What is the correct expression for the rate law of a first order reaction?

[atavistic]

OK if we are given the following first order rxn:

$$2N_2O_5 - > 4NO_2 + O_2$$

The rate constant is $$k$$. Now how would we express the rate law for the decomposition of $$N_2O_5$$.

$$- d[N_2O_5]/dt = k[N_2O_5]$$

OR

$$- d[N_2O_5]/dt = 2k[N_2O_5]$$

I think it is the latter but I see all books use the former.zzz

Its urgent.

 

[Ygggdrasil]

Well, the rate is equal to -(1/2) d[N₂O₅]/dt. You cannot, however, say a priori that the reaction will be first order with respect to the concentration of N₂O₅ without knowing the reaction mechanism.

 

[Blueshift5]

The correct expression for the rate law of a first order reaction is - d[N_2O_5]/dt = k[N_2O_5]. This means that the rate of the reaction is directly proportional to the concentration of N_2O_5. The coefficient of 2 in front of the k value represents the stoichiometric coefficient of N_2O_5 in the reaction, but it does not affect the overall expression for the rate law. Therefore, both expressions are technically correct, but the first one is the standard and preferred way of representing the rate law for a first order reaction. It is important to use the correct expression to ensure accuracy and consistency in your calculations and interpretation of the reaction.