For the reaction, 2 NX2OX5→4 NOX2+OX2\ce{2N2O5 -> 4NO2 + O2}2NX2OX54NOX2+OX2, the rate equation can be expressed in two ways −d[NX2OX5]dt=k[NX2OX5]-\dfrac{d[\ce{N2O5}]}{dt}=k[\ce{N2O5}]−dtd[NX2OX5]=k[NX2OX5] and +d[NOX2]dt=k′[NX2OX5]+\dfrac{d[\ce{NO2}]}{dt}=k'[\ce{N2O5}]+dtd[NOX2]=k′[NX2OX5]
k and k′ are related as :
Official answer: B
Four NOX2\ce{NO2}NOX2 form for every two NX2OX5\ce{N2O5}NX2OX5 used:d[NOX2]dt=2(−d[NX2OX5]dt)=2k[NX2OX5].\frac{d[\ce{NO2}]}{dt}=2\left(-\frac{d[\ce{N2O5}]}{dt}\right)=2k[\ce{N2O5}].dtd[NOX2]=2(−dtd[NX2OX5])=2k[NX2OX5].So k′=2kk'=2kk′=2k.