For the gaseous reaction, N2O5 → 2NO2 + \(\frac{1}{2}\)O2 the rate can be expressed as

\(-\frac{\mathrm{d}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]}{\mathrm{dt}}=\mathrm{K}_{1}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]\)

\(+\frac{\mathrm{d}\left[\mathrm{NO}_{2}\right]}{\mathrm{dt}}=\mathrm{K}_{2}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]\)

\(+\frac{\mathrm{d}\left[\mathrm{O}_{2}\right]}{\mathrm{dt}}=\mathrm{K}_{3}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]\)

The correct relation between K₁, K₂ and K₃ is

CONCEPT:

Rate of Reaction and Rate Constants

• The rate of a reaction is a measure of how quickly reactants are converted into products. It can be expressed in terms of the change in concentration of reactants or products per unit time.
• For the reaction: N₂O₅ → 2NO₂ + $\frac{1}{2}$ O₂
• The rate can be written as:
  • - $\frac{\mathrm{d}[N_2O_5]}{\mathrm{dt}}$ = k₁[N₂O₅]
  • + $\frac{\mathrm{d}[NO_2]}{\mathrm{dt}}$ = k₂[N₂O₅]
  • + $\frac{\mathrm{d}[O_2]}{\mathrm{dt}}$ = k₃[N₂O₅]

EXPLANATION:

• For the given reaction, we can relate the rate constants k₁, k₂, and k₃ based on the stoichiometry of the reaction:
  • The decomposition of 1 mole of N₂O₅ produces 2 moles of NO₂.
  • The decomposition of 1 mole of N₂O₅ produces 0.5 moles of O₂.
• This implies:
  • k₂ should be twice k₁ because 2 moles of NO₂ are produced for every mole of N₂O₅ decomposed.
  • k₃ should be half of k₁ because 0.5 moles of O₂ are produced for every mole of N₂O₅ decomposed.
• Thus, we can write:
  • k₂ = 2k₁
  • k₁ = 4k₃

Therefore, the correct relation between k₁, k₂, and k₃ is 2k₁ = k₂ = 4k₃.