For the reaction, `2A + B to` products, when the concentrations of A and B both were doubled, the rate of the reaction increased from `0.3 mol L^(-1)s^(-1)` to `2.4 mol L^(-1)s^(-1)`. When the concentration of A alone is doubled, the rate increased from `0.3 mol L^(-1)s^(-1)` to `0.6 mol L^(-1)s^(-1)`. What is overall order of reaction ?

Explanation

To determine the overall order of the reaction \(2A + B \to \text{products}\), we will analyze the changes in the reaction rate based on the changes in the concentrations of reactants A and B.

### Step-by-step Solution:

1. **Identify the Rate Law Expression**:
The rate of the reaction can be expressed as:
\[ \text{Rate} = k[A]^x[B]^y \]
where \(k\) is the rate constant, \(x\) is the order with respect to A, and \(y\) is the order with respect to B.

2. **Initial Conditions**:
We are given that when the concentrations of A and B are at their initial values, the rate of the reaction is:
\[ \text{Rate}_1 = 0.3 \, \text{mol L}^{-1}\text{s}^{-1} \]

3. **Case 1 - Doubling Concentrations of A and B**:
When both concentrations are doubled:
\[ [A] \to 2[A], \quad [B] \to 2[B] \]
The new rate becomes:
\[ \text{Rate}_2 = k(2[A])^x(2[B])^y = k \cdot 2^x \cdot 2^y \cdot [A]^x \cdot [B]^y = 2^{x+y} \cdot k[A]^x[B]^y \]
Given that \(\text{Rate}_2 = 2.4 \, \text{mol L}^{-1}\text{s}^{-1}\), we can set up the equation:
\[ 2.4 = 2^{x+y} \cdot 0.3 \]
Dividing both sides by \(0.3\):
\[ 8 = 2^{x+y} \]
Thus, we have:
\[ x + y = 3 \quad \text{(Equation 1)} \]

4. **Case 2 - Doubling Concentration of A Only**:
When only the concentration of A is doubled:
\[ [A] \to 2[A], \quad [B] \text{ remains the same} \]
The new rate becomes:
\[ \text{Rate}_3 = k(2[A])^x[B]^y = k \cdot 2^x \cdot [A]^x \cdot [B]^y \]
Given that \(\text{Rate}_3 = 0.6 \, \text{mol L}^{-1}\text{s}^{-1}\), we can set up the equation:
\[ 0.6 = 2^x \cdot 0.3 \]
Dividing both sides by \(0.3\):
\[ 2 = 2^x \]
Thus, we have:
\[ x = 1 \quad \text{(Equation 2)} \]

5. **Substituting x into Equation 1**:
Now substituting \(x = 1\) into Equation 1:
\[ 1 + y = 3 \]
Therefore:
\[ y = 2 \]

6. **Calculate Overall Order of Reaction**:
The overall order of the reaction is the sum of the individual orders:
\[ \text{Overall Order} = x + y = 1 + 2 = 3 \]

### Final Answer:
The overall order of the reaction is **3**.