Answer :
To determine which chemical equation obeys the law of conservation of mass, we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms of each element on the product side. Let's analyze each given equation:
### Option A: \(2 C_4H_{10} + 2 Cl_2 + 12 O_2 \rightarrow 7 CO_2 + CCl_4 + 10 H_2O\)
Reactants:
- C: \(2 \times 4 = 8\)
- H: \(2 \times 10 = 20\)
- Cl: \(2 \times 2 = 4\)
- O: \(12 \times 2 = 24\)
Products:
- C: \(7 + 1 = 8\)
- H: \(10 \times 2 = 20\)
- Cl: \(4\)
- O: \(7 \times 2 + 10 = 14 + 10 = 24\)
Balanced: Yes
### Option B: \(C_4H_{10} + Cl_2 + 2 O_2 \rightarrow 7 CO_2 + CCl_4 + 8 H_2O\)
Reactants:
- C: \(4\)
- H: \(10\)
- Cl: \(2\)
- O: \(2 \times 2 = 4\)
Products:
- C: \(7 + 1 = 8\)
- H: \(8 \times 2 = 16\)
- Cl: \(4\)
- O: \(7 \times 2 + 8 = 14 + 8 = 22\)
Balanced: No
### Option C: \(2 C_4H_{10} + 2 Cl_2 + 12 O_2 \rightarrow 4 CO_2 + CCl_4 + H_2O\)
Reactants:
- C: \(2 \times 4 = 8\)
- H: \(2 \times 10 = 20\)
- Cl: \(2 \times 2 = 4\)
- O: \(12 \times 2 = 24\)
Products:
- C: \(4 + 1 = 5\)
- H: \(1 \times 2 = 2\)
- Cl: \(4\)
- O: \(4 \times 2 + 1 = 8 + 1 = 9\)
Balanced: No
### Option D: \(2 C_4H_{10} + 2 Cl_2 + 6 O_2 \rightarrow CO_2 + CCl_4 + 6 H_2O\)
Reactants:
- C: \(2 \times 4 = 8\)
- H: \(2 \times 10 = 20\)
- Cl: \(2 \times 2 = 4\)
- O: \(6 \times 2 = 12\)
Products:
- C: \(1 + 1 = 2\)
- H: \(6 \times 2 = 12\)
- Cl: \(4\)
- O: \(1 \times 2 + 6 = 2 + 6 = 8\)
Balanced: No
### Option E: \(4 C_4H_{10} + 4 Cl_2 + 14 O_2 \rightarrow 14 CO_2 + CCl_4 + 20 H_2O\)
Reactants:
- C: \(4 \times 4 = 16\)
- H: \(4 \times 10 = 40\)
- Cl: \(4 \times 2 = 8\)
- O: \(14 \times 2 = 28\)
Products:
- C: \(14 + 1 = 15\)
- H: \(20 \times 2 = 40\)
- Cl: \(4\)
- O: \(14 \times 2 + 20 = 28 + 20 = 48\)
Balanced: No
### Conclusion
The reaction that follows the law of conservation of mass is:
[tex]\[ 2 C_4H_{10} + 2 Cl_2 + 12 O_2 \rightarrow 7 CO_2 + CCl_4 + 10 H_2O \][/tex]
So, the correct answer is Option A.
### Option A: \(2 C_4H_{10} + 2 Cl_2 + 12 O_2 \rightarrow 7 CO_2 + CCl_4 + 10 H_2O\)
Reactants:
- C: \(2 \times 4 = 8\)
- H: \(2 \times 10 = 20\)
- Cl: \(2 \times 2 = 4\)
- O: \(12 \times 2 = 24\)
Products:
- C: \(7 + 1 = 8\)
- H: \(10 \times 2 = 20\)
- Cl: \(4\)
- O: \(7 \times 2 + 10 = 14 + 10 = 24\)
Balanced: Yes
### Option B: \(C_4H_{10} + Cl_2 + 2 O_2 \rightarrow 7 CO_2 + CCl_4 + 8 H_2O\)
Reactants:
- C: \(4\)
- H: \(10\)
- Cl: \(2\)
- O: \(2 \times 2 = 4\)
Products:
- C: \(7 + 1 = 8\)
- H: \(8 \times 2 = 16\)
- Cl: \(4\)
- O: \(7 \times 2 + 8 = 14 + 8 = 22\)
Balanced: No
### Option C: \(2 C_4H_{10} + 2 Cl_2 + 12 O_2 \rightarrow 4 CO_2 + CCl_4 + H_2O\)
Reactants:
- C: \(2 \times 4 = 8\)
- H: \(2 \times 10 = 20\)
- Cl: \(2 \times 2 = 4\)
- O: \(12 \times 2 = 24\)
Products:
- C: \(4 + 1 = 5\)
- H: \(1 \times 2 = 2\)
- Cl: \(4\)
- O: \(4 \times 2 + 1 = 8 + 1 = 9\)
Balanced: No
### Option D: \(2 C_4H_{10} + 2 Cl_2 + 6 O_2 \rightarrow CO_2 + CCl_4 + 6 H_2O\)
Reactants:
- C: \(2 \times 4 = 8\)
- H: \(2 \times 10 = 20\)
- Cl: \(2 \times 2 = 4\)
- O: \(6 \times 2 = 12\)
Products:
- C: \(1 + 1 = 2\)
- H: \(6 \times 2 = 12\)
- Cl: \(4\)
- O: \(1 \times 2 + 6 = 2 + 6 = 8\)
Balanced: No
### Option E: \(4 C_4H_{10} + 4 Cl_2 + 14 O_2 \rightarrow 14 CO_2 + CCl_4 + 20 H_2O\)
Reactants:
- C: \(4 \times 4 = 16\)
- H: \(4 \times 10 = 40\)
- Cl: \(4 \times 2 = 8\)
- O: \(14 \times 2 = 28\)
Products:
- C: \(14 + 1 = 15\)
- H: \(20 \times 2 = 40\)
- Cl: \(4\)
- O: \(14 \times 2 + 20 = 28 + 20 = 48\)
Balanced: No
### Conclusion
The reaction that follows the law of conservation of mass is:
[tex]\[ 2 C_4H_{10} + 2 Cl_2 + 12 O_2 \rightarrow 7 CO_2 + CCl_4 + 10 H_2O \][/tex]
So, the correct answer is Option A.
