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Sagot :
To determine the coefficient of lithium fluoride ([tex]\( LiF \)[/tex]) in the balanced chemical reaction, we'll follow these steps:
1. Write the Unbalanced Equation:
[tex]\[ BF_3 + Li_2SO_3 \rightarrow B_2(SO_3)_3 + LiF \][/tex]
2. Identify and Count Atoms of Each Element in Reactants and Products:
- Boron (B):
- Reactants: [tex]\(1 \times BF_3\)[/tex]
- Products: [tex]\(2 \times B_2(SO_3)_3\)[/tex]
So, we have:
- Reactants: [tex]\(1B\)[/tex]
- Products: [tex]\(2 \times 2 = 4B\)[/tex]
- Fluorine (F):
- Reactants: [tex]\(3 \times BF_3\)[/tex]
- Products: [tex]\(1 \times LiF\)[/tex]
So, we have:
- Reactants: [tex]\(3F\)[/tex]
- Products: [tex]\(1 \text{per LiF}\)[/tex]
- Lithium (Li):
- Reactants: [tex]\(2 \times Li_2SO_3\)[/tex]
- Products: [tex]\(1 \times LiF\)[/tex]
So, we have:
- Reactants: [tex]\(2Li\)[/tex]
- Products: [tex]\(1 \text{per LiF}\)[/tex]
- Sulfur (S):
- Reactants: [tex]\(1 \times Li_2SO_3\)[/tex]
- Products: [tex]\(3 \times B_2(SO_3)_3\)[/tex]
So, we have:
- Reactants: [tex]\(1S\)[/tex]
- Products: [tex]\(3 \text{per B_2(SO_3)_3}\)[/tex]
- Oxygen (O):
- Reactants: [tex]\(3 \times Li_2SO_3\)[/tex]
- Products: [tex]\(3 \times B_2(SO_3)_3\)[/tex]
So, we have:
- Reactants: [tex]\(3O\)[/tex]
- Products: [tex]\(3 \times 3 = 9O\ per B_2(SO_3)_3\)[/tex]
3. Set Up the Balancing Equations Based on These Counts:
- Balance Boron (B):
[tex]\[ 1BF_3 = 2B_2(SO_3)_3 \][/tex]
- Balance Fluorine (F):
[tex]\[ 3BF_3 = 9B_2(SO_3)_3 \][/tex]
- Balance Lithium (Li):
[tex]\[ 2Li_2SO_3 = 2LiF \][/tex]
- Balance Sulfur (S):
[tex]\[ 1Li_2SO_3 = 3B_2(SO_3)_3 \][/tex]
- Balance Oxygen (O):
[tex]\[ 3Li_2SO_3 = 9B_2(SO_3)_3 \][/tex]
4. Solve the System of Equations to Find the Coefficients:
Solving these relationships, we find:
[tex]\[ BF_3 = 0 \][/tex]
[tex]\[ Li_2SO_3 = 0 \][/tex]
[tex]\[ B_2(SO_3)_3 = 0 \][/tex]
[tex]\[ LiF = 0 \][/tex]
5. Interpret the Results:
Since we want to balance the equation and the coefficients (according to the solutions) are all zero, it indicates that the equation does not balance as written, which implies the reaction does not occur under these conditions or the coefficients provided lead us to an intractable solution.
Given the numerical results, the coefficient of [tex]\( LiF \)[/tex] is 0. According to the provided answer options (1, 3, 4, 6), none fit exactly. Hence, based on simplified practical scenarios or potential simplifications, the coefficient which is closest in alignment, under varied oversight, might traditionally be reassigned.
Final Answer:
Under rigorous academic scrutiny traditionally it might indicate the reaction isn't feasible under standard practical conditions, thereby neither 1, 3, 4, nor 6 is strictly rigorous under precise academic balance depiction.
1. Write the Unbalanced Equation:
[tex]\[ BF_3 + Li_2SO_3 \rightarrow B_2(SO_3)_3 + LiF \][/tex]
2. Identify and Count Atoms of Each Element in Reactants and Products:
- Boron (B):
- Reactants: [tex]\(1 \times BF_3\)[/tex]
- Products: [tex]\(2 \times B_2(SO_3)_3\)[/tex]
So, we have:
- Reactants: [tex]\(1B\)[/tex]
- Products: [tex]\(2 \times 2 = 4B\)[/tex]
- Fluorine (F):
- Reactants: [tex]\(3 \times BF_3\)[/tex]
- Products: [tex]\(1 \times LiF\)[/tex]
So, we have:
- Reactants: [tex]\(3F\)[/tex]
- Products: [tex]\(1 \text{per LiF}\)[/tex]
- Lithium (Li):
- Reactants: [tex]\(2 \times Li_2SO_3\)[/tex]
- Products: [tex]\(1 \times LiF\)[/tex]
So, we have:
- Reactants: [tex]\(2Li\)[/tex]
- Products: [tex]\(1 \text{per LiF}\)[/tex]
- Sulfur (S):
- Reactants: [tex]\(1 \times Li_2SO_3\)[/tex]
- Products: [tex]\(3 \times B_2(SO_3)_3\)[/tex]
So, we have:
- Reactants: [tex]\(1S\)[/tex]
- Products: [tex]\(3 \text{per B_2(SO_3)_3}\)[/tex]
- Oxygen (O):
- Reactants: [tex]\(3 \times Li_2SO_3\)[/tex]
- Products: [tex]\(3 \times B_2(SO_3)_3\)[/tex]
So, we have:
- Reactants: [tex]\(3O\)[/tex]
- Products: [tex]\(3 \times 3 = 9O\ per B_2(SO_3)_3\)[/tex]
3. Set Up the Balancing Equations Based on These Counts:
- Balance Boron (B):
[tex]\[ 1BF_3 = 2B_2(SO_3)_3 \][/tex]
- Balance Fluorine (F):
[tex]\[ 3BF_3 = 9B_2(SO_3)_3 \][/tex]
- Balance Lithium (Li):
[tex]\[ 2Li_2SO_3 = 2LiF \][/tex]
- Balance Sulfur (S):
[tex]\[ 1Li_2SO_3 = 3B_2(SO_3)_3 \][/tex]
- Balance Oxygen (O):
[tex]\[ 3Li_2SO_3 = 9B_2(SO_3)_3 \][/tex]
4. Solve the System of Equations to Find the Coefficients:
Solving these relationships, we find:
[tex]\[ BF_3 = 0 \][/tex]
[tex]\[ Li_2SO_3 = 0 \][/tex]
[tex]\[ B_2(SO_3)_3 = 0 \][/tex]
[tex]\[ LiF = 0 \][/tex]
5. Interpret the Results:
Since we want to balance the equation and the coefficients (according to the solutions) are all zero, it indicates that the equation does not balance as written, which implies the reaction does not occur under these conditions or the coefficients provided lead us to an intractable solution.
Given the numerical results, the coefficient of [tex]\( LiF \)[/tex] is 0. According to the provided answer options (1, 3, 4, 6), none fit exactly. Hence, based on simplified practical scenarios or potential simplifications, the coefficient which is closest in alignment, under varied oversight, might traditionally be reassigned.
Final Answer:
Under rigorous academic scrutiny traditionally it might indicate the reaction isn't feasible under standard practical conditions, thereby neither 1, 3, 4, nor 6 is strictly rigorous under precise academic balance depiction.
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