Question 22.8: Suppose we mix 50.0 mL of 1.00 × 10^−2 M AgNO3(aq) with 100.......
Suppose we mix 50.0 mL of 1.00 × 10^{−2}\ M\ AgNO_{3}(aq) with 100.0 mL of 2.00 × 10^{−4}\ M\ K_{2}CrO_{4}(aq) at 25°C. Does Ag_{2}CrO_{4}(s) precipitate from the solution? If yes, then calculate how many millimoles of Ag_{2}CrO_{4}(s) precipitate.
The chemical equation for the precipitation reaction is
2\ Ag^+(aq) + CrO_{4}^{2−}(aq) ⇋ Ag_{2}CrO_{4}(s) (22.18)
and from Table 22.1, we have for the solubility equilibrium defined by the reverse of Equation 22.18
[Ag^+]^{2}[CrO_{4}^{2-}] = K_{sp} = 1.1 × 10^{-12}\ M^3The concentration of Ag^+(aq) immediately after mixing is
[Ag^+]_{0} =\frac{(50.0\ mL)(1.00 × 10^{–2}\ M)}{150.0\ mL} =3.33 × 10^{–3}\ Mand the concentration of CrO_{4}^{2-}(aq) immediately after mixing is
[CrO_{4}^{2-}]_{0}=\frac{(100.0\ mL)(2.00 × 10^{–4}\ M)}{150.0\ mL} =1.33 × 10^{–4}\ MTherefore, the value of Q_{sp} is
Q_{sp} = [Ag^+]^2_{0} [CrO_{4}^{2−}]_{0} = (3.33 × 10^{−3}\ M)^2(1.33 × 10^{−4}\ M) = 1.47 × 10^{−9}\ M^3Because Q_{sp} \gt K_{sp}, precipitation of Ag_{2}CrO_{4}(s) results.
To determine how much Ag_{2}CrO_{4}(s) precipitates, we must determine which, if either, reactant in Equation 22.18 is a limiting reactant. The amount of Ag^+(aq) added is given by (50.0 mL)(1.00 × 10^{-2}\ M) = 0.500 mmol, and the amount of CrO_{4}^{2-}(aq) added is given by (100.0\ mL)(2.00 × 10^{-4}\ M) = 0.0200\ mmol. Because the 0.0200 mmol of CrO_{4}^{2-}(aq) requires only 0.0400 mmol of Ag^+(aq) to react completely, we see that Ag^+(aq) is in great excess and that CrO_{4}^{2-}(aq) is a limiting reactant. Therefore, essentially 0.0200 mmol of Ag_{2}CrO_{4}(s) precipitates.
Because the value of K_{sp} for the dissolution of Ag_{2}CrO_{4}(s) is extremely small (1.1 × 10^{-12}\ M^3), we can neglect the amount of product that remains in solution compared to the amount that precipitates.
| TABLE 22.1 Solubility-product constants for various salts in water at 25°C | |||||
| Bromates | K_{sp} | Cyanides | K_{sp} | Oxalates | K_{sp} |
| AgBrO_{3} | 5.4 × 10^{-5}\ M^{2} | AgCN | 6.0 × 10^{-17}\ M^{2} | Ag_{2}C_{2}O_{4} | 5.4 × 10^{-12}\ M^{3} |
| Ba(BrO_{3})_{2} | 2.4 × 10^{-4}\ M^{3} | CuCN | 3.5 × 10^{-20}\ M^{2} | CaC_{2}O_{4} | 4 × 10^{-9}\ M^{2} |
| Pb(BrO_{3})_{2} | 7.9 × 10^{-6}\ M^{2} | Hg_{2}(CN)_{2}{^*} | 5 × 10^{-40}\ M^{3} | MgC_{2}O_{4} | 7 × 10^{-7}\ M^{2} |
| TlBrO_{3} | 1.1 × 10^{-4}\ M^{2} | Zn(CN)_{2} | 3 × 10^{-16}\ M^{3} | SrC_{2}O_{4} | 4 × 10^{-7}\ M^{2} |
| Bromides | K_{sp} | Fluorides | K_{sp} | Sulfates | K_{sp} |
| AgBr | 5.4 × 10^{-13}\ M^{2} | BaF_{2} | 1.8 × 10^{-7}\ M^{3} | Ag_{2}SO_{4} | 1.2 × 10^{-5}\ M^{3} |
| CuBr | 6.3 × 10^{-9}\ M^{2} | CaF_{2} | 3.5 × 10^{-11}\ M^{3} | BaSO_{4} | 1.1 × 10^{-10}\ M^{2} |
| Hg_{2}Br_{2}{^*} | 6.4 × 10^{-23}\ M^{3} | LiF | 1.8 × 10^{-3}\ M^{2} | CaSO_{4} | 4.9 × 10^{-5}\ M^{2} |
| HgBr_{2} | 6.2 × 10^{-20}\ M^{3} | MgF_{2} | 5.2 × 10^{-11}\ M^{3} | Hg_{2}SO_{4} | 6.5 × 10^{-7}\ M^{2} |
| PbBr_{2} | 6.6 × 10^{-6}\ M^{3} | PbF_{2} | 3.3 × 10^{-8}\ M^{3} | PbSO_{4} | 2.5 × 10^{-8}\ M^{2} |
| TlBr | 3.7 × 10^{-6}\ M^{2} | SrF_{2} | 4.3 × 10^{-9}\ M^{3} | SrSO_{4} | 3.4 × 10^{-7}\ M^{2} |
| Carbonates | K_{sp} | Hydroxides | K_{sp} | Sulfides | K_{sp} |
| Ag_{2}CO_{3} | 8.5 × 10^{-12}\ M^{3} | Al(OH)_{3} | 1.3 × 10^{-33}\ M^{4} | Ag_{2}S | 8 × 10^{-51}\ M^{3} |
| BaCO_{3} | 2.6 × 10^{-9}\ M^{2} | Ca(OH)_{2} | 5.0 × 10^{-6}\ M^{3} | CdS | 8.0 × 10^{-27}\ M^{2} |
| CaCO_{3} | 3.4 × 10^{-9}\ M^{2} | Cd(OH)_{2} | 7.2 × 10^{-15}\ M^{3} | CoS | 5 × 10^{-22}\ M^{2} |
| CdCO_{3} | 1.0 × 10^{-12}\ M^{2} | Co(OH)_{2} | 5.9 × 10^{-15}\ M^{3} | CuS | 6.3 × 10^{-36}\ M^{2} |
| CoCO_{3} | 1.0 × 10^{-10}\ M^{2} | Cr(OH)_{3} | 6.3 × 10^{-31}\ M^{4} | FeS | 6.3 × 10^{-18}\ M^{2} |
| CuCO_{3} | 1.4 × 10^{-10}\ M^{2} | Cu(OH)_{2} | 2.2 × 10^{-20}\ M^{3} | HgS | 4 × 10^{-53}\ M^{2} |
| FeCO_{3} | 3.1 × 10^{-11}\ M^{2} | Fe(OH)_{2} | 4.9 × 10^{-17}\ M^{3} | MnS | 2.5 × 10^{-13}\ M^{2} |
| MgCO_{3} | 6.8 × 10^{-6}\ M^{2} | Fe(OH)_{3} | 2.8 × 10^{-39}\ M^{4} | NiS | 1.3 × 10^{-25}\ M^{2} |
| MnCO_{3} | 2.2 × 10^{-11}\ M^{2} | Mg(OH)_{2} | 5.6 × 10^{-12}\ M^{3} | PbS | 8.0 × 10^{-28}\ M^{2} |
| NiCO_{3} | 1.4 × 10^{-7}\ M^{2} | Ni(OH)_{2} | 5.5 × 10^{-16}\ M^{3} | SnS | 1.0 × 10^{-25}\ M^{2} |
| PbCO_{3} | 7.4 × 10^{-14}\ M^{2} | Pb(OH)_{2} | 1.4 × 10^{-20}\ M^{3} | Tl_{2}S | 6 × 10^{-22}\ M^{3} |
| SrCO_{3} | 5.6 × 10^{-10}\ M^{2} | Sn(OH)_{2} | 5.5 × 10^{-27}\ M^{3} | ZnS | 1.6 × 10^{-24}\ M^{2} |
| ZnCO_{3} | 1.5 × 10^{-10}\ M^{2} | Zn(OH)_{2} | 1.0 × 10^{-15}\ M^{3} | ||
| Chlorides | K_{sp} | Iodates | K_{sp} | Thiocyanates | K_{sp} |
| AgCl | 1.8 × 10^{-10}\ M^2 | AgIO_{3} | 3.2 × 10^{-8}\ M^2 | AgSCN | 1.0 × 10^{-12}\ M^2 |
| CuCl | 1.7× 10^{-7}\ M^2 | Ba(IO_{3})_{2} | 4.0 × 10^{-9}\ M^3 | CuSCN | 1.8 × 10^{-13}\ M^2 |
| Hg_{2}Cl_{2}{^*} | 1.4 × 10^{-18}\ M^3 | Ca(IO_{3})_{2} | 6.5 × 10^{-6}\ M^3 | Cu(SCN)_{2} | 4.0 × 10^{-14}\ M^3 |
| PbCl_{2} | 1.5 × 10^{-5}\ M^3 | Cd(IO_{3})_{2} | 2.5 × 10^{-8}\ M^3 | Hg_{2}(SCN)_{2}{^*} | 3.2 × 10^{-20}\ M^3 |
| TlCl | 1.9 × 10^{-4}\ M^2 | Cu(IO_{3})_{2} | 7.4 × 10^{-8}\ M^3 | Hg(SCN)_{2} | 2.8 × 10^{-20}\ M^3 |
| Pb(IO_{3})_{2} | 3.7 × 10^{-13}\ M^3 | TlSCN | 1.6 × 10^{-4}\ M^2 | ||
| TlIO_{3} | 3.1 × 10^{-6}\ M^2 | ||||
| Zn(IO_{3})_{2} | 3.9 × 10^{-6}\ M^3 | ||||
| Chromates | K_{sp} | Iodides | K_{sp} | ||
| Ag_{2}CrO_{4} | 1.1 × 10^{-12}\ M^{3} | AgI | 8.5 × 10^{-17}\ M^{2} |
*Hg(I) exists as Hg_{2}^{2+}(aq) |
|
| BaCrO_{4} | 1.2 × 10^{-10}\ M^{2} | CuI | 1.3 × 10^{-12}\ M^{2} | ||
| CuCrO_{4} | 3.6 × 10^{-6}\ M^{2} | Hg_{2}I_{2}{^*} | 5.2 × 10^{-29}\ M^{3} | ||
| Hg_{2}CrO_{4}{^*} | 2.0 × 10^{-9}\ M^{2} | HgI_{2} | 2.9 × 10^{-29}\ M^{3} | ||
| PbCrO_{4} | 2.8 × 10^{-13}\ M^{2} | PbI_{2} | 9.8 × 10^{-9}\ M^{3} | ||
| Tl_{2}CrO_{4} | 8.7 × 10^{-13}\ M^{3} | TlI | 5.5 × 10^{-8}\ M^{2} | ||