The decreasing fugacity order of the following is:
i. `overset(o-)(C)N`, ii. `overset(o-)(O)H`, iii. `overset(o-)(O) Me`, iv. `overset(o-)(C)H_(3)`, v. `H^(o-)`

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 anions, we need to analyze their basic strengths and relate them to their conjugate acids. The basic strength of an anion is inversely related to the strength of its conjugate acid; stronger conjugate acids correspond to weaker bases, which in turn means better leaving groups.

Let's denote the anions as follows:
1. \( \overset{o-}{(C)N} \) (Cyanide ion, CN⁻)
2. \( \overset{o-}{(O)H} \) (Hydroxide ion, OH⁻)
3. \( \overset{o-}{(O)Me} \) (Methoxide ion, MeO⁻)
4. \( \overset{o-}{(C)H_3} \) (Methyl anion, CH₃⁻)
5. \( H^{(o-)} \) (Hydride ion, H⁻)

### Step 1: Identify the conjugate acids
To find the conjugate acids, we add a proton (H⁺) to each anion:
1. For \( \overset{o-}{(C)N} \): \( CN^- + H^+ \rightarrow HCN \)
2. For \( \overset{o-}{(O)H} \): \( OH^- + H^+ \rightarrow H_2O \)
3. For \( \overset{o-}{(O)Me} \): \( MeO^- + H^+ \rightarrow MeOH \)
4. For \( \overset{o-}{(C)H_3} \): \( CH_3^- + H^+ \rightarrow CH_4 \)
5. For \( H^{(o-)} \): \( H^- + H^+ \rightarrow H_2 \)

### Step 2: Determine the acidic strength of the conjugate acids
Now we compare the acidic strength of the conjugate acids:
- \( HCN \) is the most acidic.
- \( MeOH \) is more acidic than \( H_2O \).
- \( H_2 \) is less acidic than \( CH_4 \).

Thus, the order of acidic strength from strongest to weakest is:
1. \( HCN \) (most acidic)
2. \( MeOH \)
3. \( H_2O \)
4. \( H_2 \)
5. \( CH_4 \) (least acidic)

### Step 3: Determine the basic strength of the anions
Since stronger acids correspond to weaker bases, we can reverse the order of acidic strength to determine the basic strength:
1. \( CH_3^- \) (strongest base)
2. \( H^- \)
3. \( OH^- \)
4. \( MeO^- \)
5. \( CN^- \) (weakest base)

### Step 4: Determine the fugacity order (leaving group strength)
The fugacity order (or leaving group strength) is the reverse of the basic strength:
1. \( CN^- \) (best leaving group)
2. \( MeO^- \)
3. \( OH^- \)
4. \( H^- \)
5. \( CH_3^- \) (worst leaving group)

### Final Order
Thus, the decreasing fugacity order of the anions is:
1. \( CN^- \)
2. \( MeO^- \)
3. \( OH^- \)
4. \( H^- \)
5. \( CH_3^- \)

### Answer
The decreasing fugacity order of the given anions is:
\[ CN^- > MeO^- > OH^- > H^- > CH_3^- \]