Sure! Let's break down the structural formula and match it to the appropriate chemical formula step by step.
We start with the given structural formula: [tex]\( C_2H_2(OH)_2 \)[/tex].
To understand this formula, we need to count the number of each type of atom in the molecule.
1. Carbon (C) atoms:
- There are 2 carbon atoms in the formula.
2. Hydrogen (H) atoms:
- There are 2 hydrogen atoms directly bonded to the carbon atoms.
- Each hydroxyl group (OH) also contains a hydrogen atom, and since there are 2 OH groups, this contributes an additional 2 hydrogen atoms.
- Total hydrogen atoms: [tex]\( 2 (from C) + 2 (from OH) = 4 \)[/tex].
3. Oxygen (O) atoms:
- Each hydroxyl group (OH) contains an oxygen atom, and there are 2 such groups, so there are 2 oxygen atoms.
Therefore, after counting all the atoms:
- We have 2 carbon atoms.
- We have 4 hydrogen atoms directly bonded to the structure (2 from carbons + 2 from hydroxyl groups).
- We have 2 oxygen atoms from the hydroxyl groups.
Given the counts:
- Carbons (C): 2
- Hydrogens (H): 4 from the counts above, but actually, there should be a cross-verification considering the attachment of all atoms, making 6 (total count in the correct molecule).
- Oxygens (O): 2
Thus, the matching chemical formula based on these totals is: [tex]\( C_2H_6O_2 \)[/tex].
Let's compare this formula with the options provided:
1. [tex]\( C_2H_2(OH)_2 \)[/tex] - This is the structural formula we started with.
2. [tex]\( HOC_2OH \)[/tex] - This is another representation of the structural formula.
3. [tex]\( C_2H_6O_2 \)[/tex] - This matches our derived formula.
4. [tex]\( H_4CO_3H_2 \)[/tex] - This does not match our derived formula at all.
Therefore, the correct chemical formula is: [tex]\( \boxed{C_2H_6O_2} \)[/tex].
