Michael S. answered • 14d
B.S. in Chemistry, Indiana University; Organic Chem Teaching Intern
Yes, a precipitate forms. Qsp = 3.5 × 10-12, Ksp = 1.1 × 10-12.
Ksp(Ag2CrO4) = 1.1 × 10-12 is the table value; check it against your appendix since the comparison depends on it.
Step 1: concentrations of the two ions.
AgNO3, M = 169.87 g/mol: (7.0 × 10-5 g) / (169.87 g/mol) = 4.12 × 10-7 mol
[Ag+] = (4.12 × 10-7 mol) / (0.015 L) = 2.75 × 10-5 M
[CrO42-] = 4.7 × 10-3 M - the chromate is already dissolved and the problem says to ignore any volume change, so this value is used as given.
Note that AgNO3 and K2CrO4 are both soluble salts, so each dissociates completely and delivers its ion at full strength. The nitrate and potassium are spectators and never enter the calculation.
Step 2: Qsp, using the same expression as Ksp.
Ag2CrO4(s) dissolves as 2 Ag+(aq) + CrO42-(aq), so
Qsp = [Ag+]2[CrO42-] = (2.75 × 10-5)2(4.7 × 10-3) = (7.55 × 10-10)(4.7 × 10-3) = 3.5 × 10-12
The silver term is squared, because two Ag+ appear in the dissolution equation. This is the single most common way this problem is missed. Skip the square and you get Qsp = 1.3 × 10-7, which is still larger than Ksp, so you would reach the right yes/no answer by luck with a badly wrong number - exactly the situation where a grader marking the work rather than the box takes the points.
Step 3: compare.
Qsp (3.5 × 10-12) > Ksp (1.1 × 10-12), so the solution is supersaturated and solid Ag2CrO4 precipitates until Q falls back to K.
The rule in general, and it is worth stating in words because it generalises to every equilibrium you will meet:
Q < K: unsaturated, more solid could dissolve, no precipitate.
Q = K: exactly saturated, at equilibrium.
Q > K: supersaturated, precipitate forms.
Q and K use the identical expression. The only difference is that K applies at equilibrium while Q applies to whatever concentrations you happen to have right now, which is why Q is the one you compute from mixing data.
Worth noticing how close this call is: Q exceeds K by only a factor of about 3. With that little margin, using a slightly different tabulated Ksp - some sources list 9.0 × 10-12 for Ag2CrO4 - would flip the answer to "no precipitate." State which value you used.
