The Dissociation of A2B Gas

Introduction:
In the given scenario, A2B gas dissociates into 2A2 and B2. The equilibrium constant (Kp) is equal to the total pressure. We have to determine the total pressure when 4 moles of A2B undergo dissociation.

Dissociation Reaction:
The dissociation reaction of A2B can be represented as:

A2B ⇌ 2A2 + B2

Equilibrium Constant (Kp):
The equilibrium constant (Kp) is a measure of the extent to which a reaction proceeds to reach equilibrium. For the given reaction, the expression for Kp can be written as:

Kp = (PA2)^2 × (PB2) / (PA2B)

where PA2, PB2, and PA2B represent the partial pressures of A2, B2, and A2B, respectively.

Initial Conditions:
At the start of the reaction, we have 4 moles of A2B. Therefore, the initial pressure of A2B can be calculated using the ideal gas law:

PV = nRT

Assuming the temperature and volume remain constant, we can simplify the equation to:

P = nRT / V

Here, n is the number of moles, R is the ideal gas constant, T is the temperature, and V is the volume.

Calculating the Total Pressure:
To determine the total pressure when 4 moles of A2B dissociate, we need to consider the stoichiometry of the reaction. Since 1 mole of A2B dissociates into 2 moles of A2 and 1 mole of B2, the total number of moles after dissociation will be:

n = 4 moles of A2B + 2 × 4 moles of A2 + 1 × 4 moles of B2
= 4 moles of A2B + 8 moles of A2 + 4 moles of B2
= 12 moles

Using the ideal gas law, we can calculate the total pressure:

Ptotal = nRT / V

Substituting the values, we get:

Ptotal = (12 moles) × (R) × (T) / (V)

Therefore, the total pressure when 4 moles of A2B dissociate can be calculated using the above equation.

Conclusion:
In conclusion, the total pressure when 4 moles of A2B dissociate into 2A2 and B2 can be determined by considering the stoichiometry of the reaction and using the ideal gas law. The equilibrium constant (Kp) for the reaction is equal to the total pressure. By calculating the total pressure using the given equation, we can find the answer to the question.