Question

The solubility products of NiS, ZnS, CdS and HgS are $4.7 \times 10^{-1}$, $1.6 \times 10^{-24}$, $8 \times 10^{-27}$ and $4 \times 10^{-53}$ respectively. An aqueous solution contains Ni$^{2+}$, Zn$^{2+}$, Cd$^{2+}$, and Hg$^{2+}$ of equal concentration. H$_2$S gas was passed into this solution very slowly. The first and the last ions that precipitate as sulphides are respectively

• A. Ni$^{2+}$, Hg$^{2+}$
• B. Hg$^{2+}$, Cd$^{2+}$
• C. Zn$^{2+}$, Hg$^{2+}$
• D. Hg$^{2+}$, Ni$^{2+}$

Hint:

For sulfides of type MS, $K_{sp} = [\text{M}^{2+}][\text{S}^{2-}]$.
Precipitation occurs when ionic product $[\text{M}^{2+}][\text{S}^{2-}]>K_{sp}$.
If initial metal ion concentrations are equal, the sulfide with the smallest $K_{sp}$ will precipitate first (requires the lowest $[\text{S}^{2-}]$).
The sulfide with the largest $K_{sp}$ will precipitate last (requires the highest $[\text{S}^{2-}]$).
Arrange the given $K_{sp}$ values in increasing order to determine the sequence of precipitation.

Answer 1

The Correct Option is D

All the given metal sulfides (NiS, ZnS, CdS, HgS) are of the type MS, where M is a divalent metal ion (M$^{2+}$) and S is sulfide ion (S$^{2-}$). The precipitation reaction is M$^{2+}$(aq) + S$^{2-}$(aq) $\rightleftharpoons$ MS(s). The solubility product constant is $K_{sp} = [\text{M}^{2+}][\text{S}^{2-}]$. When H$_2$S gas is passed into the solution, it provides S$^{2-}$ ions. As the concentration of S$^{2-}$ ions gradually increases (due to H$_2$S being passed very slowly), precipitation of a metal sulfide MS will begin when its ionic product $[\text{M}^{2+}][\text{S}^{2-}]$ exceeds its $K_{sp}$. Given that all metal ions (Ni$^{2+}$, Zn$^{2+}$, Cd$^{2+}$, Hg$^{2+}$) have equal initial concentrations, let this concentration be $C$. So, $[\text{M}^{2+}] = C$ for all of them initially. Precipitation starts when $[\text{S}^{2-}]>\frac{K_{sp}}{[\text{M}^{2+}]} = \frac{K_{sp}}{C}$. The metal sulfide with the smallest $K_{sp}$ will require the lowest concentration of S$^{2-}$ ions to start precipitating. Therefore, it will be the first to precipitate. The metal sulfide with the largest $K_{sp}$ will require the highest concentration of S$^{2-}$ ions to start precipitating. Therefore, it will be the last to precipitate (among those that do precipitate). Given $K_{sp}$ values: $K_{sp}(\text{NiS}) = 4.7 \times 10^{-1}$ (Note: Image says $4.7 \times 10^{-1}$, but this value is extremely high for a sulfide, usually they are very insoluble. For NiS, typical $K_{sp}$ is around $10^{-19}$ to $10^{-21}$. This value of $4.7 \times 10^{-1}$ might be a typo and could mean $4.7 \times 10^{-19}$ or similar. Let's proceed with the given value and see.) $K_{sp}(\text{ZnS}) = 1.6 \times 10^{-24}$ $K_{sp}(\text{CdS}) = 8 \times 10^{-27}$ $K_{sp}(\text{HgS}) = 4 \times 10^{-53}$ Let's compare these $K_{sp}$ values: Smallest $K_{sp}$: $K_{sp}(\text{HgS}) = 4 \times 10^{-53}$. Largest $K_{sp}$: $K_{sp}(\text{NiS}) = 4.7 \times 10^{-1}$. The order of $K_{sp}$ values from smallest to largest is: HgS ($4 \times 10^{-53}$)<CdS ($8 \times 10^{-27}$)<ZnS ($1.6 \times 10^{-24}$)<NiS ($4.7 \times 10^{-1}$). The first ion to precipitate will be from the sulfide with the smallest $K_{sp}$: HgS. So, Hg$^{2+}$ is the first ion to precipitate. The last ion to precipitate will be from the sulfide with the largest $K_{sp}$: NiS. So, Ni$^{2+}$ is the last ion to precipitate. Therefore, the first ion to precipitate is Hg$^{2+}$ and the last is Ni$^{2+}$. This matches option (d). The unusually high $K_{sp}$ for NiS ($0.47$) means it's relatively soluble compared to other typical sulfides. However, the principle remains: smallest $K_{sp}$ precipitates first, largest $K_{sp}$ precipitates last. If $4.7 \times 10^{-1}$ is taken as is, NiS is by far the most soluble and would precipitate last. It is important to use the values *as given* in the problem, even if they seem unusual compared to literature values. Order of precipitation: Hg$^{2+}$ (first), then Cd$^{2+}$, then Zn$^{2+}$, then Ni$^{2+}$ (last). \[ \boxed{\text{Hg}^{2+}\text{, Ni}^{2+}} \]