\(2KMnO_4+16HCl_{đặc,nóng}\rightarrow2KCl+2MnCl_2+5Cl_2+8H_2O\\ MnO_2+4HCl_{đặc,nóng}\rightarrow MnCl_2+Cl_2+2H_2O\\ Đặt:n_{KMnO_4}=a\left(mol\right);n_{MnO_2}=b\left(mol\right)\left(a,b>0\right)\\ Vì:n_{Cl_2}=\dfrac{9,632}{22,4}=0,43\left(mol\right)\\ \Rightarrow2,5a+b=0,43\left(1\right)\\ Ta.có:n_O=4a+2b\Rightarrow m_O=16.\left(4a+2b\right)=64a+32b=0,39114.\left(158a+87b\right)\\ \Leftrightarrow64a+32b-61,80012a-34,02918b=0\\ \Leftrightarrow2,19988a-2,02918b=0\left(2\right)\\ \left(1\right),\left(2\right)\Rightarrow\left\{{}\begin{matrix}2,19988a-2,02918b=0\\2,5a+b=0,43\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=0,12\\b=0,13\end{matrix}\right.\)
\(n_{MnCl_2}=n_{MnO_2}=a+b=0,25\left(mol\right)\\ \Rightarrow m_{MnCl_2}=126.0,25=31,5\left(g\right)\)
=>Chọn D