Gay Lussac's law is not valid in the chemical reaction:

Options

A. `H_(2)(g) + Cl_(2) (g) to 2HCI (g)`
B. `3H_(2) (g) + N_(2) (g) to 2NH_(3)(g)`
C. `2 SO_(2) (g) + O_(2)(g) to 2SO_(3) (g)`
D. `CaCO_(3)(s) to CaO(s) + CO_(2) (g)`

Answer

To determine in which chemical reaction Gay-Lussac's law is not valid, we need to understand the conditions under which this law applies. Gay-Lussac's law states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. This law is applicable to gases that are reacting with each other.

### Step-by-Step Solution:

1. **Understanding Gay-Lussac's Law**:
- Gay-Lussac's law applies to gaseous reactions where the gases react with each other. It states that if the volume remains constant, the pressure of a gas increases with an increase in temperature.

2. **Identifying the Reaction Types**:
- We need to analyze the options given in the question to identify the type of reactions. The options typically include combinations of gases, solids, and liquids.

3. **Analyzing Each Option**:
- **Option 1**: Gas + Gas → Gas (Valid for Gay-Lussac's law)
- **Option 2**: Gas + Gas → Gas (Valid for Gay-Lussac's law)
- **Option 3**: Gas + Gas → Gas (Valid for Gay-Lussac's law)
- **Option 4**: Solid + Solid → Gas (Not valid for Gay-Lussac's law)

4. **Conclusion**:
- Since Gay-Lussac's law is only applicable when gases are involved in the reaction, it is not valid in the case of the fourth option, where solids are reacting to produce a gas.

5. **Final Answer**:
- The correct option where Gay-Lussac's law is not valid is **Option 4**: Solid + Solid → Gas.