empirical formula is the simplest ratio of whole numbers of components making up a compound
molecular formula is the actual number of components making up the compound
there can be many compounds having the same empirical formula
given options
1. C₂H₆ and C₄H₁₂
ratio of C to H in C₂H₆ - 2:6 --> 1:3
C₄H₁₂ - 4:12 --> 1:3
the simplified ratios for both are same
therefore both have same empirical formulas
2. C₃H₆O₃ and C₂H₄O₂
ratio of C to H to O in C₃H₆O₃ - 3:6:3 --> 1:2:1
C₂H₄O₂ - 2:4:2 --> 1:2:1
both have same empirical formulas
3. C₃H₈O and CH₂O
ratio of C to H to O in C₃H₈O - 3:8:1
CH₂O - 1:2:1
the 2 ratios of atoms are different which means they have different empirical formulas
4. C₂H₈ and CH₄
ratio of C to H in C₂H₈ - 2:8 --> 1:4
CH₄ -- 1:4
2 ratios are same so same empirical formula
correct answer is 3. C₃H₈O and CH₂O they do not share the same empirical formula