Question

If a solution contains 0.01 M $M{g}^{+2}$ and 0.1 M $S{r}^{+2}$ and $H_{2}C{O}_3$ maintained at $0.05M$, then:
$[Given:K_{sp}MgC{O}_3=2.5\times {10}^7,K_{sp}SrC{O}_3=9\times {10}^9,K_{a\left(overall\right)}{H}_{2}C{O}_3=5\times {10}^{16},log5=0.7,log3=0.5]$

• A. $pH=4$ is the minimum pH at which $SrC{O}_3$ will precipitate without any precipitation of $MgC{O}_3$
• B. $pH=4.8$ is the minimum pH at which $SrC{O}_3$ will precipitate without any precipitation of $MgC{O}_3$
• C. $pH=6$ is the maximum pH at which $SrC{O}_3$ will precipitate without any precipitation of $MgC{O}_3$
• D. $pH=6.8$ is the maximum pH at which $SrC{O}_3$ will precipitate without any precipitation of $MgC{O}_3$

Answer 1

Answer: (B), (C)

The correct options are
B $pH=4.8$ is the minimum pH at which $SrC{O}_3$ will precipitate without any precipitation of $MgC{O}_3$
C $pH=6$ is the maximum pH at which $SrC{O}_3$ will precipitate without any precipitation of $MgC{O}_3$

A solution contains 0.01M $M{g}^{+2}$ and $0.1MS{r}^{+2}$
$K_{sp}MgC{O}_3=2.5\times {10}^{-7}=\left[M{g}^{+2}\right]\left[C{O}_3^{-2}\right]$
$K_{sp}SrC{O}_3=9\times {10}^{-9}=\left[S{r}^{+2}\right]\left[C{O}_3^{-2}\right]$
$\left[C{O}_3^{-2}\right]$ required for ppt of $SrC{O}_3=9\times {10}^{-}8M$
$\left[C{O}_3^{-2}\right]$ required for ppt of $MgC{O}_3=2.5\times {10}^{-5}M$
$H_{2}C{O}_3\rightleftharpoons 2H^{+}+C{O}_3^{-2}$
$K_a=\frac{\left[H^{+}{]}^2\right[C{O}_3^{-2}]}{\left[H_{2}C{O}_3\right]}$
$[H^{+}{]}^2=\frac{5\times {10}^{-16}\times 0.05}{9\times {10}^{-8}}$ (when $S{r}^{+2}$ will ppt)
or $pH=4.8$
$[H^{+}{]}^2=\frac{5\times {10}^{-16}\times 0.05}{2.5\times {10}^{-5}}$ (when $M{g}^{+2}$ will ppt)
or pH $=6$.