To determine which pair of compounds has the same empirical formula, recall that the empirical formula of a compound is the simplest whole-number ratio of atoms in the compound. Let's evaluate each of the given pairs of compounds step by step:
1. [tex]$C _2 H _2$[/tex] and [tex]$C _2 H$[/tex]
- [tex]$C _2 H _2$[/tex]: Contains 2 carbon (C) atoms and 2 hydrogen (H) atoms.
- The ratio is 2:2, which simplifies to 1:1.
- Empirical formula is [tex]$CH$[/tex].
- [tex]$C _2 H$[/tex]: Contains 2 carbon (C) atoms and 1 hydrogen (H) atom.
- The ratio is 2:1.
- Empirical formula is [tex]$C _2 H$[/tex].
- These do not have the same empirical formula.
2. [tex]$CH _3$[/tex] and [tex]$C _2 H _6$[/tex]
- [tex]$CH _3$[/tex]: Contains 1 carbon (C) atom and 3 hydrogen (H) atoms.
- The ratio is 1:3.
- Empirical formula is [tex]$CH _3$[/tex].
- [tex]$C _2 H _6$[/tex]: Contains 2 carbon (C) atoms and 6 hydrogen (H) atoms.
- The ratio is 2:6, which simplifies to 1:3.
- Empirical formula is [tex]$CH _3$[/tex].
- These have the same empirical formula.
3. [tex]$C _3 H _8$[/tex] and [tex]$C _3 H$[/tex]
- [tex]$C _3 H _8$[/tex]: Contains 3 carbon (C) atoms and 8 hydrogen (H) atoms.
- The ratio is 3:8.
- Empirical formula is [tex]$C _3 H _8$[/tex].
- [tex]$C _3 H$[/tex]: Contains 3 carbon (C) atoms and 1 hydrogen (H) atom.
- The ratio is 3:1.
- Empirical formula is [tex]$C _3 H$[/tex].
- These do not have the same empirical formula.
4. [tex]$C _2 H _6$[/tex] and [tex]$CH$[/tex]
- [tex]$C _2 H _6$[/tex]: Contains 2 carbon (C) atoms and 6 hydrogen (H) atoms.
- The ratio is 2:6, which simplifies to 1:3.
- Empirical formula is [tex]$CH _3$[/tex].
- [tex]$CH$[/tex]: Contains 1 carbon (C) atom and 1 hydrogen (H) atom.
- The ratio is 1:1.
- Empirical formula is [tex]$CH$[/tex].
- These do not have the same empirical formula.
From the above analysis, the pair of compounds that has the same empirical formula is:
[tex]$CH _3$[/tex] and [tex]$C _2 H _6$[/tex].
