Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct regarding the given graph showing variation of reactant concentration with time?
The rate constant of reaction 3 is larger than the rate constant of reaction 2 if the order of reaction is same for both.
The SI unit of rate constant of reaction 1 is \(s^{-1}\).
Thermal decomposition of HI on gold surface is an example of reaction 2.
Show Solution
The Correct Option isB
Solution and Explanation
Step 1: Understanding the Concept:
The graph plots the concentration of reactants $[R]$ against time $t$. The steepness of the curve at any given time represents the rate of the reaction. A steeper drop indicates a faster reaction, which inherently corresponds to a higher rate constant $k$, assuming all other factors (like reaction order and initial concentration) are held constant. Step 2: Key Formula or Approach:
For any order reaction, the rate is given by $-\frac{d[R]}{dt} = k[R]^n$.
If the order $n$ is identical across multiple reactions, the rate of concentration decay $-\frac{d[R]}{dt}$ is directly proportional to the rate constant $k$. Step 3: Detailed Explanation:
Let's analyze the options based on the visual properties of the curves:
- Curve 3 decreases the most rapidly, meaning the reactant is consumed the fastest.
- Curve 2 decreases at an intermediate pace.
- Curve 1 decreases the slowest.
If we assume the reactions all have the same order (as proposed in option B), then the reaction that drops fastest must necessarily have the highest rate constant $k$.
Since Curve 3 decays much faster than Curve 2, the rate constant $k_3$ must be greater than $k_2$. Therefore, statement (B) is entirely correct.
Evaluating other options briefly:
(A) We cannot definitively prove they are all the same order just from the visual curves without log plots.
(C) If reaction 1 is zero-order (which it visually resembles as a nearly straight line), the unit of $k$ would be $M \cdot s^{-1}$, not $s^{-1}$ (which is for 1st order).
(D) Thermal decomposition of HI on a gold surface is a classic zero-order reaction. A zero-order reaction yields a perfectly straight line on a $[R]$ vs $t$ plot, which resembles Curve 1, not Curve 2. Step 4: Final Answer:
The correct statement is that the rate constant of reaction 3 is larger than reaction 2 if their orders are the same.
