Conisder a reaction `aG+bH rarr` Products. When concentration of both the reactants `G` and `H` is doubled, the rate increases eight times. However, when the concentration of `G` is doubled, keeping the concentration of `H` fixed, the rate is doubled. The overall order of reaction is

Options

A. `0`
B. `1`
C. `2`
D. `3`

Explanation

To solve the problem, we need to determine the overall order of the reaction given the information about how the rate changes with varying concentrations of the reactants.

### Step-by-Step Solution:

1. **Write the Rate Law Expression**:
The rate law for the reaction can be expressed as:
\[ \text{Rate} = k [G]^x [H]^y \]
where \(k\) is the rate constant, and \(x\) and \(y\) are the orders of the reaction with respect to reactants \(G\) and \(H\), respectively.

2. **Analyze the First Condition**:
The first condition states that when the concentrations of both \(G\) and \(H\) are doubled, the rate increases eight times. This can be mathematically expressed as:
\[ \text{Rate}' = k (2[G])^x (2[H])^y = 8 \times \text{Rate} \]
Substituting the original rate expression, we have:
\[ k (2[G])^x (2[H])^y = 8 \times k [G]^x [H]^y \]
Simplifying this gives:
\[ 2^x \cdot 2^y = 8 \]
Since \(8 = 2^3\), we can equate the exponents:
\[ x + y = 3 \quad \text{(Equation 1)} \]

3. **Analyze the Second Condition**:
The second condition states that when the concentration of \(G\) is doubled while keeping \(H\) constant, the rate doubles:
\[ \text{Rate}' = k (2[G])^x [H]^y = 2 \times \text{Rate} \]
Again substituting the original rate expression, we have:
\[ k (2[G])^x [H]^y = 2 \times k [G]^x [H]^y \]
Simplifying gives:
\[ 2^x = 2 \]
This implies:
\[ x = 1 \quad \text{(Equation 2)} \]

4. **Substitute \(x\) into Equation 1**:
Now that we have \(x = 1\), we can substitute this value into Equation 1:
\[ 1 + y = 3 \]
Solving for \(y\) gives:
\[ y = 2 \]

5. **Determine the 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**.