\(a,PTHH:2KMnO_4\rightarrow\left(t^o\right)K_2MnO_4+MnO_2+O_2\\ b,n_{KMnO_4}=\dfrac{15,8}{158}=0,1\left(mol\right)\\ n_{O_2}=\dfrac{0,1}{2}=0,05\left(mol\right)\\ V_{O_2\left(đktc\right)}=0,05.22,4=1,12\left(l\right)\\ c,4P+5O_2\rightarrow\left(t^o\right)2P_2O_5\\ n_{P_2O_5}=\dfrac{2}{5}.n_{O_2}=\dfrac{2}{5}.0,05=0,02\left(mol\right)\\ m_{P_2O_5}=0,02.142=2,84\left(g\right)\)