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 reaction's rate law is: \[ \text{Rate} = k[\text{A}]^2 \] In this equation, \( k \) represents the rate constant, and \( [\text{A}] \) denotes the concentration of reactant A. When the concentration of A is tripled, such that \( [\text{A}] \rightarrow 3[\text{A}] \), the new rate is calculated by substituting this updated concentration into the rate law: \[ \text{Rate}_{\text{new}} = k(3[\text{A}])^2 = k \times 9[\text{A}]^2 \] Consequently, the reaction rate escalates by a factor of 9.