In the reaction, `A_2(g) +4B_2(g) hArr 2AB_4(g) , DeltaH gt 0`, The decomposition of `AB_4` (g) will be favoured at

Options

A. low temperature and high pressure
B. high temperature and low pressure
C. low temperature and low pressure
D. high temperature and high pressure

Explanation

To determine the conditions under which the decomposition of \( AB_4(g) \) is favored in the reaction \( A_2(g) + 4B_2(g) \rightleftharpoons 2AB_4(g) \) with \( \Delta H > 0 \), we can follow these steps:

### Step 1: Understand the Reaction and Its Enthalpy Change
The given reaction is:
\[ A_2(g) + 4B_2(g) \rightleftharpoons 2AB_4(g) \]
Since \( \Delta H > 0 \), this indicates that the reaction is endothermic, meaning it absorbs heat.

### Step 2: Reverse the Reaction for Decomposition
To analyze the decomposition of \( AB_4 \), we need to reverse the reaction:
\[ 2AB_4(g) \rightleftharpoons A_2(g) + 4B_2(g) \]
When we reverse the reaction, the sign of \( \Delta H \) also changes. Therefore, for the decomposition reaction:
\[ \Delta H < 0 \]
This indicates that the decomposition of \( AB_4 \) is exothermic.

### Step 3: Apply Le Chatelier's Principle
According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in temperature, pressure, or concentration, the system will adjust to counteract that change.

### Step 4: Analyze Temperature Effects
Since the decomposition of \( AB_4 \) is exothermic, increasing the temperature will shift the equilibrium to the left (favoring the formation of reactants). Therefore, to favor the decomposition of \( AB_4 \), we need to lower the temperature.

### Step 5: Analyze Pressure Effects
Next, we consider the effect of pressure. The number of moles of gas on each side of the reaction is:
- Reactants: \( 2 \) moles of \( AB_4 \)
- Products: \( 1 \) mole of \( A_2 \) + \( 4 \) moles of \( B_2 \) = \( 5 \) moles

Since there are more moles of gas on the product side (5 moles) than on the reactant side (2 moles), increasing the pressure will shift the equilibrium to the side with fewer moles of gas (the reactant side). Therefore, to favor the decomposition of \( AB_4 \), we should use low pressure.

### Conclusion
To favor the decomposition of \( AB_4(g) \), the conditions should be:
- **Low Temperature**: To favor the exothermic decomposition.
- **Low Pressure**: To favor the side with fewer moles of gas.

### Final Answer
The decomposition of \( AB_4(g) \) will be favored at low temperature and low pressure.

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