Answer :
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.
