\(n_{CO_2}=\dfrac{8,96}{22,4}=0,4\left(mol\right)\)
PTHH: CH4 + 2O2 --to--> CO2 + 2H2O
0,8<------0,4
2KMnO4 --to--> K2MnO4 + MnO2 + O2
1,6<-------------------------------0,8
=> \(m_{KMnO_4\left(PTHH\right)}=1,6.158=252,8\left(g\right)\)
=> \(m_{KMnO_4\left(tt\right)}=\dfrac{252,8.100}{90}=\dfrac{2528}{9}\left(g\right)\)