Chapter 16, Problem 85AE

Nanotechnology has become an important field, with applications ranging from high-density data storage to the design of “nano machines.” One common building block of nanostructured architectures is manganese oxide nanoparticles. The particles can be formed from manganese oxalate nanorods, the formation of which can be described as follows:

$\begin{array}{l}\begin{array}{cc}{\text{Mn}}^{\text{2+}}(aq)+C_2{\text{O}}_{\text{4}}{}^{2-}(aq)\rightleftharpoons Mn{C}_2{\text{O}}_{\text{4}}(aq)& K_1=7.9\times {10}^3\\ {\text{MnC}}_{\text{2}}{\text{O}}_{\text{4}}(aq)+C_2{\text{O}}_{\text{4}}{}^{2-}(aq)\rightleftharpoons Mn{(C_2{\text{O}}_{\text{4}})}_2{}^{2-}(aq)& K_2=7.9\times {10}^1\end{array}\\ \end{array}$

Calculate the value for the overall formation constant for Mn(C₂O₄)₂²⁻:

$K=\frac{[{\text{Mn(C}}_{\text{2}}{\text{O}}_{\text{4}}{\text{)}}_{\text{2}}{}^{\text{2-}}\text{]}}{[{\text{Mn}}^{\text{2+}}{\text{][C}}_{\text{2}}{\text{O}}_{\text{4}}{}^{\text{2-}}{\text{]}}^{\text{2}}}$