Question

Calculate the solubility product of $Co_{2}\left[\right.Fe\left(\right.CN\left(\left.\right)_{6}\left]\right.$ in water at $25^\circ $ C.
Given, conductivity of saturated solutions of $Co_{2}\left[\right.Fe\left(\right.CN\left(\left.\right)_{6}\left]\right.$ is $\text{2} \text{.06} \, \text{\times } \, \text{10}^{- \text{6}} \, \text{\Omega }^{- \text{1}} \, \text{cm}^{- \text{1}}$ and that of water used is $\text{4} \text{.1} \, \text{\times } \, \text{10}^{- \text{7}} \, \text{\Omega }^{- \text{1}} \, \text{cm}^{- \text{1}}$ . The ionic molar conductivities of $Co^{2 +}$ and $\left[\right.Fe\left(\right.CN\left(\left.\right)_{6}\left(\left]\right.\right)^{4 -}$ are $\text{86} \text{.0} \, \text{\Omega } \, \text{cm}^{\text{2}} \, \text{mol}^{- \text{1}}$ and $\text{444} \text{.0} \, \text{\Omega }^{- \text{1}} \, \text{cm}^{\text{2}} \, \text{mol}^{- \text{1}}$ , respectively.

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

Answer 1

Answer: (A)

$\left(\kappa\right)_{C o_{2} \left[\right. F e \left(\right. C N \left(\left.\right)_{6} \left]\right.}=2.06\times 10^{- 6}-0.41\times 10^{- 6}=1.65\times 10^{- 6}$
$\left(\Lambda\right)_{m C o_{2} \left[\right. F e \left(\right. C N \left(\left.\right)_{6} \left]\right.}=2\left(\Lambda\right)_{m}Co^{2 +}+\left(\Lambda\right)_{m}\left[\right.Fe\left(\right.CN\left(\left.\right)_{6}\left(\left]\right.\right)^{4 -}$
$= 2 \times 86 + 444 = 616 \, \text{Scm}^{\text{2}} \, \text{mol}^{- 1}$
$\Lambda_{m}=1000\frac{\kappa}{c}$
$c=2.7\times 10^{- 6}M$
$K_{s p C o_{2} \left[\right. F e \left(\right. C N \left(\left.\right)_{6} \left]\right.}=4c^{3}=7.87\times 10^{- 17}M^{3}$ .