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Sagot :
To determine the correct equation representing the reaction, we need to examine the stoichiometry and balance of each given option. This involves ensuring that the number of atoms of each element on the reactant side equals the number on the product side.
Let's analyze each option:
Option A: [tex]\(2 \, CO + 2 \, NO \rightarrow 2 \, C_2N_2 + O_2\)[/tex]
- Reactants: [tex]\(2 \, CO\)[/tex] has [tex]\(2 \, C\)[/tex] and [tex]\(2 \, O\)[/tex], [tex]\(2 \, NO\)[/tex] has [tex]\(2 \, N\)[/tex] and [tex]\(2 \, O\)[/tex]
- Total Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]
- Products: [tex]\(2 \, C_2N_2\)[/tex] has [tex]\(2 \times 2 = 4 \, C\)[/tex] and [tex]\(2 \times 2 = 4 \, N\)[/tex], [tex]\(O_2\)[/tex] has [tex]\(2 \, O\)[/tex]
- Total Products: [tex]\(4 \, C\)[/tex], [tex]\(4 \, N\)[/tex], [tex]\(2 \, O\)[/tex]
The number of atoms is not balanced (Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]; Products: [tex]\(4 \, C\)[/tex], [tex]\(4 \, N\)[/tex], [tex]\(2 \, O\)[/tex]), so Option A is incorrect.
Option B: [tex]\(CO + NO \rightarrow 2 \, CO_2 + 2 \, N_2\)[/tex]
- Reactants: [tex]\(1 \, CO\)[/tex] has [tex]\(1 \, C\)[/tex] and [tex]\(1 \, O\)[/tex], [tex]\(1 \, NO\)[/tex] has [tex]\(1 \, N\)[/tex] and [tex]\(1 \, O\)[/tex]
- Total Reactants: [tex]\(1 \, C\)[/tex], [tex]\(1 \, N\)[/tex], [tex]\(2 \, O\)[/tex]
- Products: [tex]\(2 \, CO_2\)[/tex] has [tex]\(2 \times 1 = 2 \, C\)[/tex], [tex]\(2 \times 2 = 4 \, O\)[/tex], [tex]\(2 \, N_2\)[/tex] has [tex]\(2 \times 2 = 4 \, N\)[/tex]
- Total Products: [tex]\(2 \, C\)[/tex], [tex]\(4 \, O\)[/tex], [tex]\(4 \, N\)[/tex]
The number of atoms is not balanced (Reactants: [tex]\(1 \, C\)[/tex], [tex]\(1 \, N\)[/tex], [tex]\(2 \, O\)[/tex]; Products: [tex]\(2 \, C\)[/tex], [tex]\(4 \, N\)[/tex], [tex]\(4 \, O\)[/tex]), so Option B is incorrect.
Option C: [tex]\(2 \, CO_2 + 2 \, NO \rightarrow CO_2 + N_2\)[/tex]
- Reactants: [tex]\(2 \, CO_2\)[/tex] has [tex]\(2 \times 1 = 2 \, C\)[/tex] and [tex]\(2 \times 2 = 4 \, O\)[/tex], [tex]\(2 \, NO\)[/tex] has [tex]\(2 \, N\)[/tex] and [tex]\(2 \, O\)[/tex]
- Total Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(6 \, O\)[/tex]
- Products: [tex]\(1 \, CO_2\)[/tex] has [tex]\(1 \, C\)[/tex] and [tex]\(2 \, O\)[/tex], [tex]\(1 \, N_2\)[/tex] has [tex]\(2 \, N\)[/tex]
- Total Products: [tex]\(1 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(2 \, O\)[/tex]
The number of atoms is not balanced (Reactants: [tex]\(2 \, C\)[/tex], [tex]\(6 \, O\)[/tex], [tex]\(2 \, N\)[/tex]; Products: [tex]\(1 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(2 \, O\)[/tex]), so Option C is incorrect.
Option D: [tex]\(2 \, CO + 2 \, NO \rightarrow 2 \, CO_2 + N_2\)[/tex]
- Reactants: [tex]\(2 \, CO\)[/tex] has [tex]\(2 \, C\)[/tex] and [tex]\(2 \, O\)[/tex], [tex]\(2 \, NO\)[/tex] has [tex]\(2 \, N\)[/tex] and [tex]\(2 \, O\)[/tex]
- Total Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]
- Products: [tex]\(2 \, CO_2\)[/tex] has [tex]\(2 \times 1 = 2 \, C\)[/tex] and [tex]\(2 \times 2 = 4 \, O\)[/tex], [tex]\(1 \, N_2\)[/tex] has [tex]\(2 \, N\)[/tex]
- Total Products: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]
The number of atoms is balanced (Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]; Products: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]), so Option D is correct.
Thus, the correct answer is:
D. [tex]\(2 \, CO + 2 \, NO \rightarrow 2 \, CO_2 + N_2\)[/tex]
Let's analyze each option:
Option A: [tex]\(2 \, CO + 2 \, NO \rightarrow 2 \, C_2N_2 + O_2\)[/tex]
- Reactants: [tex]\(2 \, CO\)[/tex] has [tex]\(2 \, C\)[/tex] and [tex]\(2 \, O\)[/tex], [tex]\(2 \, NO\)[/tex] has [tex]\(2 \, N\)[/tex] and [tex]\(2 \, O\)[/tex]
- Total Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]
- Products: [tex]\(2 \, C_2N_2\)[/tex] has [tex]\(2 \times 2 = 4 \, C\)[/tex] and [tex]\(2 \times 2 = 4 \, N\)[/tex], [tex]\(O_2\)[/tex] has [tex]\(2 \, O\)[/tex]
- Total Products: [tex]\(4 \, C\)[/tex], [tex]\(4 \, N\)[/tex], [tex]\(2 \, O\)[/tex]
The number of atoms is not balanced (Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]; Products: [tex]\(4 \, C\)[/tex], [tex]\(4 \, N\)[/tex], [tex]\(2 \, O\)[/tex]), so Option A is incorrect.
Option B: [tex]\(CO + NO \rightarrow 2 \, CO_2 + 2 \, N_2\)[/tex]
- Reactants: [tex]\(1 \, CO\)[/tex] has [tex]\(1 \, C\)[/tex] and [tex]\(1 \, O\)[/tex], [tex]\(1 \, NO\)[/tex] has [tex]\(1 \, N\)[/tex] and [tex]\(1 \, O\)[/tex]
- Total Reactants: [tex]\(1 \, C\)[/tex], [tex]\(1 \, N\)[/tex], [tex]\(2 \, O\)[/tex]
- Products: [tex]\(2 \, CO_2\)[/tex] has [tex]\(2 \times 1 = 2 \, C\)[/tex], [tex]\(2 \times 2 = 4 \, O\)[/tex], [tex]\(2 \, N_2\)[/tex] has [tex]\(2 \times 2 = 4 \, N\)[/tex]
- Total Products: [tex]\(2 \, C\)[/tex], [tex]\(4 \, O\)[/tex], [tex]\(4 \, N\)[/tex]
The number of atoms is not balanced (Reactants: [tex]\(1 \, C\)[/tex], [tex]\(1 \, N\)[/tex], [tex]\(2 \, O\)[/tex]; Products: [tex]\(2 \, C\)[/tex], [tex]\(4 \, N\)[/tex], [tex]\(4 \, O\)[/tex]), so Option B is incorrect.
Option C: [tex]\(2 \, CO_2 + 2 \, NO \rightarrow CO_2 + N_2\)[/tex]
- Reactants: [tex]\(2 \, CO_2\)[/tex] has [tex]\(2 \times 1 = 2 \, C\)[/tex] and [tex]\(2 \times 2 = 4 \, O\)[/tex], [tex]\(2 \, NO\)[/tex] has [tex]\(2 \, N\)[/tex] and [tex]\(2 \, O\)[/tex]
- Total Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(6 \, O\)[/tex]
- Products: [tex]\(1 \, CO_2\)[/tex] has [tex]\(1 \, C\)[/tex] and [tex]\(2 \, O\)[/tex], [tex]\(1 \, N_2\)[/tex] has [tex]\(2 \, N\)[/tex]
- Total Products: [tex]\(1 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(2 \, O\)[/tex]
The number of atoms is not balanced (Reactants: [tex]\(2 \, C\)[/tex], [tex]\(6 \, O\)[/tex], [tex]\(2 \, N\)[/tex]; Products: [tex]\(1 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(2 \, O\)[/tex]), so Option C is incorrect.
Option D: [tex]\(2 \, CO + 2 \, NO \rightarrow 2 \, CO_2 + N_2\)[/tex]
- Reactants: [tex]\(2 \, CO\)[/tex] has [tex]\(2 \, C\)[/tex] and [tex]\(2 \, O\)[/tex], [tex]\(2 \, NO\)[/tex] has [tex]\(2 \, N\)[/tex] and [tex]\(2 \, O\)[/tex]
- Total Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]
- Products: [tex]\(2 \, CO_2\)[/tex] has [tex]\(2 \times 1 = 2 \, C\)[/tex] and [tex]\(2 \times 2 = 4 \, O\)[/tex], [tex]\(1 \, N_2\)[/tex] has [tex]\(2 \, N\)[/tex]
- Total Products: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]
The number of atoms is balanced (Reactants: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]; Products: [tex]\(2 \, C\)[/tex], [tex]\(2 \, N\)[/tex], [tex]\(4 \, O\)[/tex]), so Option D is correct.
Thus, the correct answer is:
D. [tex]\(2 \, CO + 2 \, NO \rightarrow 2 \, CO_2 + N_2\)[/tex]
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