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. 10 times

Answer

To solve the problem, we need to analyze the given elementary reaction and how the rate of the reaction changes with the concentration of the reactants.

### Step-by-Step Solution:

1. **Identify the Reaction**: The given elementary reaction is:
\[ 2A + B \rightarrow C + D \]

2. **Determine the Order of the Reaction**: For an elementary reaction, the order of the reaction is equal to its molecularity. Here, the molecularity can be calculated as the sum of the stoichiometric coefficients:
- For \(2A\), the coefficient is 2.
- For \(B\), the coefficient is 1.
- Therefore, the total molecularity (and thus the order) is:
\[ 2 + 1 = 3 \]

3. **Write the Rate Law**: The rate of the reaction can be expressed in terms of the concentrations of the reactants:
\[ \text{Rate} (R) = k[A]^2[B]^1 \]
where \(k\) is the rate constant, \([A]\) is the concentration of \(A\), and \([B]\) is the concentration of \(B\).

4. **Increase the Concentrations**: According to the problem, the concentrations of the reactants are increased threefold:
- New concentration of \(A\) becomes \(3[A]\)
- New concentration of \(B\) becomes \(3[B]\)

5. **Calculate the New Rate**: The new rate of the reaction (\(R'\)) with the increased concentrations is:
\[ R' = k(3[A])^2(3[B])^1 \]
Simplifying this:
\[ R' = k \cdot 9[A]^2 \cdot 3[B] = 27k[A]^2[B] \]

6. **Determine the Factor by Which the Rate Increases**: To find out how many times the new rate \(R'\) is compared to the original rate \(R\):
\[ \frac{R'}{R} = \frac{27k[A]^2[B]}{k[A]^2[B]} = 27 \]

7. **Conclusion**: The rate of the reaction increases by a factor of 27 when the concentrations of the reactants are increased threefold.

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

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