Question

For a reaction A \(\rightarrow\) B, the rate law is given by: \[ \text{Rate} = k[\text{A}]^2 \] If the concentration of A is increased by a factor of 3, by what factor does the rate of the reaction increase?

• A. 3
• B. 9
• C. 27
• D. 6

Hint:

The rate of reaction is proportional to the concentration of reactants raised to the power of their respective order. For a reaction where the rate law is \( \text{Rate} = k[\text{A}]^2 \), a 3-fold increase in concentration results in a 9-fold increase in the rate.

Answer 1

The Correct Option is B

The rate law for the reaction is given by: \[ \text{Rate} = k[\text{A}]^2 \] Where: - \( k \) is the rate constant, - \( [\text{A}] \) is the concentration of reactant A. If the concentration of A is increased by a factor of 3, then: \[ [\text{A}] \rightarrow 3[\text{A}] \] Substitute this new concentration into the rate law: \[ \text{Rate}_{\text{new}} = k(3[\text{A}])^2 = k \times 9[\text{A}]^2 \] Thus, the rate of the reaction increases by a factor of 9.