JEE Main 2006
LEVELJEE Main
Visualized Solution
The Sigma Insight: Order and Molecularity
The Relay Race of Reactions
Imagine a relay race where one runner is incredibly fast, but the other is walking. The team's overall time is almost entirely determined by the walking runner. Chemical reactions work the exact same way!
When a reaction occurs in multiple steps, the slowest step acts as a bottleneck. We call this the Rate Determining Step (RDS).
In our problem, the reaction between and happens in two steps. The second step is explicitly given as the slow step.
Writing the Initial Rate Law
Since the second step is the rate-determining step, it dictates the speed of the entire reaction. We can write the rate law directly from the stoichiometry of this slow step.
The slow step is:
Therefore, the rate law is:
The Intermediate Trap
But wait, there is a massive catch here! Look closely at the species in our rate law. It contains .
If you look at the overall balanced reaction, is nowhere to be found. It is produced in the first step and consumed in the second. This makes it an intermediate.
Intermediates are highly reactive and short-lived. We cannot easily measure their concentrations in a lab, so a valid rate law must never contain intermediates. We need to express it in terms of the actual measurable reactants.
The Equilibrium Rescue
To eliminate the intermediate from our equation, we look at the first step. The first step is a fast, reversible reaction that quickly reaches equilibrium.
We can write the equilibrium constant expression () for this step:
Now, we can easily isolate the concentration of our pesky intermediate:
The Final Reveal
Now for the grand finale. We substitute this expression for back into our initial rate law.
We can combine the two constants ( and ) into a single new observed rate constant, . We also combine the terms.
The question asks for the order of the reaction with respect to . By looking at our final, purified rate law, we can see that the concentration of is raised to the power of 2.
Therefore, the order with respect to is 2.
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