General Chemistry Principles, Patterns, and Applications, 2011

Asked for: whether precipitate will form
Strategy:
A Write the balanced equilibrium equation for the precipitation reaction and the expression for K sp.
B Determine the concentrations of all ions in solution when the solutions are mixed and use them to
calculate the ion product (Q).
C Compare the values of Q and K sp to decide whether a precipitate will form.
Solution:
A The only slightly soluble salt that can be formed when these two solutions are mixed is BaSO 4 because
NaCl is highly soluble. The equation for the precipitation of BaSO 4 is as follows:
BaSO4( s) Ba2 + ( aq) + SO42 -( aq)
The solubility product expression is as follows:
Ksp = [Ba2+][SO42-] =1.08 ´10 -10
B To solve this problem, we must first calculate the ion product—Q = [Ba 2+ ][SO 4
2−
]—using the
concentrations of the ions that are present after the solutions are mixed and before any reaction occurs.
The concentration of Ba 2+ when the solutions are mixed is the total number of moles of Ba 2+ in the original
100 mL of BaCl 2 solution divided by the final volume (100 mL + 10.0 mL = 110 mL):
moles Ba2+ = 100 mL[(1 L1000 mL)
(3.2 ´10 - 4 mol1 L)] = 3.2 ´10 - 5 mol Ba2 +
[Ba2+] = 3.2 ´10 - 5 mol Ba2 +110 mL(1000 mL1 L) = 2.9 ´10 - 4 M Ba2 +Similarly,
the concentration of SO 4
2−
after mixing is the total number of moles of SO 4
2−
in the original 10.0 mL of
Na 2SO 4 solution divided by the final volume (110 mL):
moles SO42- = 10.0 mL[(1 L1000 mL) \
(0.0020 mol1 L)] = 2.0 ´10 - 5 mol SO42
[SO42-] = (2.0 ´10 - 5 mol SO42 -110 mL)
[{1000 mL1 L}] = 1.8 ´10 - 4 M SO42 -
We can now calculate Q:
Q = [Ba2+][SO42-] = (2.9 ´10 - 4)(1.8 ´10 - 4) = 5.2 ´10 - 8
C We now compare Q with the K sp. If Q > K sp, then BaSO 4 will precipitate, but if Q K sp, we predict that BaSO 4 will precipitate when the two solutions are mixed. In fact, BaSO 4 will
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