`(P)overset(Delta)to(Q)`Metallic solid `+(R)uarr+(S)uarr`
`(X)overset(Delta)to(Y)`amphoteric`+(R)uarr+(S)uarr`
P& X are respectively:

Options

A. `AgNO_(3),LiNO_(3)`
B. `AgNO_(3),Pb(NO_(3))_(2)`
C. `Hg_(2)(NO_(3))_(2),Ca(NO_(3))_(2)`
D. `NaNO_(3),Zn(NO_(3))_(2)`

Explanation

To solve the question, we need to identify the compounds P and X based on the given reactions and their products. Let's break down the steps:

### Step 1: Analyze the first reaction
The first reaction is represented as:
\[ (P) \overset{\Delta}{\rightarrow} (Q) + (R) + (S) \]
This indicates that compound P undergoes thermal decomposition to form a metallic solid Q and releases gases R and S.

### Step 2: Identify possible candidates for P
From the video, we consider the thermal decomposition of silver nitrate (AgNO3):
\[ 2 \text{AgNO}_3 \overset{\Delta}{\rightarrow} 2 \text{Ag} + 2 \text{NO}_2 + \text{O}_2 \]
Here, Ag is the metallic solid (Q), and NO2 and O2 are the gases (R and S). This satisfies the first reaction.

### Step 3: Analyze the second reaction
The second reaction is:
\[ (X) \overset{\Delta}{\rightarrow} (Y) + (R) + (S) \]
This indicates that compound X undergoes thermal decomposition to form an amphoteric compound Y and releases the same gases R and S.

### Step 4: Identify possible candidates for X
We consider the thermal decomposition of lead nitrate (Pb(NO3)2):
\[ 2 \text{Pb(NO}_3)_2 \overset{\Delta}{\rightarrow} 2 \text{PbO} + 4 \text{NO}_2 + \text{O}_2 \]
Here, PbO is the amphoteric compound (Y), and the gases released are NO2 and O2, which are the same as R and S from the first reaction.

### Step 5: Conclusion
From the analysis:
- Compound P is silver nitrate (AgNO3).
- Compound X is lead nitrate (Pb(NO3)2).

Thus, the required pairs are:
- P = Silver Nitrate (AgNO3)
- X = Lead Nitrate (Pb(NO3)2)

### Final Answer
P and X are:
- P = Silver Nitrate (AgNO3)
- X = Lead Nitrate (Pb(NO3)2)

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