# How pH can relate to the Ksp

-the relationship with the Ksp

Now that we have understood pH and concentration of sulfide ion are related to each other, we are ready to see actually when and how the sulfides precipitate of group 2 precipitate.

Take, as a cornerstone, the equation that we have just written:

$\dpi{120}&space;\dpi{120}&space;[S^{2-}]&space;=&space;\frac{1,1&space;\cdot&space;10^{-23}}{[H^+]^2}&space;(1)$

We know that a "tool" called Ksp, allows us to describe well the behaviour of poorly soluble salts. In our case:

$\dpi{120}&space;Ksp&space;=&space;[Me^{2+}][S^{2-}]$  whence
$\dpi{120}&space;\dpi{120}&space;[S^{2-}]&space;=&space;\frac{Ksp}{[Me^{2+}]}&space;(2)$

We just want to put together these two equations to see if we can get an equation even more useful. We wiil then replace the value of $\dpi{120}&space;[S^{2-}]$ in (2) in the equation (1).

The result is:

$\dpi{120}&space;[H^+]^2&space;=&space;\frac{1,1&space;\cdot&space;10^{-23}[Me^{2+}]&space;}{Ksp}$

Well, does this tell us something new? Perhaps it is not easy to understand, but we take into account that the analysis we're conducting is a semimicro analysis whose concentration extremes are 10-2 M / 10-5 M.

In this perspective, we can relate the precipitation of a sulfide with pH. This is, after all, quite obvious, given that the concentration of sulfide ion depends on precisely, pH.

We consider that our sulfide starts to precipitate when its concentration in solution is equal to 10-2 M and is completely precipitated when its concentration in solution is equal to 10-5 M (considering that this concentration is not detectable without electronic instruments).

Take for example the cobalt sulfide, CoS, which has a ksp of 10-18.

$\dpi{120}&space;[H^+]^2&space;=&space;\frac{1,1\cdot&space;10^{-23}&space;[10^{-2}]}{10^{-18}}$  whence  $\dpi{120}&space;[H^+]&space;=&space;\sqrt{1,1\cdot&space;10^{-7}}$ → the precipitation begins at pH 3.5

$\dpi{120}&space;\dpi{120}&space;[H^+]^2&space;=&space;\frac{1,1\cdot&space;10^{-23}&space;[10^{-5}]}{10^{-18}}$  whence  $\dpi{120}&space;[H^+]&space;=&space;\sqrt{1,1\cdot&space;10^{-10}}$ → the precipitation is complete at pH 5

We found that the cobalt sulfide begins to precipitate at pH 3.5 and is completely precipitated at pH 5. Not a big surprise, the cobalt sulfide is not analysed at group 2, but at group 4.

Why does the cobalt sulfide precipitate in this pH range? Let's check up the concentration of sulfide ions at pH 5.

$\dpi{120}&space;[S^{2-}]&space;=&space;\frac{1,1&space;\cdot&space;10^{-23}}{[H^+]^2}$

$\dpi{120}&space;\dpi{120}&space;[S^{2-}]&space;=&space;\frac{1,1\cdot&space;10^{-23}}{[\sqrt{1,1\cdot&space;10^{-10}}]^2}&space;=&space;10^{-13}$

$\dpi{120}&space;\dpi{120}&space;[Me^{2+}]&space;=&space;\frac{Ksp}{[S^{2-}]}&space;=&space;\frac{1,1\cdot&space;10^{-18}}{10^{-13}}&space;=&space;10^{-5}$

and this doesn't come as a surprise to us, because 10-5 is right the minimum concentration that we can't detect.