`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_(2)[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 problem step by step, we will analyze each reaction and identify the products involved.

### Step 1: Decomposition of Silver Nitrate (AgNO₃)
When silver nitrate (AgNO₃) is heated, it decomposes into three products:
\[ \text{AgNO}_3 \xrightarrow{\Delta} \text{W} + \text{X} + \text{O}_2 \]

From the video transcript, we know:
- **W** is silver (Ag).
- **X** is nitrogen dioxide (NO₂).

Thus, the decomposition reaction can be summarized as:
\[ \text{AgNO}_3 \xrightarrow{\Delta} \text{Ag} + \text{NO}_2 + \frac{1}{2} \text{O}_2 \]

### Step 2: Reaction of X (NO₂) with Water
Next, we treat product X (NO₂) with water:
\[ \text{X} + \text{H}_2\text{O} \rightarrow \text{HNO}_2 + \text{HNO}_3 \]

This indicates that:
- **X** (NO₂) reacts with water to form nitrous acid (HNO₂) and nitric acid (HNO₃).

### Step 3: Reaction of W (Ag) with Nitric Acid (HNO₃)
Now, we take product W (Ag) and react it with nitric acid:
\[ \text{W} + \text{HNO}_3 \rightarrow \text{Y} + \text{NO} + \text{H}_2\text{O} \]

From the transcript, we know that:
- When silver (Ag) reacts with nitric acid (HNO₃), it forms silver nitrate (AgNO₃) as product Y, along with nitrogen monoxide (NO) and water (H₂O).

### Step 4: Reaction of Y (AgNO₃) with Sodium Thiosulfate (Na₂S₂O₃)
Finally, we treat product Y (AgNO₃) with excess sodium thiosulfate:
\[ \text{Y} + \text{Na}_2\text{S}_2\text{O}_3 \rightarrow \text{Z} + \text{NaNO}_3 \]

From the video, we find that:
- The reaction produces a complex of silver thiosulfate (NaAgS₂O₃) and sodium nitrate (NaNO₃).

### Summary of Products
- **W** = Ag (Silver)
- **X** = NO₂ (Nitrogen Dioxide)
- **Y** = AgNO₃ (Silver Nitrate)
- **Z** = NaAgS₂O₃ (Sodium Silver Thiosulfate)

### Final Answer
The correct option that matches the products is option C.

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