Let's carefully analyze the chemical formula [tex]\(4 \, \text{Ca}(\text{ClO}_3)_2\)[/tex] to determine the correct number of atoms for each element and identify Carl's mistake.
The given formula, [tex]\(4 \, \text{Ca}(\text{ClO}_3)_2\)[/tex], contains a coefficient 4, which means there are 4 molecules of [tex]\(\text{Ca}(\text{ClO}_3)_2\)[/tex]. Let's break down the contributions of each element step-by-step:
1. Calcium (Ca):
- Each molecule contains 1 calcium atom.
- Since there are 4 molecules, the total number of calcium atoms is:
[tex]\[
4 \times 1 = 4 \quad \text{calcium atoms}
\][/tex]
2. Chlorine (Cl):
- Each molecule contains [tex]\((\text{ClO}_3)_2\)[/tex], which means 2 chlorine atoms.
- Since there are 4 molecules, the total number of chlorine atoms is:
[tex]\[
4 \times 2 = 8 \quad \text{chlorine atoms}
\][/tex]
3. Oxygen (O):
- Each molecule contains [tex]\(3\)[/tex] oxygen atoms per [tex]\(\text{ClO}_3\)[/tex], and there are 2 [tex]\(\text{ClO}_3\)[/tex] groups in each molecule, so each molecule contains [tex]\(3 \times 2 = 6\)[/tex] oxygen atoms.
- Since there are 4 molecules, the total number of oxygen atoms is:
[tex]\[
4 \times 6 = 24 \quad \text{oxygen atoms}
\][/tex]
By combining these contributions, we can fill in the correct table for each element:
[tex]\[
\begin{array}{|l|c|c|}
\hline \text{Element} & \text{Calculation} & \text{Total Atoms} \\
\hline \text{Calcium} & 1 \times 4 & 4 \\
\hline \text{Chlorine} & 2 \times 4 & 8 \\
\hline \text{Oxygen} & 6 \times 4 & 24 \\
\hline
\end{array}
\][/tex]
Now, let's compare this to Carl's table and find his mistake:
[tex]\[
\begin{array}{|l|c|c|}
\hline \text{Element} & \text{Calculation} & \text{Total atoms} \\
\hline \text{Calcium} & 1 \times 4 & 4 \\
\hline \text{Chlorine} & 1 \times 2 & 2 \\
\hline \text{Oxygen} & 3 \times 2 & 6 \\
\hline
\end{array}
\][/tex]
The correct calculation for chlorine and oxygen atoms involves multiplying by the coefficient 4, which Carl missed. Therefore, Carl's mistake is:
- He did not multiply the chlorine and oxygen atoms by the coefficient 4.
Hence, the correct answer is:
He did not multiply the chlorine and oxygen atoms by the coefficient 4.
