SectionC7_BB - Tagged
Integrated Rate Equations Overview
Focus on analyzing chemical kinetics through integrated rate laws.
Page 1: Introduction
Course Title: CHEM10021 Chemistry for Bioscientists I
Section C7: Integrated Rate Equations
Initial discussion of reaction kinetics and the concept of order of reactions.
Page 2: Finding the Order of Reaction
Integrated rate laws used to analyze the rates of chemical reactions.
Example Reaction: H2O2 + 3I- + 2H+ → 2H2O
Rate equation:
rate = -d[H2O2]/dt = -d[I-]/3dt = -d[H+]/2dt
Page 3: Integrated Rate Laws - 0th Order
Zeroth order reaction representation: A → P
Rate law for zeroth order:
rate = k
-d[A]/dt = k
Integrating gives:
[A] = [A]0 - kt
Page 4: Derivation of 0th Order
Differential equation:
d[A] = -k dt
Integration leads to:
[A] = [A]0 - kt
[A] decays linearly over time.
Page 5: Summary of 0th Order Laws
Final expression from integration:
[A] = [A]0 - kt
Concentration decays linearly from its initial value, indicating a constant reaction rate independent of [A].
Page 6: Integrated Rate Laws - 1st Order
First order reaction representation: A → P
Rate equation:
d[A]/dt = -k[A]
Integration yields:
ln[A] = ln[A]0 - kt
[A] = [A]0e^(-kt)
Page 7: Derivation of 1st Order
Starting equation:
d[A] = -k[A] dt
Integration leads to:
ln[A] = ln[A]0 - kt
Exponential decay characterized in the first order process.
Page 8: Finding Reaction Order - 1st Order
Used integrated form to plot:
ln[A] = -kt + ln[A]0
A straight-line relationship where slope (m) is -k.
Page 9: Integrated Rate Laws - 2nd Order
Second order reaction represented as: A + A → P
Rate equation:
d[A]/dt = -k[A]^2
Integrating gives:
1/[A] = kt + 1/[A]0
Indicates reciprocal concentration rises linearly over time.
Page 10: Derivation of 2nd Order
Starts from d[A] = -k[A]^2 dt
Integration yields:
1/[A] = kt + 1/[A]0
This form indicates linearity for 1/[A] versus time.
Page 11: Integrated Rate Laws Summary
Common orders summarized:
0th Order: d[A]/dt = -k, [A] = [A]0 - kt
1st Order: d[A]/dt = -k[A], [A] = [A]0e^(-kt)
2nd Order: d[A]/dt = -k[A]^2, 1/[A] = kt + 1/[A]0
Page 12: Concentration vs Time for Different Orders
Graphical representation of concentration as a function of time for different orders:
0th Order: k = 1 mol dm^-3 s^-1
1st Order: k = 1 s^-1
2nd Order: k = 1 dm³ mol^-1 s^-1
Page 13: Half-Lives - 1st Order
Definition of half-life (t1/2): time for concentration to decrease to half its initial value.
Relationship for first order reactions:
t1/2 = ln(2)/k
[A] after n half-lives is initially reduced by factors of 2 (e.g., after t1/2: [A] = [A]0/2, after 2t1/2: [A] = [A]0/4)
Page 14: Half-Lives - Other Orders
Summary of t1/2 for reactions of different orders:
0th Order: t1/2 = [A]0/(2k)
2nd Order: t1/2 = 1/(k[A]0)
Page 15: Conclusion
Review of Integrated Rate Equations essential for understanding chemical kinetics in bioscientific contexts.