To solve the given problem of matching the structural formula to the chemical formula, let's analyze and compare each of the formulas provided:
1. Formula: [tex]\(C_2H_2(OH)_2\)[/tex]
- To understand this, note that it implies there are two hydroxyl groups (OH) attached to a two-carbon molecule. This can be rewritten as:
- 2 Carbon atoms (C) = [tex]\(C_2\)[/tex]
- 2 Hydrogen atoms from hydroxyl groups (OH) [tex]\( \rightarrow 2 \times (OH) = 2H + 2O\)[/tex]
- When written in a complete molecular form, this becomes:
- [tex]\(C_2H_4O_2\)[/tex]
2. Formula: [tex]\(HOC_2OH\)[/tex]
- Looking closely, this has a hydroxyl group (OH) on each end of a two-carbon backbone. This is ethylene glycol (a common compound):
- [tex]\(HOC_2OH\)[/tex]
can also be rearranged to show:
- 2 Carbon atoms (C) = [tex]\(C_2\)[/tex]
- 2 Hydroxyl groups [tex]\(2 \times (OH) = 2 \;H\)[/tex] and [tex]\(2 \;O\)[/tex]
- 4 additional Hydrogen atoms (H) bound to carbons
- The resulting molecular formula is:
- [tex]\(C_2H_6O_2\)[/tex]
3. Formula: [tex]\(C_2H_6O_2\)[/tex]
- This is a standard chemical formula indicating:
- 2 Carbon atoms (C)
- 6 Hydrogen atoms (H)
- 2 Oxygen atoms (O)
- This matches what we calculated for ethylene glycol ([tex]\(HOC_2OH\)[/tex]).
4. Formula: [tex]\(H_4CO_3H_2\)[/tex]
- Analyzing it, this formula looks incorrect or unbalanced:
- 4 Hydrogen atoms (H4) + 2 Hydrogen atoms (H2) = [tex]\(H_6\)[/tex]
- 1 Carbon atom (C1)
- 3 Oxygen atoms (O3)
- This should normally be rewritten or adjusted to balance properly, and finding a correct common molecule for this formula is difficult without modification.
Concluding from our careful analysis:
- The structural formula [tex]\(HOC_2OH\)[/tex] matches the chemical formula [tex]\(C_2H_6O_2\)[/tex].
