\(2KMnO_4\underrightarrow{to}K_2MnO_4+MnO_2+O_2\\ 3Fe+2O_2\underrightarrow{to}Fe_3O_4\\ n_{Fe_3O_4}=\dfrac{69,6}{232}=0,3\left(mol\right)\\ \Rightarrow n_{O_2}=2.0,3=0,6\left(mol\right)\\ n_{KMnO_4}=2.n_{O_2}=2.0,6=1,2\left(mol\right)\\ m=m_{KMnO_4}=158.1,2=189,6\left(g\right)\\ V=V_{O_2\left(đktc\right)}=0,6.22,4=13,44\left(l\right)\)