# 17.74 Mercury(II) ion is often precipitated as mercury(II) sulfide in qualitative analysis. Using the solubility pr...

17.74 Mercury(II) ion is often precipitated as mercury(II) sulfide in qualitative analysis. Using the solubility product con- stant (Table 17.1), calculate the molar solubility of mercury(II) Sulfide in water, assuming that no other reactions occur.

HgS in water dissociates as

HgS (s)  $\small \overset{H_{2}O}{\rightleftharpoons }$ Hg2+ (aq) + S-2 (aq)

let solubility of HgS = S ( mol/ L or M)

then, [Hg2+] = [S2-] = S ( mol/ L or M)

hence , K = $\small \frac{[Hg^{2+}][S^{2-}]}{{[HgS]}}$

as HgS is sparingly soluble salt so,

or, K [HgS] = constant = Ksp

Ksp is called solubility product.

hence, Ksp = [Hg2+] [S2-] = S $\small \times$ S

or, Ksp = S2

theoretical value of Ksp of HgS = 1 $\small \times$10-54

then

1 $\small \times$10-54 = S2

or, S = (1 $\small \times$10-54)0.5 = 1 $\small \times$10-27 M

hence molar solubility of mercury(II) sulfide in water =  1 $\small \times$10-27 M

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