Understanding Rate of Reaction via Tangents

Introduction

• Objective: By the end of this lesson, you should:
  • Be capable of drawing tangents on a curve of a rate of reaction graph.
  • Use the slope of the tangent as a measure of the rate of reaction.
  • Calculate the gradient of a tangent as a measure of the rate of reaction at a specific point (for higher-tier students).

Rate of Reaction Basics

• Rate of reaction is illustrated by measuring the quantity of product formed over time.
• Graph Analysis:
  • Initial Phase: Reaction is extremely fast.
  • Progression: Reaction slows down over time.
  • Conclusion: Reaction eventually stops.

Challenge in Measuring Rate

• The slope of the curve changes constantly, indicating a constantly changing rate of reaction.
• Problem: Difficult to determine the rate at a specific point due to changing slopes.

Solution: Use of Tangents

• Tangent Definition: A straight line that just touches the curve at a specific point, providing the slope at that point.
• Purpose: Slope of tangent gives an idea of the rate of reaction.
  • Example: Tangent at the start shows a steeper slope, indicating a faster reaction than later points.

Drawing Tangents

• Draw tangents at any point on the curve to assess the rate of reaction at that point.
• Higher-tier Insight:
  • Using tangents to calculate the rate of reaction.

Calculating Rate of Reaction

• Example Calculation:
  • Objective: Measure rate at 30 seconds.
  • Using Tangent:
    1. Construct a triangle using the tangent.
    2. Measure the vertical side (y-axis): 26 grams to 40 grams = 14 grams.
    3. Measure the horizontal side (x-axis): 17 seconds to 42 seconds = 25 seconds.
    4. Formula: Rate of reaction = ( \frac{\text{Y}}{\text{X}} )
    5. Result: ( \frac{14}{25} = 0.56 \text{ grams/second} )

Conclusion

• You should now be able to:
  • Draw tangents on the rate of reaction graphs.
  • Use the slope of these tangents as a measure of reaction rate.
  • For higher-tier students: Calculate the gradient of a tangent to find the precise rate at specific points.

Additional Resources

• Practice problems available in the vision workbook (refer to the video link for access).