The decreasing fugacity order of the following compounds is:
i. `PhSO_(3)^(o-)`, ii. `C_(2)H_(5)SO_(3)^(o-)`, iii. `C_(2)H_(5)COO^(o-)`, iv. `overset(o-)(C)N`, v. `overset(o-)(O)H`

Options

A. `(v) gt (iv) gt (iii) gt (ii) gt (i)`
B. `(i) gt (ii) gt (iii) gt (iv) gt (v)`
C. `(iv) gt (v) gt (iii) gt (ii) gt (i)`
D. `(i) gt (ii) gt (iii) gt (v) gt (iv)`

Explanation

To determine the decreasing fugacity order of the given compounds, we can analyze their basic strength and subsequently their leaving group ability. Here’s a step-by-step solution:

### Step 1: Identify the Compounds
The compounds given are:
1. `PhSO3^-` (Phenyl sulfonate)
2. `C2H5SO3^-` (Ethyl sulfonate)
3. `C2H5COO^-` (Ethanoate)
4. `CN^-` (Cyanide)
5. `OH^-` (Hydroxide)

### Step 2: Determine Conjugate Acids
To analyze the basic strength, we first determine the conjugate acids of each compound by adding a proton (H⁺):
1. `PhSO3^-` → `PhSO3H` (Phenyl sulfonic acid)
2. `C2H5SO3^-` → `C2H5SO3H` (Ethyl sulfonic acid)
3. `C2H5COO^-` → `C2H5COOH` (Propanoic acid)
4. `CN^-` → `HCN` (Hydrogen cyanide)
5. `OH^-` → `H2O` (Water)

### Step 3: Analyze Acidic Strength
Now we will analyze the acidic strength of these conjugate acids:
- **Sulfonic acids** (like `PhSO3H` and `C2H5SO3H`) are generally stronger acids than **carboxylic acids** (like `C2H5COOH`).
- Among sulfonic acids, `PhSO3H` is more acidic than `C2H5SO3H` due to the electron-withdrawing effect of the phenyl group.
- `C2H5COOH` is less acidic than both sulfonic acids but more acidic than `HCN` and `H2O`.
- `HCN` is less acidic than `C2H5COOH`, and `H2O` is the least acidic.

Thus, the order of acidic strength is:
1. `PhSO3H` (most acidic)
2. `C2H5SO3H`
3. `C2H5COOH`
4. `HCN`
5. `H2O` (least acidic)

### Step 4: Determine Basic Strength
The basic strength is inversely related to acidic strength. Therefore, the basic strength order is:
1. `OH^-` (most basic)
2. `CN^-`
3. `C2H5COO^-`
4. `C2H5SO3^-`
5. `PhSO3^-` (least basic)

### Step 5: Determine Leaving Group Strength
The leaving group ability is also inversely related to basic strength. Thus, the order of leaving group strength (or fugacity order) is:
1. `PhSO3^-` (strongest leaving group)
2. `C2H5SO3^-`
3. `C2H5COO^-`
4. `CN^-`
5. `OH^-` (weakest leaving group)

### Conclusion
The decreasing fugacity order of the given compounds is:
`PhSO3^- > C2H5SO3^- > C2H5COO^- > CN^- > OH^-`