`2A rarrC+D`
In this reaction, if we double the concentration of A, reaction rate become , two time .. What is the order of this reaction ?

Options

A. 1
B. 3
C. 2
D. 1.5

Answer

To determine the order of the reaction \(2A \rightarrow C + D\) based on the information given, we can follow these steps:

### Step 1: Write the Rate Law Expression
The rate of a reaction can be expressed using the rate law:
\[ \text{Rate} = k [A]^x \]
where \(k\) is the rate constant, \([A]\) is the concentration of reactant A, and \(x\) is the order of the reaction.

### Step 2: Analyze the Given Information
We are told that if the concentration of A is doubled (i.e., \([A] \rightarrow 2[A]\)), the reaction rate becomes twice the original rate. This means:
\[ \text{New Rate} = 2 \times \text{Old Rate} \]

### Step 3: Substitute the New Concentration into the Rate Law
Substituting the new concentration into the rate law gives us:
\[ \text{New Rate} = k (2[A])^x \]
This can be simplified to:
\[ \text{New Rate} = k \cdot 2^x \cdot [A]^x \]

### Step 4: Set Up the Equation Based on the Rate Change
Since we know that the new rate is twice the old rate, we can set up the following equation:
\[ k \cdot 2^x \cdot [A]^x = 2 \cdot (k \cdot [A]^x) \]

### Step 5: Cancel Out Common Terms
We can cancel \(k\) and \([A]^x\) from both sides of the equation (assuming \([A] \neq 0\)):
\[ 2^x = 2 \]

### Step 6: Solve for \(x\)
From the equation \(2^x = 2\), we can express 2 as \(2^1\):
\[ 2^x = 2^1 \]
Since the bases are the same, we can equate the exponents:
\[ x = 1 \]

### Step 7: Conclusion
The order of the reaction is equal to \(x\), which we found to be 1. Therefore, the order of the reaction is:
\[ \text{Order} = 1 \]