A) the reaction is unimolecular
B) the reaction is bimolecular
C) \[{{t}_{1/2}}\propto {{a}^{0}}\]
D) None of the above
Correct Answer: C
Solution :
Decomposition of N205 follows first order kinetics. \[2{{N}_{2}}{{O}_{5}}\xrightarrow{{}}4N{{O}_{2}}+{{O}_{2}}\] The half-life period of nth order of reaction is inversely proportional to (n - 1) th power of initial concentration. \[{{t}_{1/2}}\propto \frac{1}{{{a}^{n-1}}}\] where, n is order of reaction. Here, \[n=1\] \[{{t}_{1/2}}\propto \frac{1}{{{d}^{1-1}}}\] \[{{t}_{1/2}}\propto {{a}^{0}}\] ie, half-life period of a first order reaction is independent of the initial concentration of the reactant. Note - For a first order reaction \[k=\frac{2.303}{t}\log \,\frac{{{[A]}_{0}}}{[A]}\] \[{{[A]}_{0}}=\] initial concentration of the reactants [A] = concentration of reactants at time t.
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