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Sagot :
To determine which of the following reactions would have a decrease in entropy, we'll analyze the change in the number of gas molecules for each reaction. Entropy (S) is a measure of disorder or randomness in a system, and in the context of gas molecules, an increase in the number of gas molecules typically leads to an increase in entropy, while a decrease suggests a decrease in entropy.
Here are the reactions:
A. [tex]\(2 \, \text{SO}_3\, (g) \rightarrow 2 \, \text{SO}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
B. [tex]\(2 \, \text{NO}_2\, (g) \rightarrow \, \text{N}_2\text{O}_4\, (g)\)[/tex]
C. [tex]\(2 \, \text{NH}_3\, (g) \rightarrow \, \text{N}_2\, (g) + 3 \, \text{H}_2\, (g)\)[/tex]
D. [tex]\(2 \, \text{H}_2\text{O}\, (g) \rightarrow 2 \, \text{H}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
### Analysis:
1. Reaction A: [tex]\(2 \, \text{SO}_3\, (g) \rightarrow 2 \, \text{SO}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{SO}_3\, (g) \)[/tex]
- Products: 2 molecules of [tex]\( \text{SO}_2\, (g) \)[/tex] and 1 molecule of [tex]\( \text{O}_2\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 3.
- Entropy change: Increase (since the number of gas molecules increases)
2. Reaction B: [tex]\(2 \, \text{NO}_2\, (g) \rightarrow \, \text{N}_2\text{O}_4\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{NO}_2\, (g) \)[/tex]
- Products: 1 molecule of [tex]\( \text{N}_2\text{O}_4\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 1.
- Entropy change: Decrease (since the number of gas molecules decreases)
3. Reaction C: [tex]\(2 \, \text{NH}_3\, (g) \rightarrow \, \text{N}_2\, (g) + 3 \, \text{H}_2\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{NH}_3\, (g) \)[/tex]
- Products: 1 molecule of [tex]\( \text{N}_2\, (g) \)[/tex] and 3 molecules of [tex]\( \text{H}_2\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 4.
- Entropy change: Increase (since the number of gas molecules increases)
4. Reaction D: [tex]\(2 \, \text{H}_2 \text{O}\, (g) \rightarrow 2 \, \text{H}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{H}_2 \text{O}\, (g) \)[/tex]
- Products: 2 molecules of [tex]\( \text{H}_2\, (g) \)[/tex] and 1 molecule of [tex]\( \text{O}_2\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 3.
- Entropy change: Increase (since the number of gas molecules increases)
From this analysis, it can be concluded that:
The reaction that results in a decrease in entropy is:
B. [tex]\(2 \, \text{NO}_2\, (g) \rightarrow \, \text{N}_2\text{O}_4\, (g)\)[/tex]
Here are the reactions:
A. [tex]\(2 \, \text{SO}_3\, (g) \rightarrow 2 \, \text{SO}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
B. [tex]\(2 \, \text{NO}_2\, (g) \rightarrow \, \text{N}_2\text{O}_4\, (g)\)[/tex]
C. [tex]\(2 \, \text{NH}_3\, (g) \rightarrow \, \text{N}_2\, (g) + 3 \, \text{H}_2\, (g)\)[/tex]
D. [tex]\(2 \, \text{H}_2\text{O}\, (g) \rightarrow 2 \, \text{H}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
### Analysis:
1. Reaction A: [tex]\(2 \, \text{SO}_3\, (g) \rightarrow 2 \, \text{SO}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{SO}_3\, (g) \)[/tex]
- Products: 2 molecules of [tex]\( \text{SO}_2\, (g) \)[/tex] and 1 molecule of [tex]\( \text{O}_2\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 3.
- Entropy change: Increase (since the number of gas molecules increases)
2. Reaction B: [tex]\(2 \, \text{NO}_2\, (g) \rightarrow \, \text{N}_2\text{O}_4\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{NO}_2\, (g) \)[/tex]
- Products: 1 molecule of [tex]\( \text{N}_2\text{O}_4\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 1.
- Entropy change: Decrease (since the number of gas molecules decreases)
3. Reaction C: [tex]\(2 \, \text{NH}_3\, (g) \rightarrow \, \text{N}_2\, (g) + 3 \, \text{H}_2\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{NH}_3\, (g) \)[/tex]
- Products: 1 molecule of [tex]\( \text{N}_2\, (g) \)[/tex] and 3 molecules of [tex]\( \text{H}_2\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 4.
- Entropy change: Increase (since the number of gas molecules increases)
4. Reaction D: [tex]\(2 \, \text{H}_2 \text{O}\, (g) \rightarrow 2 \, \text{H}_2\, (g) + \, \text{O}_2\, (g)\)[/tex]
- Reactants: 2 molecules of [tex]\( \text{H}_2 \text{O}\, (g) \)[/tex]
- Products: 2 molecules of [tex]\( \text{H}_2\, (g) \)[/tex] and 1 molecule of [tex]\( \text{O}_2\, (g) \)[/tex]
- Total number of gas molecules changes from 2 to 3.
- Entropy change: Increase (since the number of gas molecules increases)
From this analysis, it can be concluded that:
The reaction that results in a decrease in entropy is:
B. [tex]\(2 \, \text{NO}_2\, (g) \rightarrow \, \text{N}_2\text{O}_4\, (g)\)[/tex]
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