High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ How many grams of LiOH are produced when 18.5 grams of [tex]$Li_3N$[/tex] are used?

[tex]$Li_3N + 3H_2O \rightarrow NH_3 + 3LiOH$[/tex]

A. 381.6 g
B. 42.4 g
C. 38.2 g
D. 4.24 g

Answer :

Sure! Let's solve the problem step-by-step:

1. Understanding the Equation:
The balanced chemical equation is:
[tex]\[
Li_3N + 3H_2O \rightarrow NH_3 + 3LiOH
\][/tex]
This equation shows that 1 mole of [tex]\(Li_3N\)[/tex] reacts to produce 3 moles of [tex]\(LiOH\)[/tex].

2. Calculate the Molar Masses:
- Molar mass of [tex]\(Li_3N\)[/tex]:
- Lithium ([tex]\(Li\)[/tex]) has an atomic mass of approximately 6.94 g/mol.
- Nitrogen ([tex]\(N\)[/tex]) has an atomic mass of approximately 14.01 g/mol.
- The molar mass of [tex]\(Li_3N\)[/tex] is calculated as:
[tex]\[
(3 \times 6.94) + 14.01 = 34.83 \text{ g/mol}
\][/tex]

- Molar mass of [tex]\(LiOH\)[/tex]:
- Oxygen ([tex]\(O\)[/tex]) has an atomic mass of approximately 16.00 g/mol.
- Hydrogen ([tex]\(H\)[/tex]) has an atomic mass of approximately 1.01 g/mol.
- The molar mass of [tex]\(LiOH\)[/tex] is calculated as:
[tex]\[
6.94 + 16.00 + 1.01 = 23.95 \text{ g/mol}
\][/tex]

3. Calculate the Moles of [tex]\(Li_3N\)[/tex]:
- Given that 18.5 grams of [tex]\(Li_3N\)[/tex] are used, the number of moles of [tex]\(Li_3N\)[/tex] is:
[tex]\[
\frac{18.5 \text{ g}}{34.83 \text{ g/mol}} \approx 0.531 \text{ mol}
\][/tex]

4. Determine the Moles of [tex]\(LiOH\)[/tex] Produced:
- According to the balanced equation, 1 mole of [tex]\(Li_3N\)[/tex] produces 3 moles of [tex]\(LiOH\)[/tex]. Therefore, the moles of [tex]\(LiOH\)[/tex] are:
[tex]\[
3 \times 0.531 = 1.593 \text{ mol}
\][/tex]

5. Calculate the Grams of [tex]\(LiOH\)[/tex] Produced:
- Finally, to find the mass of [tex]\(LiOH\)[/tex] produced, use the moles of [tex]\(LiOH\)[/tex] and its molar mass:
[tex]\[
1.593 \text{ mol} \times 23.95 \text{ g/mol} \approx 38.16 \text{ g}
\][/tex]

Based on these calculations, approximately 38.2 grams of [tex]\(LiOH\)[/tex] are produced when 18.5 grams of [tex]\(Li_3N\)[/tex] are used, which matches the option [tex]\(38.2 \text{ g}\)[/tex].