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Elena makes the table below to determine the number of atoms of each element in the chemical formula [tex]3\left( NH _4\right)_2 SO _4[/tex].

\begin{tabular}{|l|c|c|}
\hline
Element & Calculation & Total atoms \\
\hline
Nitrogen & [tex]1 \times 2 \times 3[/tex] & 6 \\
\hline
Hydrogen & [tex]4 \times 2 \times 3[/tex] & 24 \\
\hline
Sulfur & [tex]1 \times 4 \times 3[/tex] & 12 \\
\hline
Oxygen & [tex]4 \times 3[/tex] & 12 \\
\hline
\end{tabular}

What mistake did Elena make?

A. She should not have multiplied the sulfur atoms by the subscript 4.
B. She should not have multiplied the nitrogen atoms by the subscript 2.
C. She should not have multiplied the oxygen atoms by the coefficient 3.
D. She should not have multiplied the hydrogen atoms by the coefficient 3.

Sagot :

GinnyAnswer
Let's carefully analyze the chemical formula [tex]\(3 \left( NH_4 \right)_2 SO_4\)[/tex] and Elena's calculations to identify the mistake:

1. Understanding the chemical formula:
- The expression [tex]\(3 \left( NH_4 \right)_2 SO_4\)[/tex] means we have 3 units of the compound [tex]\(\left( NH_4 \right)_2 SO_4\)[/tex].
- Within each unit of [tex]\(\left( NH_4 \right)_2 SO_4\)[/tex]:
- [tex]\(\left( NH_4 \right)_2\)[/tex]:
- 2 Nitrogen atoms because [tex]\(N\)[/tex] appears once and the subscript 2 indicates there are 2 of them.
- 2 groups of [tex]\(H_4\)[/tex], so we have [tex]\(4 \times 2 = 8\)[/tex] Hydrogen atoms.
- [tex]\(SO_4\)[/tex]:
- 1 Sulfur atom.
- 4 Oxygen atoms.
- Multiplying these by 3 because we have 3 such units in the entire formula.

2. Elena's Calculations:
- Nitrogen:
- Calculation: [tex]\(1 \times 2 \times 3 = 6\)[/tex]
- Elena's result is correct: there are 6 Nitrogen atoms.
- Hydrogen:
- Calculation: [tex]\(4 \times 2 \times 3 = 24\)[/tex]
- Elena's result is correct: there are 24 Hydrogen atoms.
- Sulfur:
- Calculation: [tex]\(1 \times 4 \times 3 = 12\)[/tex]
- Elena's result here is incorrect.
- Correct calculation: Sulfur does not have any subscript following it (other than implicitly 1), so it should be [tex]\(1 \times 3 = 3\)[/tex]. Elena mistakenly multiplied by the subscript 4 of [tex]\(O_4\)[/tex].
- Oxygen:
- Calculation: [tex]\(4 \times 3 = 12\)[/tex]
- Elena's result is correct: there are 12 Oxygen atoms.

3. Identifying the mistake:
- Elena erroneously included the subscript 4 in the calculation for the total number of sulfur atoms. She incorrectly multiplied 1 sulfur atom by 4 and then by 3, leading to [tex]\(1 \times 4 \times 3 = 12\)[/tex].

Therefore, the mistake Elena made is:
- She should not have multiplied the sulfur atoms by the subscript 4.
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