The order of a reaction refers to the mathematical relationship between the concentration of a reactant and the rate of the reaction. It can be determined by analyzing the data obtained from the reaction.

To determine the order of the reaction, we can use the method of initial rates. This method involves comparing the initial rates of the reaction at different concentrations of the reactant. The order of the reaction can be determined by observing how the rate changes with respect to changes in the concentration of the reactant.

In this case, the concentration of the reactant undergoing decomposition was measured at three different time intervals: 1.0 hr, 2.0 hr, and 3.0 hr. The concentrations measured were 0.1 mol/L, 0.08 mol/L, and 0.067 mol/L, respectively.

To determine the order of the reaction, we need to calculate the rate of the reaction at each time interval. The rate of the reaction can be calculated using the formula:

Rate = Δ[A] / Δt

where Δ[A] is the change in concentration of the reactant and Δt is the change in time.

Let's calculate the rates of the reaction at each time interval:

- At 1.0 hr:
Rate = (0.1 mol/L - 0 mol/L) / (1.0 hr - 0 hr) = 0.1 mol/L/hr

- At 2.0 hr:
Rate = (0.08 mol/L - 0.1 mol/L) / (2.0 hr - 1.0 hr) = -0.02 mol/L/hr

- At 3.0 hr:
Rate = (0.067 mol/L - 0.08 mol/L) / (3.0 hr - 2.0 hr) = -0.013 mol/L/hr

Now, let's analyze the rates of the reaction:

- At 1.0 hr, the rate of the reaction is positive, indicating that the concentration of the reactant is decreasing with time.

- At 2.0 hr, the rate of the reaction is negative, indicating that the concentration of the reactant is increasing with time.

- At 3.0 hr, the rate of the reaction is negative, indicating that the concentration of the reactant is increasing with time.

From the above analysis, we can conclude that the reaction is a second-order reaction. The negative rates at 2.0 hr and 3.0 hr indicate that the concentration of the reactant is increasing with time, which is a characteristic of a second-order reaction.

Therefore, the correct answer is (c) 2, which indicates that the order of the reaction is 2.