# Calculating the solubility of cuprous iodide

I am clearly missing something obvious here. I get the $$\mathrm{K_{sp}}$$ from the CRC for $$\ce{CuI}$$ as $$1.27\cdot10^{-12}$$.

So, $$\ce{CuI-> Cu+ + I-}$$

So the formula ought to be

$$\mathrm{K_{sp}} = \ce{[Cu+][I-]} =[s][s]= s^2$$

Doing the square root and all gives me a solubility of 2.1 mg/L. Hooray, except that everywhere I look, if the solubility is listed at all, it lists 4.2, exactly double my answer.

I have been wracking my brain on this one. It has to be a scalar but I don’t see how you would introduce it without throwing the entire calculation off by turning the square into a cube or something similar. What am I missing?

Edit: updated to reflect the full Ksp value in the CRC which I was using for my calculations (I had accidentally truncated it to 1 rather than 1.27 when posting this). I am using the online CRC from hbcponline.com, so this is current, not an old edition.

• "Kinetics" is a wrong word to use here. – Ivan Neretin Feb 18 '20 at 20:32
• FYI, CuI is a photocatalyst. This could result in the production of solvated electrons and an electron-hole (turning the OH- in water into the hydroxyl radical). Measure in low light conditions. – AJKOER Feb 18 '20 at 20:37
• Your math seems to be wrong. From the $\mathrm{K_{sp}}$, $s = 1\cdot10^{-6}$ molar, and given FW of 190, I get 0.19 mg/liter. Wikipedia lists same $\mathrm{K_{sp}}$, and 0.42 mg/liter (Wikipedia has g/100ml). – MaxW Feb 18 '20 at 21:31
• As far as the difference, I don't know. You'd have to research where the data came from, and then conditions of the experiments. The concentrations are so low that any number of experimental problems could have affected the data. For example the temperature, and oxygen/CO2 content of the water. // One last point. Much chemical data has been experimentally determined. All in all there isn't any absolute check on consistency. As inconsistent data is found, some researcher will do a literature search, then experiments to correct the data. – MaxW Feb 18 '20 at 21:46
• In my Handbook of Chemistry and Physics, I find $5·10^{-12}$ for the solubility product of CuI. The solubility is then exactly twice your result. – Maurice Feb 18 '20 at 21:53

First of all, as MaxW pointed out in the above comment, your math seems to be wrong. From the the $$K_\mathrm{sp}$$ value given in your question: $$s = \sqrt{K_\mathrm{sp}}= \sqrt{1.0 \times 10^{-12}}= \pu{1.0 \times 10^{-6} mol/L}= \pu{1.0 \times 10^{-6} mol/L} \times \frac{\pu{190.45 g}}{\pu{1 mol}}\times \frac{\pu{1000 mg}}{\pu{1 g}} \\ = \pu{0.190 mg/L}$$

Other than that, there seems to be a problem with online value of $$K_\mathrm{sp}$$ of $$\ce{CuI}$$. Some sites listed it as $$1.1 \times 10^{-12}$$ while other sites listed as $$5.3 \times 10^{-12}$$. However, I'd like the value $$5.3 \times 10^{-12}$$, because at least it's given in one of reliable sources (Ref.1).

If you use this value (instead of $$1.1 \times 10^{-12}$$), you'd get:

$$s = \sqrt{K_\mathrm{sp}}= \sqrt{5.3 \times 10^{-12}}= \pu{2.30 \times 10^{-6} mol/L}= \pu{2.30 \times 10^{-6} mol/L} \times \frac{\pu{190.45 g}}{\pu{1 mol}}\times \frac{\pu{1000 mg}}{\pu{1 g}} \\ = \pu{0.438 mg/L}$$

This value is in a good agreement with the literature value ($$\pu{0.00042 g/L}$$ at $$\pu{25 ^\circ C}$$; Ref.2), which listed the properties of $$\ce{CuI}$$ as:

Copper (I) iodide is a dense, pure white solid, crystallizing with a zinc-blende structure below $$300^\circ$$. It is less sensitive to light than either the chloride or bromide, although passage of air over the solid at room temperature in daylight for $$\pu{3 hr}$$ results in the liberation of a small amount of iodine. It melts at $$588^\circ$$, boils at $$1293^\circ$$, and, unlike the other copper halides, is not associated in the vapor state. Being extremely insoluble ($$\pu{0.00042 g/L}$$ at $$25^\circ$$), it is not perceptibly decomposed by water. It is insoluble in dilute acids but dissolves in aqueous solutions of ammonia, potassium iodide, potassium cyanide, and sodium thiosulfate. It is decomposed by concentrated sulfuric and nitric acids.

References:

1. Steven S. Zumdahl, Donald J. DeCoste, In Chemical Principles; 8th Edition; Cengage Learning: Boston, MA, 2017, “Chapter 8: Applications of Aqueous Equilibria,” pp. 241–298 ($$K_\mathrm{sp}$$ of value $$5.3 \times 10^{-12}$$ is given for $$\ce{CuI}$$ in example 8.13, page 288).
2. George B. Kauffman, Lawrence Y. Fang (Checked by N. Viswanathan, G. Townsend), “Chapter 2: Transition metal Complexes and Compounds – 20. Purification of Copper (I) Iodide,” In Inorganic Syntheses: Volume 22; Smith L. Holt Jr., Ed.; John Wiley & Sons: New York, NY, 1983, pp. 103–107 (https://doi.org/10.1002/9780470132531.ch20).
• Quoting data sources is good, but neither of these is the source of the original data, and neither likely references the original source. I think the best that can be said is that the data (solubility vs Ksp) is inconsistent. Trying to figure of why there is an inconsistency is a research project. – MaxW Feb 19 '20 at 3:27

Figured it out, thought I would share the solution to the mystery with you folks:

The 1902 value for Ksp is 5.06 e-12 based on cell measurements and the value for solubility if CuBr.

In the 50’s and 60’s, the solubility product at zero ionic strength, Kso was found to be 1.2e-12.

So, that explains the confusion in K values. My math was not wrong, the reported Ksp values were confused, in part because places never seem to cite their sources.

Speaking of which, I found this by going to the IUPAC Solubility Data Series, volume 65, page 195.