`AgNO_(3)overset(Delta)(rarr)(W)+(X)+O_(2)`
`(X)+H_(2)OrarrHNO_(2)+HNO_(3)`
`(W)+HNO_(3)rarrY+NO+H_(2)O`
`(Y)+Na_(2)S_(2)O_(3)("excess")rarr(Z)+NaNO_(3)`

Options

A. `W=Ag, X=N_(2)O,Y=AgNO_(3),Z=Na_(2)[Ag(S_(2)O_(3))_(2)]`
B. `W=Ag_(2)O, X=NO,Y=AgNO_(3),Z=Na_(3)[Ag(S_(2)O_(3))_(2)]`
C. `W=Ag, X=NO_(2),Y=AgNO_(3),Z=Na_(3)[Ag(S_(2)O_(3))_(2)]`
D. `W=Ag_(2)O, X=N_(2),Y=AgNO_(3),Z=Na[Ag(S_(2)O_(3))_(2)]`

Explanation

To solve the given reactions step by step, we will identify the products W, X, Y, and Z based on the provided reactions.

### Step 1: Identify W and X from the first reaction
The first reaction is:
\[ \text{AgNO}_3 \overset{\Delta}{\rightarrow} (W) + (X) + O_2 \]

When silver nitrate (AgNO₃) is heated, it decomposes into silver (Ag), nitrogen dioxide (NO₂), and oxygen (O₂). The balanced reaction is:
\[ 2 \text{AgNO}_3 \overset{\Delta}{\rightarrow} 2 \text{Ag} + 2 \text{NO}_2 + O_2 \]

From this, we can identify:
- \( W = \text{Ag} \) (silver)
- \( X = \text{NO}_2 \) (nitrogen dioxide)

### Step 2: Identify the products from the second reaction
The second reaction is:
\[ (X) + H_2O \rightarrow HNO_2 + HNO_3 \]

Here, nitrogen dioxide (NO₂) reacts with water to form a mixture of nitrous acid (HNO₂) and nitric acid (HNO₃). This reaction is well-known in chemistry.

### Step 3: Identify Y from the third reaction
The third reaction is:
\[ (W) + HNO_3 \rightarrow (Y) + NO + H_2O \]

Substituting \( W \) with silver (Ag):
\[ \text{Ag} + 3 \text{HNO}_3 \rightarrow \text{AgNO}_3 + NO + H_2O \]

From this, we can identify:
- \( Y = \text{AgNO}_3 \) (silver nitrate)

### Step 4: Identify Z from the fourth reaction
The fourth reaction is:
\[ (Y) + Na_2S_2O_3 \text{ (excess)} \rightarrow (Z) + NaNO_3 \]

Substituting \( Y \) with silver nitrate (AgNO₃):
\[ 2 \text{AgNO}_3 + Na_2S_2O_3 \rightarrow \text{Na}_3\text{AgS}_2\text{O}_3 + 2 \text{NaNO}_3 \]

From this, we can identify:
- \( Z = \text{Na}_3\text{AgS}_2\text{O}_3 \) (sodium argento thiosulphate)

### Final Identification of Products
- \( W = \text{Ag} \) (silver)
- \( X = \text{NO}_2 \) (nitrogen dioxide)
- \( Y = \text{AgNO}_3 \) (silver nitrate)
- \( Z = \text{Na}_3\text{AgS}_2\text{O}_3 \) (sodium argento thiosulphate)

### Summary of Results
- \( W = \text{Ag} \)
- \( X = \text{NO}_2 \)
- \( Y = \text{AgNO}_3 \)
- \( Z = \text{Na}_3\text{AgS}_2\text{O}_3 \)