Question #44860

Consider the hexaaqua complexes of \ce{Cr^{3+}}, \ce{Cr^{2+}}, \ce{Mn^{3+}}, and \ce{Mn^{2+}} in an aqueous medium at $298\text{ K}$. The standard reduction potentials are $E^\circ(\ce{Cr^{3+}}/\ce{Cr^{2+}}) = -0.41\text{ V}$ and $E^\circ(\ce{Mn^{3+}}/\ce{Mn^{2+}}) = +1.57\text{ V}$.

Let $P$ = Magnitude of the Crystal Field Stabilization Energy (CFSE) in units of $\Delta_o$ (ignoring pairing energy) for the $+3$ hexaaqua complex that corresponds to the more negative $E^\circ(M^{3+}/M^{2+})$ value. Let $Q$ = Total number of unpaired electrons in the ground state of the $+3$ hexaaqua complex that corresponds to the highly positive $E^\circ(M^{3+}/M^{2+})$ value. Let $R$ = Number of complexes among the four mentioned above that experience strong Jahn-Teller distortion. Let $S$ = Number of $d$-electrons in the metal ion of the complex that acts as the strongest reducing agent among the four. Let $T$ = Number of $d$-electrons in the metal ion of the complex that acts as the strongest oxidizing agent among the four.

Calculate the value of the expression: $(P \times 10) + (Q \times R) + (S \times T)$.