Question about Today's Lecture - Why multiply by 2? [ENDORSED]

[Bella Wachter 1A]

When using the pre-equilibrium approximation, we multiplied by 2 to find the rate of production of NO2.

However, if we wanted for our rate derived from the elementary step (found after substituting in info from the fast step to remove the intermediate) to match the experimentally determined rate law, wouldn't we want the reaction rate, (1/2 times the rate of production of NO2) not just the rate of production of NO2?

In other words, why did we need to multiply by 2? I've looked up several video tutorials and online articles on the pre-equilibrium approach and I haven't seen any of them multiply by the coefficient of the product. Why did we solve for the rate of production of NO2 instead of the overall reaction rate (which would match the experimentally determined rate law)?

[Chem_Mod]

In class I wrote it as the rate of formation of product.

I could have left it as the unique rate and not multiplied by 2.

They both match the experimentally determined rate law.

The factor of 2 is the difference between writing the unique rate versus the rate of change of product concentration.