Question

Taking the example of decomposition of N₂O₅, describe how a first order reaction is studied kinetically.

Answer 1

The kinetic study of the decomposition of nitrogen pentoxide (N₂O₅) a first-order reaction, can be described as follows:

Nitrogen pentoxide (N₂O₅), in an inert solvent like carbon tetrachloride (CCl₄) or chloroform (CHCl₃), decomposes in two steps:

Step 1: \[\ce{N2O5 -> N2O4 + \frac{1}{2}O2}\]

Step 2: \[\ce{N2O4 -> 2NO2}\]

While N₂O₄ and NO₂ remain in solution, oxygen gas is evolved. Since the volume of O₂ evolved is directly proportional to the amount of N₂O₅ decomposed, the reaction’s progress can be monitored by measuring the volume of oxygen collected at various time intervals.

Let,

V_t​ = volume of O₂ collected at time t

V_∞​ = volume of O₂ collected at the end of the reaction (i.e., at infinite time)

Then:

V_t ∝ x (amount decomposed at time t)

V_∞ ∝ a (initial amount of N₂O₅)

Using the integrated rate law for a first-order reaction

\[\ce{k = \frac{2.303}{t} log_10 \frac{a}{a - x}}\]

Since a ∝ V_∞ and a − x ∝ V_∞ − V_t, this becomes

\[\ce{k = \frac{2.303}{t} log_10 \frac{V_\infty}{V_\infty - V_t}}\]

If the value of k calculated at different times is nearly constant, it confirms that the reaction follows first-order kinetics.