9.1 Rate laws for photochemical reactions

Photochemical rate laws govern reactions triggered by light absorption. They differ from thermal reactions in energy input, temperature sensitivity, and reaction order. Understanding these laws helps predict and control light-driven processes in chemistry and biology.

Factors like light intensity, reactant concentration, and environmental conditions influence photochemical rates. Applying these laws allows scientists to calculate reaction rates, determine quantum yields, and predict how changes in conditions will affect reaction outcomes.

Fundamentals of Photochemical Rate Laws

Rate laws for photochemical reactions

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  The Rate Law | Introduction to Chemistry View original

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  Reaction Mechanisms View original

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• Steady-state approximation assumes reactive intermediate concentrations remain constant when consumption rate equals formation rate
• Deriving rate laws involves:
  1. Writing all elementary reactions in mechanism
  2. Identifying reactive intermediates
  3. Applying steady-state approximation to intermediates
  4. Solving for intermediate concentrations
  5. Substituting into rate equation for product formation
• Quantum yield measures reaction efficiency as ratio of reacted molecules to absorbed photons incorporated into rate laws

Factors in photochemical reaction rates

• Light intensity directly proportional to reaction rate increases photon absorption
• Reactant concentration affects light absorption (Beer-Lambert law) potentially increasing reaction rate
• Temperature influences non-radiative decay processes and may affect quantum yield
• Solvent effects impact excited state lifetimes and alter reaction pathways
• Photosensitizers increase reaction rate while quenchers decrease it

Application and Analysis of Photochemical Rate Laws

Thermal vs photochemical rate laws

• Initiation step differs molecular collisions (thermal) vs photon absorption (photochemical)
• Energy requirements involve overcoming activation energy barrier (thermal) vs electronic excitation (photochemical)
• Temperature dependence follows Arrhenius equation (thermal) vs less sensitive (photochemical)
• Reaction order typically integer (thermal) vs potentially fractional due to light absorption (photochemical)
• Rate-determining step slowest step in mechanism (thermal) vs often photon absorption or excited state decay (photochemical)

Applications of photochemical rate laws

• General rate law form: Rate = $k[A]^a[B]^b[I_0]^c$ where $k$ is rate constant, $[A]$ and $[B]$ are reactant concentrations, $[I_0]$ is incident light intensity, and exponents determined experimentally
• Calculating reaction rates uses experimentally determined rate law inputting known concentrations and light intensity to solve for rate or unknown parameter
• Determining quantum yield measures reaction rate and absorbed light intensity using $\Phi = \frac{\text{Rate of reaction}}{\text{Rate of photon absorption}}$
• Predicting rate changes assesses concentration or light intensity effects on rate using rate law to quantify impacts