Hỗn hơp X gồm: \(\left\{{}\begin{matrix}C_nH_{2n+2}:a\left(mol\right)\\C_mH_{2m-2}:b\left(mol\right)\end{matrix}\right.\)
Ta có: \(\dfrac{14n+2}{14m-2}=\dfrac{22}{13}\)
\(\Leftrightarrow182n+26=308m-44\)
\(\Leftrightarrow182n-308m=-70\)\(\left(I\right)\)
Khi đốt cháy hoàn toàn 0,2 mol hỗn hợp X thì:
Ta có: \(a+b=0,2\) \((II)\)
\(C_nH_{2n+2}\left(a\right)+\left(\dfrac{3n+1}{2}\right)O_2-t^o->nCO_2\left(an\right)+\left(n+1\right)H_2O\left(an+a\right)\)
\(C_mH_{2m-2}\left(b\right)+\left(\dfrac{3m-1}{2}\right)O_3-t^o->mCO_3\left(bm\right)+\left(m-1\right)H_2O\left(bm-b\right)\)
\(n_{CO_2}=0,5\left(mol\right)\)
\(\Rightarrow an+bm=0,5\)\((III)\)
\(n_{H_2O}=0,5\left(mol\right)\)
\(\Rightarrow an+bm+a-b=0,5\)\((IV)\)
Thay (III) vào (IV), ta được: \(a-b=0\) \((V)\)
Từ (II) và (V) => \(\left\{{}\begin{matrix}a+b=0,2\\a-b=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}a=0,1\\b=0,1\end{matrix}\right.\)
Thay vào (III), ta được: \(0,1n+0,1m=0,5\)\(\left(VI\right)\)
Từ (I) và (VI) => \(\left\{{}\begin{matrix}182n-308m=-70\\0,1n+0,1m=0,5\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}n=3\\m=2\end{matrix}\right.\)
\(\Rightarrow A\left\{{}\begin{matrix}C_3H_8\\C_2H_2\end{matrix}\right.\)