The given chemical equation represents a first-order reaction, where reactant A(g) is converting into product B(g). We need to find the total pressure of the system as a function of time.

In a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. The rate equation for a first-order reaction is given by:

Rate = k[A]

Where:
- Rate is the rate of reaction
- k is the rate constant
- [A] is the concentration of reactant A

To solve this problem, we need to consider the stoichiometry of the reaction. According to the equation, for every molecule of A(g) that reacts, n molecules of B(g) are formed. Therefore, the concentration of B(g) is directly related to the concentration of A(g) by the factor n:

[B] = n[A]

Now, let's consider the total pressure of the system. The total pressure is the sum of the partial pressures of A(g) and B(g). According to Dalton's law of partial pressures, the partial pressure of a gas is directly proportional to its concentration.

Total pressure = P(A) + P(B)

Since P = n/V, where n is the number of moles and V is the volume, we can write:

Total pressure = (n(A)/V) + (n(B)/V)
= (n(V)/V)[A] + (n(V)/V)[B]
= n[A] + n[B]
= n[A] + n(n[A])
= n(1 + n)[A]

Now, we need to express the concentration of reactant A as a function of time. In a first-order reaction, the concentration of the reactant decreases exponentially with time according to the equation:

[A] = [A0]e^(-kt)

Where:
- [A] is the concentration of reactant A at time t
- [A0] is the initial concentration of reactant A
- k is the rate constant
- t is the time

Substituting this equation into the total pressure equation, we get:

Total pressure = n(1 + n)[A]
= n(1 + n)[A0]e^(-kt)

This matches with option (a): p0[n(1 - n)e^(-kt)]. Therefore, the correct answer is option (a).