To find the correct formula for ammonium carbonate, we need to consider the composition of both the ammonium ion and the carbonate ion. Let's break it down step by step.
1. Identify the ions involved:
- The ammonium ion has the formula [tex]\( NH_4^+ \)[/tex].
- The carbonate ion has the formula [tex]\( CO_3^{2-} \)[/tex].
2. Determine the charges on the ions:
- The ammonium ion [tex]\( NH_4^+ \)[/tex] has a charge of [tex]\( +1 \)[/tex].
- The carbonate ion [tex]\( CO_3^{2-} \)[/tex] has a charge of [tex]\( -2 \)[/tex].
3. Balance the charges:
- Since the carbonate ion has a charge of [tex]\( -2 \)[/tex] and each ammonium ion has a charge of [tex]\( +1 \)[/tex], we need two ammonium ions to balance out the charge of one carbonate ion.
- Therefore, the number of ammonium ions [tex]\( NH_4^+ \)[/tex] needed to balance one carbonate ion [tex]\( CO_3^{2-} \)[/tex] is 2.
4. Write the balanced formula:
- To correctly represent the compound formed by two ammonium ions and one carbonate ion, we use parentheses to show that two ammonium ions [tex]\( NH_4^+ \)[/tex] are needed. This gives us the formula [tex]\( (NH_4)_2CO_3 \)[/tex].
Given the options:
- [tex]\( NH_4 HCO_3 \)[/tex]: Incorrect, as it represents ammonium bicarbonate, not ammonium carbonate.
- [tex]\( NH_4 CO_3 \)[/tex]: Incorrect, as it doesn’t represent the correct combination to balance the charges.
- [tex]\( (NH_4)_2 CO_3 \)[/tex]: Correct, as it properly shows two ammonium ions balancing one carbonate ion.
Thus, the correct formula for ammonium carbonate is [tex]\( \left( NH_4 \right)_2 CO_3 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \left( NH_4 \right)_2 CO_3 \][/tex]
Given these options, the index number corresponding to [tex]\( \left( NH_4 \right)_2 CO_3 \)[/tex] is 2.
