Instantaneous Rate of Reaction Calculator
To find the instantaneous rate, identify two points on the tangent line drawn to the concentration-time curve at your specific time of interest.
Point 1 on Tangent
Point 2 on Tangent
Calculated Results:
Understanding the Instantaneous Rate of Reaction
In chemical kinetics, the rate of reaction is rarely constant. The instantaneous rate is the reaction rate at a specific moment in time (t). Unlike the average rate, which measures changes over a long interval, the instantaneous rate provides a "snapshot" of the speed of the chemical process.
The Mathematical Formula
Mathematically, the instantaneous rate is the derivative of the concentration with respect to time:
Since the rate of reaction is always expressed as a positive value, we use a negative sign for the disappearance of reactants and a positive sign for the appearance of products.
How to Calculate It Graphically
- Plot the Data: Create a graph of Concentration (y-axis) vs. Time (x-axis).
- Identify the Point: Locate the specific time (t) for which you want to find the rate.
- Draw a Tangent: Use a ruler to draw a straight line that touches the curve exactly at that point without crossing through it.
- Calculate Slope: Pick two points on this straight tangent line and use the slope formula: m = (C₂ – C₁) / (t₂ – t₁).
Example Calculation
Imagine a reaction where at 30 seconds, you draw a tangent line. On this tangent line, you pick two points:
- Point 1: (t = 10s, C = 0.85 M)
- Point 2: (t = 50s, C = 0.45 M)
Step 1: ΔConcentration = 0.45 – 0.85 = -0.40 mol/L
Step 2: ΔTime = 50 – 10 = 40 s
Step 3: Rate = | -0.40 / 40 | = 0.01 mol/L·s
The instantaneous rate at 30 seconds is 0.01 M/s.