If the concentration of the reactants in the elementary reaction 2A + B `to` C + D is increased three folds, the rate of the reaction will be increased by:

Options

A. 27 times
B. 9 times
C. 64 times
D. 01 times

Answer

To solve the problem, we need to determine how the rate of the reaction changes when the concentrations of the reactants are increased threefold. The reaction given is:

\[ 2A + B \rightarrow C + D \]

### Step 1: Write the rate law for the reaction.
For an elementary reaction, the rate law can be expressed based on the stoichiometry of the reactants. The rate law for this reaction can be written as:

\[ \text{Rate} = k [A]^2 [B]^1 \]

Where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of reactant A,
- \( [B] \) is the concentration of reactant B.

### Step 2: Determine the new concentrations after increasing them threefold.
If the concentrations of A and B are increased threefold, we can express the new concentrations as:

\[ [A]_{\text{new}} = 3[A] \]
\[ [B]_{\text{new}} = 3[B] \]

### Step 3: Substitute the new concentrations into the rate law.
Now, we substitute the new concentrations into the rate law:

\[ \text{Rate}_{\text{new}} = k (3[A])^2 (3[B])^1 \]

### Step 4: Simplify the expression.
Now, we simplify the expression:

\[ \text{Rate}_{\text{new}} = k \cdot 9[A]^2 \cdot 3[B] \]
\[ \text{Rate}_{\text{new}} = 27k [A]^2 [B] \]

### Step 5: Compare the new rate with the original rate.
The original rate is:

\[ \text{Rate} = k [A]^2 [B] \]

Thus, we can see that:

\[ \text{Rate}_{\text{new}} = 27 \times \text{Rate} \]

### Conclusion:
Therefore, if the concentration of the reactants is increased threefold, the rate of the reaction will increase by a factor of 27.

### Final Answer:
The rate of the reaction will be increased by 27 times.

---