To determine the number of moles of lithium nitride ([tex]\(Li_3N\)[/tex]) produced when 12 moles of lithium ([tex]\(Li\)[/tex]) react with excess nitrogen gas ([tex]\(N_2\)[/tex]), we'll use the stoichiometric relationships from the balanced chemical equation:
[tex]\[
6 \text{Li} + N_2 \rightarrow 2 \text{Li}_3\text{N}
\][/tex]
Step-by-step solution:
1. Identify the stoichiometric coefficients from the balanced chemical equation:
- For [tex]\(Li\)[/tex], the coefficient is 6.
- For [tex]\(Li_3N\)[/tex], the coefficient is 2.
This means 6 moles of lithium produce 2 moles of lithium nitride.
2. Set up the stoichiometric ratio:
- The ratio of moles of [tex]\(Li\)[/tex] to moles of [tex]\(Li_3N\)[/tex] is 6:2, which simplifies to 3:1.
3. Calculate the number of moles of lithium nitride produced:
- Given 12 moles of [tex]\(Li\)[/tex], and knowing it takes 3 moles of [tex]\(Li\)[/tex] to produce 1 mole of [tex]\(Li_3N\)[/tex], we can use this ratio to find the moles of [tex]\(Li_3N\)[/tex].
[tex]\[
\text{Moles of } Li_3N = \frac{\text{Moles of } Li}{3}
\][/tex]
4. Insert the given moles of lithium into the equation:
[tex]\[
\text{Moles of } Li_3N = \frac{12 \text{ moles } Li}{3}
\][/tex]
[tex]\[
\text{Moles of } Li_3N = 4 \text{ moles}
\][/tex]
Therefore, when 12 moles of lithium react with excess nitrogen gas, 4.0 moles of lithium nitride will be produced.
So, the correct answer is:
[tex]\[
4.0 \text{ mol}
\][/tex]
