Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
For an elementary reaction, the rate law is determined by its stoichiometry. Given the reaction $2\text{A} + \text{B} \longrightarrow 2\text{C}$, the rate law is:
$$Rate_1 = k[A]^2[B]^1$$Concentration is defined as $C = \frac{n}{V}$. If the volume $V$ is reduced to $\frac{V}{3}$, the new concentration $C'$ becomes:
$$C' = \frac{n}{V/3} = 3 \times \frac{n}{V} = 3C$$Step 2 (Step-by-Step Mathematical Working): [1.0 Mark]
Let the initial concentrations be $[A]$ and $[B]$. When volume is reduced to one-third, the new concentrations are $[A]' = 3[A]$ and $[B]' = 3[B]$. Substituting these into the rate expression for the new rate ($Rate_2$):
$$Rate_2 = k[A]'^2[B]'^1$$ $$Rate_2 = k(3[A])^2(3[B])$$ $$Rate_2 = k(9[A]^2)(3[B])$$ $$Rate_2 = 27 \times k[A]^2[B]$$ $$Rate_2 = 27 \times Rate_1$$Step 3 (Final Concluded Answer): [0.5 Mark]
- Change in Rate: The rate of the reaction will increase by 27 times its original rate.
- Change in Order: There will be no change in the order of the reaction. The order is an intrinsic property of the reaction mechanism and remains constant regardless of changes in concentration or volume.
💡 EL10 Concept Insight: Think of the reaction like people trying to dance in a room; if you shrink the room to one-third the size, everyone gets packed much tighter, making it 27 times more likely for them to bump into each other and "react." However, the "rules of the dance" (the order of the reaction) don't change just because the room got smaller!