Question

A reaction is first order with respective to $\mathrm{A}$ and second order with respective to $\mathrm{B}$. What is the effect on reaction rate if concentration of $\mathrm{B}$ is increased 3 times?

• A. Rate increases 6 times
• B. Rate increases 2 times
• C. Rate increases 9 times
• D. Rate increases 3 times

Hint:

For any reactant of order $n$, increasing its concentration by a factor of $x$ changes the reaction rate by a factor of $x^n$. Since $\mathrm{B}$ is second-order ($n=2$) and its concentration is tripled ($x=3$), the rate must increase by $3^2 = 9$ times!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given a kinetic chemical system where the reaction rate is first-order with respect to reactant $\mathrm{A}$ and second-order with respect to reactant $\mathrm{B}$. We need to calculate the proportional change in the net reaction rate when the concentration of reactant $\mathrm{B}$ is scaled up by a factor of 3, while keeping reactant $\mathrm{A}$ constant.

Step 2: Key Formula or Approach:
From the problem description, we can write down the initial experimental rate law expression as: $$R_1 = k [\mathrm{A}]^1 [\mathrm{B}]^2$$ Where $k$ is the specific reaction rate constant. Let the new concentration of $\mathrm{B}$ be $[\mathrm{B}'] = 3[\mathrm{B}]$.

Step 3: Detailed Explanation:
Set up the rate law expression for the modified concentration conditions ($R_2$): $$R_2 = k [\mathrm{A}]^1 [\mathrm{B}']^2$$ Substitute $[\mathrm{B}'] = 3[\mathrm{B}]$ into this new equation: $$R_2 = k [\mathrm{A}]^1 (3[\mathrm{B}])^2$$ $$R_2 = k [\mathrm{A}]^1 \cdot 9[\mathrm{B}]^2$$ Rearrange the constants to compare the expression with our initial rate equation: $$R_2 = 9 \cdot \left( k [\mathrm{A}]^1 [\mathrm{B}]^2 \right) = 9 \cdot R_1$$ This shows that the reaction rate scales up by a factor of $3^2 = 9$.

Step 4: Final Answer:
The reaction rate increases 9 times, which matches option (C).