\(CH_4+2O_2\underrightarrow{^{t^0}}CO_2+2H_2O\)
\(C_2H_4+3O_2\underrightarrow{^{t^0}}2CO_2+2H_2O\)
\(n_{CH_4}=a\left(mol\right),n_{C_2H_4}=b\left(mol\right)\)
\(n_{hh}=\dfrac{2.24}{22.4}=0.1\left(mol\right)\)
\(\Rightarrow a+b=0.1\left(1\right)\)
\(n_{BaCO_3}=\dfrac{27.58}{197}=0.14\left(mol\right)\)
\(\Rightarrow n_{CO_2}=0.14\left(mol\right)\)
\(\Rightarrow a+2b=0.14\left(2\right)\)
\(\left(1\right),\left(2\right):a=0.06,b=0.04\)
\(\%V_{CH_4}=\dfrac{0.06}{0.1}\cdot100\%=60\%\)
\(\%V_{C_2H_4}=40\%\)