What is instantaneous rate?

• A. The rate constant
• B. The rate at a particular time, given by the slope of a tangent to a plot of reactant concentration vs. time
• C. The rate over a finite interval
• D. The average rate

Answer: (B)

The instantaneous rate is the rate at a single, specific moment in time. On a plot of concentration versus time, it corresponds to the slope of the tangent line to the curve at that moment, which is the derivative d[A]/dt. This is effectively the limit of the average rate as the time interval around that moment becomes infinitesimally small. The rate constant is a parameter in the rate law, not a rate at a particular time. The rate over a finite interval, or the average rate, uses two points on the curve and is represented by the slope of the secant line between those points, not the tangent. Therefore, the description that matches instantaneous rate is the slope of the tangent line at that time.