From beginner to expert, IDNLearn.com has answers for everyone. Our platform provides accurate, detailed responses to help you navigate any topic with ease.
Sagot :
To determine the mass percentage of each compound in the mixture, we need to follow a systematic approach. Here’s a step-by-step solution:
### Given Data
Elemental composition by mass:
- Lithium (Li): 14.19%
- Chlorine (Cl): 10.56%
- Carbon (C): 6.198%
- Oxygen (O): 59.06%
- Nitrogen (N): 10.01%
### Known Molar Masses of Elements (in g/mol)
- Molar mass of Li: 6.94 g/mol
- Molar mass of Cl: 35.45 g/mol
- Molar mass of C: 12.01 g/mol
- Molar mass of O: 16.00 g/mol
- Molar mass of N: 14.01 g/mol
### Calculating Molar Masses of Compounds (in g/mol)
1. Molar mass of lithium chloride (LiCl):
[tex]\[ \text{LiCl} = 6.94 + 35.45 = 42.39 \, \text{g/mol} \][/tex]
2. Molar mass of lithium carbonate ([tex]$Li_2CO_3$[/tex]):
[tex]\[ \text{Li}_2\text{CO}_3 = 2 \times 6.94 + 12.01 + 3 \times 16.00 = 73.89 \, \text{g/mol} \][/tex]
3. Molar mass of lithium nitrate ([tex]$LiNO_3$[/tex]):
[tex]\[ \text{LiNO}_3 = 6.94 + 14.01 + 3 \times 16.00 = 68.95 \, \text{g/mol} \][/tex]
### Calculating the Masses of Compounds
Using the elemental mass percentages to deduce the masses of each compound in a 100 g mixture:
1. Mass of lithium chloride (LiCl):
[tex]\[ \text{Mass of LiCl} = \frac{\text{mass \% of Cl} \times \text{molar mass of LiCl}}{\text{molar mass of Cl}} = \frac{10.56 \times 42.39}{35.45} \approx 12.63 \, \text{g} \][/tex]
2. Mass of lithium carbonate ([tex]$Li_2CO_3$[/tex]):
[tex]\[ \text{Mass of Li}_2\text{CO}_3 = \frac{\text{mass \% of C} \times \text{molar mass of }Li_2CO_3}{\text{molar mass of C}} = \frac{6.198 \times 73.89}{12.01} \approx 38.13 \, \text{g} \][/tex]
3. Mass of lithium nitrate ([tex]$LiNO_3$[/tex]):
[tex]\[ \text{Mass of LiNO}_3 = \frac{\text{mass \% of N} \times \text{molar mass of LiNO}_3}{\text{molar mass of N}} = \frac{10.01 \times 68.95}{14.01} \approx 49.26 \, \text{g} \][/tex]
### Calculating Total Mass and Mass Percentages of Each Compound
Sum of the masses of the compounds:
[tex]\[ \text{Total mass} = 12.63 \, \text{g} (\text{LiCl}) + 38.13 \, \text{g} (\text{Li}_2\text{CO}_3) + 49.26 \, \text{g} (\text{LiNO}_3) = 100.02 \, \text{g} \][/tex]
Now calculate the mass percentages of each compound:
1. Percentage of LiCl:
[tex]\[ \text{Percent of LiCl} = \left( \frac{\text{Mass of LiCl}}{\text{Total mass}} \right) \times 100 = \left( \frac{12.63}{100.02} \right) \times 100 \approx 12.62\% \][/tex]
2. Percentage of lithium carbonate ([tex]$Li_2CO_3$[/tex]):
[tex]\[ \text{Percent of Li}_2\text{CO}_3 = \left( \frac{\text{Mass of Li}_2\text{CO}_3}{\text{Total mass}} \right) \times 100 = \left( \frac{38.13}{100.02} \right) \times 100 \approx 38.12\% \][/tex]
3. Percentage of lithium nitrate ([tex]$LiNO_3$[/tex]):
[tex]\[ \text{Percent of LiNO}_3 = \left( \frac{\text{Mass of LiNO}_3}{\text{Total mass}} \right) \times 100 = \left( \frac{49.26}{100.02} \right) \times 100 \approx 49.25\% \][/tex]
### Summary
- Mass of lithium chloride (LiCl): 12.63 g
- Mass of lithium carbonate ([tex]$Li_2CO_3$[/tex]): 38.13 g
- Mass of lithium nitrate ([tex]$LiNO_3$[/tex]): 49.26 g
- Percentage of lithium chloride (LiCl): 12.62%
- Percentage of lithium carbonate ([tex]$Li_2CO_3$[/tex]): 38.12%
- Percentage of lithium nitrate ([tex]$LiNO_3$[/tex]): 49.25%
These are the calculated values for the masses and mass percentages of each compound in the mixture based on the given elemental analysis.
### Given Data
Elemental composition by mass:
- Lithium (Li): 14.19%
- Chlorine (Cl): 10.56%
- Carbon (C): 6.198%
- Oxygen (O): 59.06%
- Nitrogen (N): 10.01%
### Known Molar Masses of Elements (in g/mol)
- Molar mass of Li: 6.94 g/mol
- Molar mass of Cl: 35.45 g/mol
- Molar mass of C: 12.01 g/mol
- Molar mass of O: 16.00 g/mol
- Molar mass of N: 14.01 g/mol
### Calculating Molar Masses of Compounds (in g/mol)
1. Molar mass of lithium chloride (LiCl):
[tex]\[ \text{LiCl} = 6.94 + 35.45 = 42.39 \, \text{g/mol} \][/tex]
2. Molar mass of lithium carbonate ([tex]$Li_2CO_3$[/tex]):
[tex]\[ \text{Li}_2\text{CO}_3 = 2 \times 6.94 + 12.01 + 3 \times 16.00 = 73.89 \, \text{g/mol} \][/tex]
3. Molar mass of lithium nitrate ([tex]$LiNO_3$[/tex]):
[tex]\[ \text{LiNO}_3 = 6.94 + 14.01 + 3 \times 16.00 = 68.95 \, \text{g/mol} \][/tex]
### Calculating the Masses of Compounds
Using the elemental mass percentages to deduce the masses of each compound in a 100 g mixture:
1. Mass of lithium chloride (LiCl):
[tex]\[ \text{Mass of LiCl} = \frac{\text{mass \% of Cl} \times \text{molar mass of LiCl}}{\text{molar mass of Cl}} = \frac{10.56 \times 42.39}{35.45} \approx 12.63 \, \text{g} \][/tex]
2. Mass of lithium carbonate ([tex]$Li_2CO_3$[/tex]):
[tex]\[ \text{Mass of Li}_2\text{CO}_3 = \frac{\text{mass \% of C} \times \text{molar mass of }Li_2CO_3}{\text{molar mass of C}} = \frac{6.198 \times 73.89}{12.01} \approx 38.13 \, \text{g} \][/tex]
3. Mass of lithium nitrate ([tex]$LiNO_3$[/tex]):
[tex]\[ \text{Mass of LiNO}_3 = \frac{\text{mass \% of N} \times \text{molar mass of LiNO}_3}{\text{molar mass of N}} = \frac{10.01 \times 68.95}{14.01} \approx 49.26 \, \text{g} \][/tex]
### Calculating Total Mass and Mass Percentages of Each Compound
Sum of the masses of the compounds:
[tex]\[ \text{Total mass} = 12.63 \, \text{g} (\text{LiCl}) + 38.13 \, \text{g} (\text{Li}_2\text{CO}_3) + 49.26 \, \text{g} (\text{LiNO}_3) = 100.02 \, \text{g} \][/tex]
Now calculate the mass percentages of each compound:
1. Percentage of LiCl:
[tex]\[ \text{Percent of LiCl} = \left( \frac{\text{Mass of LiCl}}{\text{Total mass}} \right) \times 100 = \left( \frac{12.63}{100.02} \right) \times 100 \approx 12.62\% \][/tex]
2. Percentage of lithium carbonate ([tex]$Li_2CO_3$[/tex]):
[tex]\[ \text{Percent of Li}_2\text{CO}_3 = \left( \frac{\text{Mass of Li}_2\text{CO}_3}{\text{Total mass}} \right) \times 100 = \left( \frac{38.13}{100.02} \right) \times 100 \approx 38.12\% \][/tex]
3. Percentage of lithium nitrate ([tex]$LiNO_3$[/tex]):
[tex]\[ \text{Percent of LiNO}_3 = \left( \frac{\text{Mass of LiNO}_3}{\text{Total mass}} \right) \times 100 = \left( \frac{49.26}{100.02} \right) \times 100 \approx 49.25\% \][/tex]
### Summary
- Mass of lithium chloride (LiCl): 12.63 g
- Mass of lithium carbonate ([tex]$Li_2CO_3$[/tex]): 38.13 g
- Mass of lithium nitrate ([tex]$LiNO_3$[/tex]): 49.26 g
- Percentage of lithium chloride (LiCl): 12.62%
- Percentage of lithium carbonate ([tex]$Li_2CO_3$[/tex]): 38.12%
- Percentage of lithium nitrate ([tex]$LiNO_3$[/tex]): 49.25%
These are the calculated values for the masses and mass percentages of each compound in the mixture based on the given elemental analysis.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.
