The rate of the reaction 2N₂O₅ → 4NO₂ + O₂ can be written in three ways: −d[N₂O₅]/dt = k[N₂O₅], d[NO₂]/dt = k′[N₂O₅], d[O₂]/dt = k″[N₂O₅]. The relationship between k and k′ and between k and k″ are:

The expression for the rate of the reaction can be written as :
−d(N₂O₅)/dt = +d(NO₂)/dt/2 = d(O₂)/dt
1/2k(N₂O₅) = 1/4k′(N₂O₅) = k″(N₂O₅)
k/2 = k′/4 = k″
k′=2k, k″=k/2
Thus, the relationship between k and k′ and between k and k″ are
k′=2k; k″=k/2.
Hence, the correct option is C.