Step 1: Understanding the Concept:
The relationship between the rate of reaction and the concentration of reactants is given by the rate law: \( Rate = k[A]^n \), where \(n\) is the order.
By observing how the rate changes when concentration is varied, we can determine the value of \(n\).
Key Formula or Approach:
Let the initial rate be \(R_1 = k[A]^n\).
If the concentration is doubled, the new concentration is \(2[A]\).
The new rate \(R_2 = k(2[A])^n = 2^n \cdot k[A]^n = 2^n \cdot R_1\).
Step 2: Detailed Explanation:
The problem states that when the concentration is doubled, the rate also doubles.
This means \(R_2 = 2 \times R_1\).
Comparing this with our derived expression:
\[ 2 \times R_1 = 2^n \times R_1 \]
This simplifies to:
\[ 2 = 2^n \]
For this mathematical equality to hold true, the power \(n\) must be equal to 1.
Since \(n = 1\), the reaction is of the first order.
If the reaction were zero-order, the rate wouldn't change at all (\(2^0 = 1\)).
If it were second-order, the rate would quadruple (\(2^2 = 4\)).
Since it follows a 1:1 proportionality between concentration increase and rate increase, it is first order.
Step 3: Final Answer:
The order of the reaction is first order.