(This is a reprint from the May 2007 issue of *Chem 13 News*, page 16.)

*How many moles of solid sodium fluoride should be added to 1.0 L of a saturated solution of barium fluoride, BaF _{2}, at 25^{o}C to raise the fluoride concentration to 3.0×*

*10*^{−2}mol L^{−1}? The solubility product constant for BaF_{2}is K_{sp}= 1.7×10^{−6}at 25^{o}C.On the 2006 CHEM 13 NEWS Exam, the above question stumped practically all students. Only 11% of the students answered this question correctly, and about 60% entered no answer at all. For most of the other questions, the percentage of students who entered “no answer” ranged from 3% to 30%. * *

The CHEM 13 NEWS Exam consists of 40 multiple-choice questions intended for a well-read senior high school chemistry student. Carey Bissonnette, one of the exam authors, stated “We knew that students would find this question difficult. To obtain the answer, one must take account of the fact that adding NaF to a saturated solution of BaF_{2} will cause BaF_{2} to precipitate.” The following are two approaches to solving this problem.

**Approach #1:** In a saturated solution of BaF_{2}, [F^{−}] = 2 [Ba^{2+}] and *K*_{sp} = [Ba^{2+}] [F^{−}]^{2} , so

When NaF is added, BaF_{2} will precipitate from the solution. Let “x” be the number of moles of NaF added and let “z” be the amount of BaF_{2} that precipitates.

Starting with the reaction and then adding in the calculated concentrations above, the steps to solving for x and z are as follows:

Reactants/Products | Ba^{2+}(aq) |
2 F^{−}(aq) |
BaF_{2}(s) |
---|---|---|---|

Initial (mol) | 0.007518 | 0.01504 + x | - |

Final (mol) | 0.007518 − z | 0.01504 + x − 2z | - |

But the final concentration of F^{−} is 3.0×10^{−2} mol L^{−1}. Therefore, the final concentration of Ba^{2+} must be:

[Ba^{2+}]=*K*_{sp}/(3.0x10^{-2})^{2} = 0.001889 mol^{-1}.

So, we have:

0.007518 − z = 0.001889 ⇒ z = 0.005629

and

0.01504 + x − 2(0.005629) = 3.0×10^{−2} ⇒ x = 0.026 mol L^{−1}

Therefore, we must add 0.026 moles of NaF.

**Approach #2:** Use charge balance! (Not normally taught in high school, but a simple and useful concept.) The positive charge in solution must offset the negative charge.

In equation form: [Na^{+}] + 2 [Ba^{2+}] = [F^{−}]. (Note: There is a “2” in front of [Ba^{2+}] because 1 mol of Ba^{2+} carries twice as much positive charge as does 1 mol of Na^{+}.)

Since K_{sp} = [Ba^{2+}] [F^{−}]^{2} and [F^{−}] = 3.0×10^{−2} mol L^{−1}, we can write:

[Na^{+}] + 2 K_{sp}/(3.0×10^{−2})^{2} = 3.0x10^{−2}

[Na^{+}] = 0.026 mol L^{−1}

But [Na^{+}] tells us exactly how much NaF must be added to the solution.