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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].
Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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