Question

The order of a reaction \( W + X \rightarrow Y + Z \) with respect to W is 3 and with respect to X is 1. If the concentrations of both W and X are tripled, the rate of reaction will increase by -------- times.

• A. 81
• B. 27
• C. 51
• D. 15

Hint:

For rate law \( r = k[A]^m[B]^n \), multiplying concentration by a factor multiplies rate by that factor raised to its order.

Answer 1

The Correct Option is A

Step 1: Write rate law.
\[ \text{Rate} = k[W]^3[X]^1 \]

Step 2: Apply change in concentration.
Both concentrations are tripled:
\[ [W] \rightarrow 3[W], \quad [X] \rightarrow 3[X] \]

Step 3: Substitute into rate law.
\[ \text{New Rate} = k(3[W])^3 (3[X]) \]

Step 4: Simplify expression.
\[ = k \cdot 3^3 [W]^3 \cdot 3[X] \]
\[ = k \cdot 27 \cdot 3 \cdot [W]^3[X] \]

Step 5: Compare with original rate.
\[ \text{New Rate} = 81 \times \text{Original Rate} \]

Step 6: Interpretation.
Rate increases by a factor of 81.

Step 7: Final conclusion.
\[ \boxed{81} \]