Order of Reaction Calculation

To determine the order of the reaction, we can use the method of initial rates. The order of reaction is the power to which the concentration of the reactant is raised in the rate equation.

Given:
Concentration at t = 0 hr (C₀) = 0.1 mol L⁻¹
Concentration at t = 1 hr (C₁) = 0.08 mol L⁻¹
Concentration at t = 2 hr (C₂) = 0.067 mol L⁻¹

We can compare the initial rates of the reaction at t = 0 hr and t = 1 hr to determine the order of the reaction.

Rate at t = 0 hr = k[C₀]ⁿ
Rate at t = 1 hr = k[C₁]ⁿ

Since the reaction is undergoing decomposition, the concentration of the reactant decreases over time. Therefore, the rate of the reaction should decrease as well.

If we divide the rate at t = 1 hr by the rate at t = 0 hr, the concentration term cancels out, and we are left with:

(Rate at t = 1 hr) / (Rate at t = 0 hr) = (C₁ / C₀)ⁿ

Substituting the given values:

(0.08 / 0.1)ⁿ = 0.8ⁿ

Similarly, we can compare the rates at t = 2 hr and t = 1 hr:

(Rate at t = 2 hr) / (Rate at t = 1 hr) = (C₂ / C₁)ⁿ

Substituting the given values:

(0.067 / 0.08)ⁿ = 0.8375ⁿ

From the above two equations, we can write:

(0.8ⁿ) / (0.8375ⁿ) = (0.8 / 0.8375)ⁿ

Simplifying further:

(0.9573)ⁿ = 0.8ⁿ

Now, we can take logarithm on both sides:

log(0.9573)ⁿ = log(0.8ⁿ)

Multiplying the power with the logarithm:

n * log(0.9573) = n * log(0.8)

Dividing both sides by n:

log(0.9573) = log(0.8)

As the logarithms of both sides are equal, the value of n cancels out. This implies that n is not required to determine the order of the reaction.

Therefore, the order of the reaction is independent of the value of n and is equal to 1. Thus, the correct answer is option 'C' (1).