How do you write complete net ionic equations for chemical reactions?

xnonamex0206
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I'm having trouble understanding the CNIE process. It would be very much appreciated if someone could show me how to solve a sample problem.
 
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See http://www.chem.vt.edu/RVGS/ACT/notes/Notes_on_Net_ionic_rxns.html"
 
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Thread 'Confusion regarding a chemical kinetics problem'

Thread 'Confusion regarding a chemical kinetics problem'

TL;DR Summary: cannot find out error in solution proposed. [![question with rate laws][1]][1] Now the rate law for the reaction (i.e reaction rate) can be written as: $$ R= k[N_2O_5] $$ my main question is, WHAT is this reaction equal to? what I mean here is, whether $$k[N_2O_5]= -d[N_2O_5]/dt$$ or is it $$k[N_2O_5]= -1/2 \frac{d}{dt} [N_2O_5] $$ ? The latter seems to be more apt, as the reaction rate must be -1/2 (disappearance rate of N2O5), which adheres to the stoichiometry of the...
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