Unique rate of reaction

[YINMEICHAN_3F]

Conceptually, what is the difference between a unique rate of the reaction and the reaction rate? Mathematically, how are these two different when trying to solve for them?

[Ashley_Thomas_3C]

The rate of reaction:
1. is change in concentration of a reactant or product per unit time
2. at any instant of time depends upon the molar concentrations of the reactants at that time
3. units are always mols

The reaction rate constant:
1. is a constant of proportionality in the rate law equation and is equal to the rate of reaction when the molar concentration of each of the reaction is unity
2. is constant for a particular reaction at a particular temperature and does not depend upon the concentrations of the reactants
3. units depend upon the order or reaction

[Kevin Tam 1J]

I've been trying to decipher the distinction between the average reaction rate and the unique average rate.

On pg. 612-613, the book says that the average reaction rate is defined as

average rate of consumption of R = - Δ[R]/Δt

On the other hand, the book says that the unique average rate of reaction is related by the stoichiometric coefficients of the reaction

unique average reaction rate = - (1/a)*(ΔA/Δt) = - (1/b)*(ΔB/Δt)=...

In essence, I think that the average reaction rate is just the change in concentration of reactants or products over the change in time, while the unique average rate of reaction is related by the stoichiometric coefficients of the reaction. Hope this helps.