Question #44681

A metal $M$ (Atomic mass = $115 \text{ g mol}^{-1}$) forms two chlorides, $A$ and $B$. Elemental analysis reveals that $1.00 \text{ g}$ of $M$ combines with $0.308 \text{ g}$ of chlorine in compound $A$, and with $0.924 \text{ g}$ of chlorine in compound $B$.

$0.30 \text{ moles}$ of solid $A$ is dissolved in $1 \text{ L}$ of water at $298 \text{ K}$. Upon dissolution, the metal ion undergoes complete disproportionation into solid metal $M$ and the higher oxidation state metal ion found in $B$.

The resulting aqueous mixture is filtered, and the filtrate is electrolyzed using a current of $9.65 \text{ A}$ for $1000 \text{ s}$. Due to concurrent $H_2$ gas evolution at the cathode, the current efficiency for the deposition of $M$ is only $60\%$.

Calculate the total mass of solid metal $M$ recovered from both the initial dissolution process and the subsequent electrolysis. (Given: $F = 96500 \text{ C mol}^{-1}$, Atomic mass of $Cl = 35.5 \text{ g mol}^{-1}$)