Carl made a mistake when determining the number of chlorine and oxygen atoms in the chemical formula [tex]\(4 \, \text{Ca}\left(\text{ClO}_3\right)_2\)[/tex]. He forgot to multiply the chlorine and oxygen atoms by the coefficient 4.
Here is the detailed, step-by-step correct calculation:
1. Calcium (Ca):
- The chemical formula shows 4 units of [tex]\( \text{Ca}\left( \text{ClO}_3 \right)_2 \)[/tex].
- Each unit has 1 calcium atom.
- Therefore, the total number of calcium atoms is [tex]\( 1 \text{ Ca/unit} \times 4 \text{ units} = 4 \text{ calcium atoms} \)[/tex].
- The number of calcium atoms Carl calculated is correct.
2. Chlorine (Cl):
- Each unit of [tex]\( \text{Ca}\left( \text{ClO}_3 \right)_2 \)[/tex] has [tex]\(2\)[/tex] chlorine atoms (from [tex]\( \left( \text{ClO}_3 \right)_2 \)[/tex]).
- Therefore, in one unit, we have [tex]\(1 \times 2 = 2\)[/tex] chlorine atoms.
- Since there are 4 units, the total number of chlorine atoms should be [tex]\( 2 \text{ Cl/unit} \times 4 \text{ units} = 8 \text{ chlorine atoms} \)[/tex].
- Carl incorrectly calculated 2 chlorine atoms by forgetting to multiply by the coefficient 4. The correct number is indeed 8.
3. Oxygen (O):
- Each [tex]\( \text{ClO}_3 \)[/tex] has 3 oxygen atoms.
- Since we have [tex]\(\left( \text{ClO}_3 \right)_2\)[/tex], we get [tex]\(3 \times 2 = 6\)[/tex] oxygen atoms in each unit.
- With 4 units, the total oxygen atoms are [tex]\( 6 \text{ O/unit} \times 4 \text{ units} = 24 \text{ oxygen atoms} \)[/tex].
- Carl incorrectly calculated 6 oxygen atoms by forgetting to multiply by the coefficient 4. The correct number is indeed 24.
Hence, Carl's mistake was that he did not multiply the chlorine and oxygen atoms by the coefficient 4.
