`Hg(NO_(3))_(2) overset(Delta) to W + X + O_(2)`
`X + H_(2)O rarr HNO_(2) + HNO_(3)`
`W + HNO_(3) rarr Y + NO + H_(2)O`
`Y + Na_(2)S_(2)O_(3) ("excess") rarr Z + 2NaNO_(3)`

Options

A. `{:("W"," X"," Y"," Z"),(Hg,NO,Hg(NO_(3))._(2),Na[Hg(S_(2)O_(3))_(2)]):}`
B. `{:("W"," X"," Y"," Z"),(Hg,NO_2,Hg(NO_(3))._(2),Na_2[Hg(S_(2)O_(3))_(2)]):}`
C. `{:("W"," X"," Y"," Z"),(Hg,N_(2)O,Hg(NO_(3))._(2),Na_(2)[Hg(S_(2)O_(3))_(2)]):}`
D. `{:("W"," X"," Y"," Z"),(Hg,N_(2)O_(3),Hg(NO_(3))._(2),Na_(3)[Hg(S_(2)O_(3))_(2)]):}`

Explanation

To solve the given question step by step, we will analyze each reaction and identify the compounds W, X, Y, and Z.

### Step 1: Decomposition of Mercury(II) Nitrate
The first reaction is:
\[ \text{Hg(NO}_3\text{)}_2 \overset{\Delta}{\rightarrow} W + X + O_2 \]

When mercury(II) nitrate is heated, it decomposes to form mercury (W), nitrogen dioxide (X), and oxygen gas. The balanced reaction is:
\[ \text{Hg(NO}_3\text{)}_2 \rightarrow \text{Hg} + 2\text{NO}_2 + \text{O}_2 \]

**Identifying W and X:**
- W = Hg (Mercury)
- X = NO₂ (Nitrogen Dioxide)

### Step 2: Reaction of Nitrogen Dioxide with Water
The second reaction is:
\[ X + H_2O \rightarrow HNO_2 + HNO_3 \]

Here, nitrogen dioxide (X) reacts with water to form nitrous acid (HNO₂) and nitric acid (HNO₃). The balanced reaction is:
\[ 2\text{NO}_2 + H_2O \rightarrow HNO_2 + HNO_3 \]

### Step 3: Reaction of Mercury with Nitric Acid
The third reaction is:
\[ W + HNO_3 \rightarrow Y + NO + H_2O \]

Mercury (W) reacts with nitric acid to produce mercury(II) nitrate (Y), nitrogen monoxide (NO), and water. The balanced reaction is:
\[ \text{Hg} + 4\text{HNO}_3 \rightarrow \text{Hg(NO}_3\text{)}_2 + 2\text{NO} + 2\text{H}_2O \]

**Identifying Y:**
- Y = Hg(NO₃)₂ (Mercury(II) Nitrate)

### Step 4: Reaction of Mercury(II) Nitrate with Sodium Thiosulfate
The fourth reaction is:
\[ Y + Na_2S_2O_3 \text{ (excess)} \rightarrow Z + 2NaNO_3 \]

Mercury(II) nitrate (Y) reacts with excess sodium thiosulfate to form a complex and sodium nitrate. The balanced reaction is:
\[ \text{Hg(NO}_3\text{)}_2 + 2\text{Na}_2\text{S}_2\text{O}_3 \rightarrow \text{Na}_2\text{HgS}_2\text{O}_3 + 2\text{NaNO}_3 \]

**Identifying Z:**
- Z = Na₂HgS₂O₃ (Sodium Thiosulfate Complex)

### Summary of Identifications
- W = Hg (Mercury)
- X = NO₂ (Nitrogen Dioxide)
- Y = Hg(NO₃)₂ (Mercury(II) Nitrate)
- Z = Na₂HgS₂O₃ (Sodium Thiosulfate Complex)

### Final Answer
The correct option is **Option B**:
- W = Hg
- X = NO₂
- Y = Hg(NO₃)₂
- Z = Na₂HgS₂O₃

---