksp

for BaSO 4 is 1.1 10 ^10. Substituting [Ba^2 
]0.0050 Mand [SO 42 ]0.00050 Minto the

Qspexpression for BaSO 4 , we get

Qsp[Ba^2 
][SO 42 ](5.0 10 ^3 )(5.0 10 ^4 )2.5 10 ^6 (QspKsp)

Because QspKspsolid BaSO 4 will precipitate until [Ba^2 
][SO 42 ] just equals Kspfor BaSO 4.

You should now work Exercises 28 and 30.

0.75 mmol BaCl 2



150. mL

0.075 mmol Na 2 SO 4



150. mL

0.015 mmol BaCl 2



mL

0.00075 mmol Na 2 SO 4



mL

832 CHAPTER 20: Ionic Equilibria III: The Solubility Product Principle

Recall that Qhas the same form as
the equilibrium constant, in this case
Ksp, but the concentrations are not
necessarily equilibrium concentrations.

When white solid potassium iodide, KI, and white solid lead(II) nitrate, Pb(NO 3 ) 2 , are

stirred together, some yellow lead(II) iodide, PbI 2 , forms. This reaction occurs in the small

amount of water present in these solids.