**a. Identify P, Q, R, and S:**

- P: P is a white crystalline solid.
- Q: On heating, P changes to a yellow solid Q.
- R: A colorless gas R is evolved during the reaction.
- S: A reddish-brown gas S is also evolved.

**b. Identify the type of reaction:**

Based on the given information, the reaction can be identified as a thermal decomposition reaction.

**c. Write the balanced chemical equation and explain in detail:**

The balanced chemical equation for the thermal decomposition reaction can be represented as follows:

P(s) → Q(s) + R(g) + S(g)

In this equation:
- P represents the initial white crystalline solid.
- Q represents the yellow solid obtained after heating P.
- R represents the colorless gas evolved during the reaction.
- S represents the reddish-brown gas evolved during the reaction.

During the thermal decomposition reaction, P undergoes a chemical change when heated. This change results in the formation of Q, R, and S. The reaction is typically endothermic, meaning it requires an input of heat to proceed.

The change from P to Q indicates a physical change in the solid state, resulting in a change in color. The formation of Q is likely due to the breakdown of the crystal lattice structure of P, leading to a different arrangement of atoms or molecules.

The evolution of R and S gases suggests the release of certain compounds or elements during the reaction. The colorless gas R is likely a product of the decomposition of P, while the reddish-brown gas S may indicate the formation of a new compound or the presence of impurities in the reaction mixture.

Overall, the thermal decomposition reaction of P to Q, with the evolution of R and S gases, represents a chemical transformation where the original substance P undergoes a structural or compositional change.

(a) P is Lead Nitrate, Q is Lead Oxide, R is Oxygen and S is Nitrogen dioxide.
(b) The given rraction is a decomposition reaction.
(c) 2Pb(NO3)2 --> 2PbO + 4NO2+ O2