Overview
This lecture covers first and second order reaction kinetics with a focus on radioactive decay, its applications, rate laws, activity, and introduces elementary steps and molecularity in reaction mechanisms.
Radioactive Decay & Applications
- Radioactive decay is a classic example of a first order process.
- Used in medicine for organ imaging, such as with the compound Cardiolite (uses the metastable isotope Tc-99m).
- Management of nuclear waste raises challenges, including long-term containment due to long half-lives.
Radioactive Decay: Kinetics and Equations
- Decay of a nucleus is independent of other nuclei, making it a first order process.
- Integrated first order rate law: N = N₀e^(-kt), where N is nuclei at time t, N₀ is the original amount, k is the decay constant.
- The decay constant (k) for radioactivity is sometimes called the decay constant or rate constant.
- Always use the atomic mass of the isotope (not the element’s average atomic mass) and Avogadro's number in calculations.
Measuring Radioactivity & Units
- Geiger counters are used to measure decay events by detecting ionizing radiation.
- Decay rate, also known as activity (A), is proportional to the number of nuclei: A = kN.
- Activity at time t: A = A₀e^(-kt), analogous to N = N₀e^(-kt).
- SI unit for activity is the Becquerel (Bq), 1 Bq = 1 disintegration/second; older unit is Curie (Ci), 1 Ci = 3.7 × 10¹⁰ disintegrations/second.
Types of Radioactive Decay
- Alpha decay: emission of α particle (helium-4 nucleus).
- Beta decay: emission of an electron.
- Gamma decay: emission of a photon.
- Different isotopes have vastly different half-lives, from milliseconds to billions of years.
Second Order Kinetics
- Second order integrated rate law: 1/[A] = kt + 1/[A]₀.
- Plotting 1/[A] vs. time yields a straight line; slope = k.
- Second order half-life: t₁/₂ = 1/(k[A]₀), depends on initial concentration.
- Determine order by fitting data to first or second order equations.
Rate Constants & Equilibrium
- At equilibrium, forward and reverse reaction rates are equal.
- For a reaction A + B ⇌ C + D: K_eq = k₁/k₋₁, relating rate constants to the equilibrium constant.
- Large equilibrium constant (K > 1) means more products; K₁ > K₋₁.
Elementary Steps & Molecularity
- Most reactions occur in multiple elementary steps.
- For an elementary step, the molecularity (number of reactants colliding) defines the rate law.
- Unimolecular: one reactant; bimolecular: two reactants; termolecular: three reactants (rare).
Key Terms & Definitions
- First Order Reaction — reaction rate depends linearly on one reactant’s concentration.
- Decay Constant (k) — proportionality constant in radioactive decay.
- Activity (A) — number of radioactive decays per second.
- Becquerel (Bq) — SI unit of activity, 1 decay/second.
- Curie (Ci) — older unit of activity, 3.7 × 10¹⁰ decays/second.
- Half-life (t₁/₂) — time taken for half the radioactive nuclei to decay.
- Elementary Step — a single step in a reaction mechanism.
- Molecularity — number of reactant molecules involved in an elementary step.
Action Items / Next Steps
- Review rate laws and half-life formulas for both first and second order kinetics.
- Practice using the correct isotope mass and Avogadro's number in calculations.
- Prepare for next lecture on reaction mechanisms and elementary steps.