Explanation:

The order of the reaction can be determined by analyzing the rate of change of the concentration of the reactants or products with respect to time. However, in this case, we are given information about the change in pressure, not concentration. Therefore, we need to use the ideal gas law to relate pressure to concentration:

PV = nRT

where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. If we assume that the volume and temperature are constant, we can write:

P ∝ n

where ∝ means proportional to. Therefore, we can say that the rate of change of pressure is proportional to the rate of change of the number of moles.

Now let's consider the reaction:

2A(g) + 3B(g) → C(g)

If we assume that the reaction is elementary (i.e., it occurs in a single step), we can write the rate law as:

Rate = k[A]^x[B]^y

where k is the rate constant and x and y are the orders of the reaction with respect to A and B, respectively. Since we are given that the total pressure doubled in 3 hours, we can write:

ΔP/Δt = k[A]^x[B]^y

where ΔP/Δt is the rate of change of pressure and k, x, and y are constants. Since we are starting with pure A, we can assume that [B] is constant and equal to zero. Therefore, we can simplify the rate law to:

ΔP/Δt = k[A]^x

Now we can use the given information to determine the order of the reaction.

Solution:

If the total pressure doubled in 3 hours, it means that the rate of change of pressure is proportional to the initial pressure:

ΔP/Δt ∝ P

or

ΔP/Δt = kP

where k is a constant of proportionality. Since we are starting with pure A, the initial pressure is the pressure of A, which is the same as the total pressure. Therefore, we can write:

ΔP/Δt = kP = k[A]

This is the rate law for a first-order reaction. Therefore, the order of the reaction is (B) first.