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First-Order Kinetics Decay
AP Chemistry · Kinetics & Rate Laws
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Learning Objectives
Understand that First-Order Reactions have a constant Half-Life (\( t_{1/2} \)) independent of starting concentration.
Observe the strictly exponential decay of reactant \( [A] \) over time.
Verify that the Natural Logarithm graph \( \ln[A] \) vs \( t \) yields a perfectly straight line with slope \( -k \).
Key Equations
Integrated Rate Law:
\( \ln[A]_t = -kt + \ln[A]_0 \)
Exponential Decay Form:
\( [A]_t = [A]_0 e^{-kt} \)
Half-Life:
\( t_{1/2} = \frac{\ln(2)}{k} \approx \frac{0.693}{k} \)
Tags
kinetics
half-life
first-order
rate law
AP Chemistry
Initial Concentration \([A]_0\)
1.00 M
Rate Constant \( k \)
0.10 s⁻¹
Half-Life \( (t_{1/2}) \)
6.93 s
Graph Axes Transformation
Normal ([A] vs t)
Logarithmic (ln[A] vs t)
Initial Conc. \([A]_0\) (M)
1.0
Rate Constant \(k\) (s⁻¹)
0.10
Display Toggles
Show Half-Lives (\(t_{1/2}\))