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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].
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].
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