# Tough questions series – 2011 CHEM 13 NEWS Exam

(This is a reprint from the December 2011 and January 2012 issue of Chem 13 News, page 11.)

In a particular solution, [Br] = 0.020 mol L−1 and [CrO42-] = 0.0030 mol L−1. Finely-divided solid silver nitrate, AgNO3, is slowly added to the solution. What is [Br] when Ag2CrO4(s) just begins to precipitate? Ksp  for Ag2CrO4 is 1.9×10−12 and AgBr  is 5.2×10−13.
A    2.1×10−8 mol L−1

6.0×10−8 mol L−1

C    2.7×10−7 mol L−1

D   5.2×10−13 mol L−1

E   6.4×10−4 mol L−1

An important step in solving this problem is to decide whether AgBr or Ag2CrO4 precipitates first. If Ag2CrO4 precipitates first, then [Br] is 0.020 mol L−1 when Ag2CrO4 just begins to precipitate. This value is not among the choices, and so it is reasonable to assume that AgBr, not Ag2CrO4, precipitates first. When solid Ag2CrO4 just begins to form, we must have Ksp(Ag2CrO4) = [Ag+]2[CrO42-], with [CrO42-] = 0.0030 mol L−1. Thus:

What is [Br] at this point? Because Ksp(AgBr) = [Ag+] [Br], we find that [Br] = Ksp(AgBr) / 2.5×10−5 = 2.1×10−8 mol L−1. Thus, the answer is “A”. Notice that [Br] is reduced from 0.020 mol L−1 to about 2×10−8 mol L−1 by the time Ag2CrO4 precipitates. In other words, 99.9999% of the Br will have precipitated from solution at the instant Ag2CrO4 begins to form.

Although we did not do it above, it is a simple matter to demonstrate that AgBr precipitates first. AgBr begins to precipitate from the solution when [Ag+] = Ksp(AgBr) / 0.020 = 2.6×10−11 mol L−1 and, as shown above, Ag2CrO4 begins to precipitate when [Ag+] is 2.5×10−5 mol L−1. The precipitation of AgBr requires a lower concentration of Ag+ and thus, AgBr precipitates first. However, it may not be obvious that the controlled addition of AgNO3 results in the precipitation of AgBr exclusively, or that the precipitation of AgBr keeps [Ag+] quite low, at least until [Br] is also quite low. Figure 1 shows that [Ag+] is rather low, less than 1×10−8 mol L−1, until [NO3] is almost 0.020 mol L−1, the initial concentration of Br. (Keep in mind that [NO3] provides a measure of how much AgNO3 has been added to the solution, because NO3 is not involved in any reaction.) Figure 2 shows that [CrO42−] does not decrease (i.e. Ag2CrO4 does not precipitate) until [NO3] exceeds 0.020 mol L−1

Figure 1: The solid curve shows how [Ag+] changes as AgNO3 is added to the solution. The dashed vertical lines at 0.020 and 0.026 mol L−1 are the values of [NO3] required by stoichiometry to precipitate first all of the Br and then all of the CrO42−. The rapid increase in [Ag+] terminates abruptly at [NO3] = 0.020 mol L−1 because, at that point, Ag2CrO4 begins to precipitate. The dotted curve shows how [Ag+] would change if CrO42− was not present.

Figure 2: This figure shows how [Br ] and [CrO42− ] change as AgNO3 is added to the solution. The vertical scale is the same as in figure 1. The significance of the dashed vertical lines at 0.020 and 0.026 mol L−1 is explained in the caption of Figure 1. The rapid decrease in [Br ] terminates abruptly at [NO3] = 0.020 mol L−1 because, at that point, Ag2CrO4 begins to precipitate.