Question

Calculate the solubility product of $Co _{2}\left[ Fe ( CN )_{6}\right]$ in water at $25^{\circ} C$ Given, conductivity of saturated solutions of $Co _{2}\left[ Fe ( CN )_{6}\right]$ is $2.06 \times 10^{-6} \Omega^{-1} cm ^{-1}$ and that of water used is $4.1 \times 10^{-7} \Omega^{-1} cm ^{-1}$. The ionic molar conductivities of $Co ^{2+}$ and $\left[ Fe ( CN )_{6}\right]^{4-}$ are $86.0 \Omega cm ^{2} mol ^{-1}$ and $444.0 \Omega^{-1} cm ^{2} mol ^{-1}$, respectively.

• A. $\text{7} \text{.87} \, \times \, \text{10}^{- \text{17}}$
• B. $7.87\times 10^{- 6}$
• C. $7.87\times 10^{- 8}$
• D. $7.87\times 10^{- 9}$

Answer 1

Answer: (A)

$\kappa_{ Co _{2}\left[ Fe ( CN )_{6}\right]}=2.06 \times 10^{-6}-0.41 \times 10^{-6}=1.65 \times 10^{-6}$

$\Lambda_{ mCo _{2}\left[ Fe ( CN )_{6}\right]}=2 \Lambda_{ m } Co ^{2+}+\Lambda_{ m }\left[ Fe ( CN )_{6}\right]^{4-}$

$=2 \times 86+444=616 Scm ^{2} mol ^{-1}$

$\Lambda_{ m }=1000 \frac{\kappa}{ c }$

$c =2.7 \times 10^{-6} M$

$K _{ spCo _{2}\left[ Fe ( CN )_{6}\right]}=4 c ^{3}=7.87 \times 10^{-17} M ^{3}$