Question

Find the $pH$ of the saturated solution $Co(OH{)}_3$ and then mark the option in which $pH$ exists between color transition range of an indicator.

For saturated aqueous solution of $Co(OH{)}_3,K_{sp}=2.7\times {10}^{-43}$.

• A. Methyl orange (3.0 to 4.4)
• B. Propyl red (4.6 to 6.4)
• C. Phenolphthalein (8.3 to 10.1)
• D. Malachite green (11.4 to 13)

Answer 1

The correct option is A Methyl orange (3.0 to 4.4)

The dissociation reaction for $Co(OH{)}_3$ is as shown below.

$Co(OH{)}_3\to C{o}^{3+}+3O{H}^{-}$

The expression for the solubility product is as given below.

$K_{sp}=\left[C{o}^{3+}\right][O{H}^{-}{]}^3=2.7\times {10}^{-43}$

Now,

$\left[C{o}^{3+}\right]=s,\left[O{H}^{-}\right]=3s$

Substitute values in the above expression.

$K_{sp}=s(3s{)}^3=2.7\times {10}^{-43}$

Hence,

$27s^4=2.7\times {10}^{-43}$ or $s=1\times {10}^{-11}$

$pOH=-log\left[O{H}^{-}\right]=-log(3\times {10}^{-11})=10.5$

$pH=14-pOH=14-10.5=3.5$

Hence, the suitable indicator is methyl orange having $pH$ range 3.0 to 4.4.