To determine which reaction causes an increase in entropy, we need to focus on the behavior of gases in each reaction. Entropy, a measure of the disorder or randomness in a system, often increases when there are more gas molecules created or when those molecules are more dispersed in the final state compared to the initial state.
Let's examine each reaction step by step:
Reaction A:
[tex]\[ SO_2Cl_2(g) \rightarrow SO_2(g) + Cl_2(g) \][/tex]
- Reactants: 1 molecule of gas ([tex]$SO_2Cl_2$[/tex])
- Products: 2 molecules of gas ([tex]$SO_2$[/tex] and [tex]$Cl_2$[/tex])
In this reaction, we start with one gas molecule and end up with two gas molecules. The increase in the number of gas molecules suggests an increase in entropy because there are more possible ways to distribute the energy among the particles.
Reaction B:
[tex]\[ PCl_3(g) + Cl_2(g) \rightarrow PCl_5(g) \][/tex]
- Reactants: 2 molecules of gas ([tex]$PCl_3$[/tex] and [tex]$Cl_2$[/tex])
- Products: 1 molecule of gas ([tex]$PCl_5$[/tex])
Here, we start with two gas molecules and end up with one gas molecule. The decrease in the number of gas molecules suggests a decrease in entropy because the particles have fewer ways to distribute their energy.
Reaction C:
[tex]\[ C_2H_2(g) + H_2(g) \rightarrow C_2H_4(g) \][/tex]
- Reactants: 2 molecules of gas ([tex]$C_2H_2$[/tex] and [tex]$H_2$[/tex])
- Products: 1 molecule of gas ([tex]$C_2H_4$[/tex])
Similar to Reaction B, we start with two gas molecules and end up with one gas molecule, which means a decrease in the number of molecules, indicating a decrease in entropy.
Reaction D:
[tex]\[ 2CO(g) + O_2(g) \rightarrow 2CO_2(g) \][/tex]
- Reactants: 3 molecules of gas (2 [tex]$CO$[/tex] and 1 [tex]$O_2$[/tex])
- Products: 2 molecules of gas (2 [tex]$CO_2$[/tex])
In this reaction, we start with three gas molecules and end up with two gas molecules. The decrease in the number of gas molecules suggests a decrease in entropy.
Based on the analysis of each reaction, Reaction A:
[tex]\[ SO_2Cl_2(g) \rightarrow SO_2(g) + Cl_2(g) \][/tex]
is the one that causes an increase in entropy, as it results in more gas molecules in the products than in the reactants.
So, the correct answer is:
A. [tex]\( SO_2Cl_2(g) \rightarrow SO_2(g) + Cl_2(g) \)[/tex]
