Consider the chemical equation.

[tex]\[ 2 \text{NBr}_3 + 3 \text{NaOH} \rightarrow \text{N}_2 + 3 \text{NaBr} + 3 \text{HOBr} \][/tex]

If there are 40 mol of [tex]\(\text{NBr}_3\)[/tex] and 48 mol of [tex]\(\text{NaOH}\)[/tex], what is the excess reactant?

A. [tex]\(\text{N}_2\)[/tex]
B. [tex]\(\text{NBr}_3\)[/tex]
C. [tex]\(\text{NaOH}\)[/tex]
D. [tex]\(\text{HOBr}\)[/tex]



Answer :

To determine the excess reactant in the given chemical reaction:
[tex]\[ 2 NBr_3 + 3 NaOH \rightarrow N_2 + 3 NaBr + 3 HOBr \][/tex]

we need to follow these steps:

1. Identify the stoichiometric coefficients:
- For [tex]\(NBr_3\)[/tex]: 2
- For [tex]\(NaOH\)[/tex]: 3

2. Determine the moles of each reactant:
- [tex]\(NBr_3\)[/tex]: 40 moles
- [tex]\(NaOH\)[/tex]: 48 moles

3. Calculate the stoichiometric ratios:
- For [tex]\(NBr_3\)[/tex]: [tex]\(\frac{40}{2} = 20\)[/tex]
- For [tex]\(NaOH\)[/tex]: [tex]\(\frac{48}{3} = 16\)[/tex]

4. Compare the stoichiometric ratios to identify the limiting reactant:
- [tex]\(NBr_3\)[/tex] has a ratio of 20
- [tex]\(NaOH\)[/tex] has a ratio of 16

Since the stoichiometric ratio of [tex]\(NaOH\)[/tex] is smaller (16 < 20), [tex]\(NaOH\)[/tex] is the limiting reactant.

5. Determine the excess reactant:
- Since [tex]\(NaOH\)[/tex] is the limiting reactant, [tex]\(NBr_3\)[/tex] is the excess reactant.

6. Calculate the amount of [tex]\(NBr_3\)[/tex] remaining after the reaction:
[tex]\[ \text{Used } NaOH = 48 \text{ moles} \][/tex]
- From the stoichiometric ratio, 2 moles of [tex]\(NBr_3\)[/tex] react with 3 moles of [tex]\(NaOH\)[/tex].
- Therefore, to react with 48 moles of [tex]\(NaOH\)[/tex], the required [tex]\(NBr_3\)[/tex] is:
[tex]\[ \left(\frac{2}{3}\right) \times 48 = 32 \text{ moles of } NBr_3 \][/tex]

- The initial amount of [tex]\(NBr_3\)[/tex] is 40 moles, so the excess [tex]\(NBr_3\)[/tex] is:
[tex]\[ 40 - 32 = 8 \text{ moles} \][/tex]

Given this analysis, the excess reactant is [tex]\(NBr_3\)[/tex], and 8 moles of [tex]\(NBr_3\)[/tex] remain unreacted. Thus, the answer to the question is:
[tex]\[ \boxed{NBr_3} \][/tex]