To determine which pair of compounds share the same empirical formula, we must first understand what an empirical formula is. An empirical formula represents the simplest whole-number ratio of atoms in a compound.
Let's analyze each pair of compounds and simplify their formulas step by step.
1. Pair: [tex]\(C_2H_4\)[/tex] and [tex]\(C_6H_6\)[/tex]
- For [tex]\(C_2H_4\)[/tex]:
- Carbon atoms: 2
- Hydrogen atoms: 4
- The ratio is [tex]\(2:4\)[/tex], which simplifies to [tex]\(1:2\)[/tex]. The empirical formula is [tex]\(CH_2\)[/tex].
- For [tex]\(C_6H_6\)[/tex]:
- Carbon atoms: 6
- Hydrogen atoms: 6
- The ratio is [tex]\(6:6\)[/tex], which simplifies to [tex]\(1:1\)[/tex]. The empirical formula is [tex]\(CH\)[/tex].
These do not share the same empirical formula.
2. Pair: [tex]\(CH_2\)[/tex] and [tex]\(CH_4\)[/tex]
- For [tex]\(CH_2\)[/tex]:
- Carbon atoms: 1
- Hydrogen atoms: 2
- The ratio is already [tex]\(1:2\)[/tex]. The empirical formula remains [tex]\(CH_2\)[/tex].
- For [tex]\(CH_4\)[/tex]:
- Carbon atoms: 1
- Hydrogen atoms: 4
- The ratio is already [tex]\(1:4\)[/tex]. The empirical formula remains [tex]\(CH_4\)[/tex].
These do not share the same empirical formula.
3. Pair: [tex]\(CH_3\)[/tex] and [tex]\(C_2H_6\)[/tex]
- For [tex]\(CH_3\)[/tex]:
- Carbon atoms: 1
- Hydrogen atoms: 3
- The ratio is already [tex]\(1:3\)[/tex]. The empirical formula remains [tex]\(CH_3\)[/tex].
- For [tex]\(C_2H_6\)[/tex]:
- Carbon atoms: 2
- Hydrogen atoms: 6
- The ratio is [tex]\(2:6\)[/tex], which simplifies to [tex]\(1:3\)[/tex]. The empirical formula is [tex]\(CH_3\)[/tex].
These do share the same empirical formula.
4. Pair: [tex]\(CH\)[/tex] and [tex]\(C_2H_4\)[/tex]
- For [tex]\(CH\)[/tex]:
- Carbon atoms: 1
- Hydrogen atoms: 1
- The ratio is already [tex]\(1:1\)[/tex]. The empirical formula remains [tex]\(CH\)[/tex].
- For [tex]\(C_2H_4\)[/tex]:
- Carbon atoms: 2
- Hydrogen atoms: 4
- The ratio is [tex]\(2:4\)[/tex], which simplifies to [tex]\(1:2\)[/tex]. The empirical formula is [tex]\(CH_2\)[/tex].
These do not share the same empirical formula.
After comparing all pairs, we find that the third pair, [tex]\(CH_3\)[/tex] and [tex]\(C_2H_6\)[/tex], shares the same empirical formula [tex]\(CH_3\)[/tex].
Thus, the pair that shares the same empirical formula is:
[tex]\[ \boxed{3} \][/tex]
