Read the passage carefully and answer the Questions.
The decomposition of \( N_2O_5 (g) \) is given as
\( N_2O_5 (g) → 2NO_2(g) +\frac{1}{2}O_2(g) \)
The above reaction is found to be of first order.
Choose the correct statement about the rate of the reaction
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The rate of the reaction doubles as the initial amount of \(N_2O_5\) is doubled
For a first order reaction the rate is directly proportional to the first power of the reactant concentration:
\( \displaystyle \text{rate} = k[\ce{N2O5}] \)
If the amount of \( \ce{N2O5} \) in the same vessel is doubled, its concentration doubles, and
\( \displaystyle \text{rate}' = k(2[\ce{N2O5}]) = 2\times\text{rate} \)
So the rate doubles when the initial amount of \( \ce{N2O5} \) is doubled.
Why the other options are incorrect
Option (2) Changing the amount of reactant has no effect on the rate of the reaction — Incorrect. This is true only of a zero order reaction, whose rate does not depend on concentration.
Option (3) The rate of the reaction becomes half as the initial amount of \(N_2O_5\) is doubled — Incorrect. That would need an order of −1; for a first order reaction the rate rises with concentration.
Option (4) The order of reaction will be doubled as the temperature is increased by 10 °C — Incorrect. The order is fixed by the rate law and does not change with temperature; a 10° rise roughly doubles the rate constant, not the order.