In the group scheme, hydrogen sulphide is bubbled through a solution that holds a metal ion at…

Step 1. $\log(1.1 \times 10^{-26} \times 0.10) = -26.96$. So $\log[\text{S}^{2-}] = -26.96 + 2\,\text{pH}$ and $\text{pS} = 26.96 - 2\,\text{pH}$.

Step 2. At pH 0.5: $\text{pS} = 26.96 - 1.0 = 25.96$. At pH 9.0: $\text{pS} = 26.96 - 18.0 = 8.96$.

Step 3. $\log Q = \log 0.010 - \text{pS} = -2 - \text{pS}$. At pH 0.5 it is $-27.96$. At pH 9.0 it is $-10.96$.

Step 4. $\log K_{sp}(\text{CuS}) = -36.22$ and $\log K_{sp}(\text{MnS}) = -13.52$. So CuS in acid: $-27.96 + 36.22 = 8.26$. MnS in acid: $-27.96 + 13.52 = -14.44$. MnS in ammonia: $-10.96 + 13.52 = 2.56$.