Under which condition is the average rate of a reaction equal to its instantaneous rate at a specific time?

• A. When the concentration of reactants remains constant
• B. When the reaction is first-order
• C. When the reaction is at equilibrium
• D. When the time interval considered approaches zero

Answer: (D)

Verified step by step guidance

1. Understand the difference between average rate and instantaneous rate: The average rate of a reaction is the change in concentration of a reactant or product over a finite time interval, while the instantaneous rate is the rate at a specific moment in time.
2. Recall the mathematical definition of average rate: It is given by \(\frac{\Delta [A]}{\Delta t}\), where \(\Delta [A]\) is the change in concentration and \(\Delta t\) is the time interval.
3. Recall the mathematical definition of instantaneous rate: It is the derivative of concentration with respect to time, expressed as \(-\frac{d[A]}{dt}\) for reactants or \(\frac{d[P]}{dt}\) for products.
4. Recognize that the instantaneous rate is the limit of the average rate as the time interval \(\Delta t\) approaches zero, i.e., \(\lim_{\Delta t \to 0} \frac{\Delta [A]}{\Delta t} = -\frac{d[A]}{dt}\).
5. Therefore, the average rate equals the instantaneous rate only when the time interval considered becomes infinitesimally small, approaching zero.