Certainly! Let's walk through the solution step-by-step.
### Step 1: Determine the molar masses
- Molar mass of lithium (Li): 6.94 grams per mole
- Molar mass of lithium nitride (Li₃N): 34.83 grams per mole
### Step 2: Calculate the moles of lithium (Li)
Given the mass of lithium is 5.0 grams:
[tex]\[ \text{Moles of Li} = \frac{\text{Mass of Li}}{\text{Molar mass of Li}} \][/tex]
[tex]\[ \text{Moles of Li} = \frac{5.0 \text{ grams}}{6.94 \text{ grams/mole}} \][/tex]
[tex]\[ \text{Moles of Li} \approx 0.7205 \text{ moles} \][/tex]
### Step 3: Utilize the stoichiometry of the reaction
The reaction between lithium and nitrogen gas to form lithium nitride is:
[tex]\[ 6 \text{ Li} + \text{N}_2 \rightarrow 2 \text{ Li}_3\text{N} \][/tex]
From this stoichiometry, 6 moles of lithium produce 2 moles of lithium nitride, which simplifies to:
[tex]\[ 3 \text{ moles of Li} \rightarrow 1 \text{ mole of Li}_3\text{N} \][/tex]
### Step 4: Calculate the moles of lithium nitride (Li₃N)
Using the ratio from the reaction, the moles of Li₃N formed can be calculated as follows:
[tex]\[ \text{Moles of Li₃N} = \frac{\text{Moles of Li}}{3} \][/tex]
[tex]\[ \text{Moles of Li₃N} = \frac{0.7205 \text{ moles}}{3} \][/tex]
[tex]\[ \text{Moles of Li₃N} \approx 0.2402 \text{ moles} \][/tex]
### Step 5: Calculate the mass of lithium nitride (Li₃N)
Finally, we need to find the mass of lithium nitride by using its molar mass:
[tex]\[ \text{Mass of Li₃N} = \text{Moles of Li₃N} \times \text{Molar mass of Li₃N} \][/tex]
[tex]\[ \text{Mass of Li₃N} = 0.2402 \text{ moles} \times 34.83 \text{ grams/mole} \][/tex]
[tex]\[ \text{Mass of Li₃N} \approx 8.36 \text{ grams} \][/tex]
Therefore, the theoretical mass of lithium nitride formed when 5.0 grams of lithium reacts in excess nitrogen gas is approximately 8.36 grams.
