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average, in terms of reaction rates, is the change in molar concentration during an interval divided by that time interval. Instantaneous is pretty much the same thing but regarding a specific point of interest. So instead of a rate over a period of time, instantaneous is like a snapshot of what the rate is at an instant in time I believe.
The average rate can be found by looking at change in concentration over change in time, and can describe the general change in rate. While instantaneous change can be found by solving for the derivative as time approaches zero. This will be the rate change at a specific time.
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