Instantaneous Rate of Reaction Calculator
Understanding and Calculating the Instantaneous Rate of Reaction
In chemical kinetics, understanding how fast a reaction proceeds is crucial. The rate of reaction describes the change in concentration of a reactant or product per unit time. While the average rate of reaction can be calculated over a time interval, the instantaneous rate of reaction provides a more precise measure of how fast the reaction is occurring at a specific moment.
What is the Instantaneous Rate of Reaction?
The instantaneous rate of reaction is the rate at which a reaction is proceeding at any given point in time. It's analogous to the instantaneous speed of a car shown on its speedometer, as opposed to the average speed over an entire trip. For a chemical reaction, the instantaneous rate is determined by the slope of the tangent line to the concentration-versus-time curve at a particular time.
How to Calculate the Instantaneous Rate of Reaction
Mathematically, the instantaneous rate of reaction for a reactant A is given by the derivative of its concentration with respect to time:
Rate = – d[A] / dt
The negative sign is used because the concentration of a reactant decreases over time. For a product B, the rate is:
Rate = + d[B] / dt
In practice, especially in introductory chemistry, we often approximate the instantaneous rate by calculating the average rate over a very small time interval. This calculator uses this approximation:
Approximate Instantaneous Rate = (Change in Concentration) / (Change in Time)
This means:
Rate ≈ ( [Concentration at Time t2] – [Concentration at Time t1] ) / ( t2 – t1 )
Where:
- [Concentration at Time t2] is the concentration of the substance at the final time.
- [Concentration at Time t1] is the concentration of the substance at the initial time.
- t2 is the final time.
- t1 is the initial time.
The units for the rate of reaction are typically M/s (molarity per second) or mol/(L·s).
Example Calculation:
Consider a reaction where the concentration of a reactant decreases over time. If the initial concentration of a reactant at time 0.5 seconds was 0.850 M, and at time 3.2 seconds, its concentration dropped to 0.520 M, we can calculate the approximate instantaneous rate of reaction during this interval.
Initial Concentration ([A] at t1) = 0.850 M
Final Concentration ([A] at t2) = 0.520 M
Initial Time (t1) = 0.5 s
Final Time (t2) = 3.2 s
Change in Concentration = 0.520 M – 0.850 M = -0.330 M
Change in Time = 3.2 s – 0.5 s = 2.7 s
Approximate Instantaneous Rate = -0.330 M / 2.7 s ≈ -0.122 M/s
The negative sign indicates that the reactant is being consumed. The rate of reaction (which is conventionally expressed as a positive value) is approximately 0.122 M/s.
Using the Calculator
Enter the initial and final concentrations (in Molarity, M) and their corresponding times (in seconds, s) into the fields above. Click "Calculate" to find the approximate instantaneous rate of reaction for that time interval. Remember that a smaller time interval will yield a more accurate approximation of the true instantaneous rate.