Arrange the following in the increasing order of their ability as a leaving group:
(a) `CH_(3)S^(-). CH_(3)O^(-), CF_(3)^(-)` and `F^(-)`
(b) `CF_(3)SO_(3)^(-), CH_(3)SO_(3)^(-)` and `CH_(3)COO^(-)`

Answer

To solve the problem of arranging the given groups in increasing order of their ability as leaving groups, we need to consider the acidity of the leaving groups. The more acidic a compound is, the better it is as a leaving group. This is because stronger acids have weaker conjugate bases, which are better leaving groups.

### Part (a):
Given groups: `CH3S^(-), CH3O^(-), CF3^(-), F^(-)`

**Step 1: Determine the acidity of each group.**
- **F^(-)**: The conjugate base of HF, which is a strong acid. Therefore, F^(-) is very weak as a base and a good leaving group.
- **CF3^(-)**: The conjugate base of trifluoroacetic acid (CF3COOH), which is also a strong acid due to the electronegative fluorine atoms stabilizing the negative charge. This makes CF3^(-) a good leaving group.
- **CH3O^(-)**: The conjugate base of methanol (CH3OH), which is a weaker acid than HF and trifluoroacetic acid. Thus, CH3O^(-) is a poorer leaving group compared to F^(-) and CF3^(-).
- **CH3S^(-)**: The conjugate base of methanethiol (CH3SH), which is a weaker acid than methanol. Therefore, CH3S^(-) is the least effective leaving group among the four.

**Step 2: Arrange them in increasing order of their leaving group ability.**
- The order based on acidity (and thus leaving group ability) is:
1. CH3S^(-) (least acidic)
2. CH3O^(-)
3. CF3^(-)
4. F^(-) (most acidic)

**Final order for Part (a)**:
**CH3S^(-) < CH3O^(-) < CF3^(-) < F^(-)**

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### Part (b):
Given groups: `CF3SO3^(-), CH3SO3^(-), CH3COO^(-)`

**Step 1: Determine the acidity of each group.**
- **CF3SO3^(-)**: The conjugate base of trifluoromethanesulfonic acid (CF3SO3H), which is a very strong acid due to the presence of electronegative fluorine atoms. Therefore, CF3SO3^(-) is a very good leaving group.
- **CH3SO3^(-)**: The conjugate base of methanesulfonic acid (CH3SO3H), which is a weaker acid than trifluoromethanesulfonic acid. Thus, CH3SO3^(-) is a good leaving group but not as good as CF3SO3^(-).
- **CH3COO^(-)**: The conjugate base of acetic acid (CH3COOH), which is a weaker acid than both trifluoromethanesulfonic acid and methanesulfonic acid. Therefore, CH3COO^(-) is the least effective leaving group among the three.

**Step 2: Arrange them in increasing order of their leaving group ability.**
- The order based on acidity (and thus leaving group ability) is:
1. CH3COO^(-) (least acidic)
2. CH3SO3^(-)
3. CF3SO3^(-) (most acidic)

**Final order for Part (b)**:
**CH3COO^(-) < CH3SO3^(-) < CF3SO3^(-)**

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