13.3 Temperature-jump and pressure-jump methods

Temperature-jump and pressure-jump methods are powerful techniques for studying fast chemical reactions. These methods rapidly perturb reaction systems, allowing scientists to observe and analyze quick relaxation processes that occur in microseconds to milliseconds.

By applying sudden changes in temperature or pressure, researchers can shift reaction equilibria and monitor the system's return to equilibrium. This provides valuable kinetic data on reaction rates, equilibrium constants, and activation energies for various types of chemical reactions.

Temperature-Jump and Pressure-Jump Methods

Principles of temperature-jump and pressure-jump methods

Top images from around the web for Principles of temperature-jump and pressure-jump methods

• 

  JSSS - Novel method for the detection of short trace gas pulses with metal oxide semiconductor ... View original

  Is this image relevant?

• 

  Laser induced temperature-jump time resolved IR spectroscopy of zeolites - Chemical Science (RSC ... View original

  Is this image relevant?

• 

  JSSS - Novel method for the detection of short trace gas pulses with metal oxide semiconductor ... View original

  Is this image relevant?

• 

  Laser induced temperature-jump time resolved IR spectroscopy of zeolites - Chemical Science (RSC ... View original

  Is this image relevant?

1 of 2

Top images from around the web for Principles of temperature-jump and pressure-jump methods

• 

  JSSS - Novel method for the detection of short trace gas pulses with metal oxide semiconductor ... View original

  Is this image relevant?

• 

  Laser induced temperature-jump time resolved IR spectroscopy of zeolites - Chemical Science (RSC ... View original

  Is this image relevant?

• 

  JSSS - Novel method for the detection of short trace gas pulses with metal oxide semiconductor ... View original

  Is this image relevant?

• 

  Laser induced temperature-jump time resolved IR spectroscopy of zeolites - Chemical Science (RSC ... View original

  Is this image relevant?

1 of 2

• Temperature-jump (T-jump) method rapidly heats a reaction mixture by applying a short pulse of electrical discharge or laser radiation to perturb the system from equilibrium and observe fast relaxation processes
  • Reaction cell contains electrodes or laser setup for rapid heating
  • Detection system (spectrophotometer, conductivity meter) monitors the relaxation process
• Pressure-jump (P-jump) method rapidly increases the pressure of a reaction mixture by applying a sudden mechanical compression to perturb the system from equilibrium and observe fast relaxation processes
  • High-pressure reaction cell with a pressure-generating device (piezoelectric crystal)
  • Detection system (spectrophotometer, conductivity meter) monitors the relaxation process

Applications in fast reaction kinetics

• T-jump and P-jump methods induce rapid perturbations in the system allowing observation of fast relaxation processes (microsecond to millisecond range)
  • Obtain kinetic data by monitoring time-dependent changes in the system after perturbation
    • Concentration changes of reactants, intermediates, or products
    • Changes in physical properties (absorbance, conductivity)
• T-jump and P-jump methods shift the equilibrium of a reaction as temperature or pressure changes affect the equilibrium constant ($K$)
  • Monitor the relaxation process after perturbation to determine the equilibrium constant and rate constants

Advantages vs limitations of jump methods

• Advantages enable studying fast reactions with half-lives in microsecond to millisecond range, direct observation of relaxation processes without rapid mixing, and versatility in studying various reaction types (unimolecular, bimolecular, enzyme-catalyzed)
• Limitations include constrained temperature and pressure ranges due to instrumentation, potential for unwanted side reactions or sample degradation at high temperatures or pressures, requirement for specialized and expensive instrumentation, and limited applicability to reactions with very large activation energies or volume changes

Interpretation of jump experiment data

• Relaxation kinetics involve the system relaxing back to equilibrium after perturbation
  • Fit relaxation profile to exponential functions to obtain relaxation times ($\tau$)
    1. Single-step reaction: $A(t) = A_0 + \Delta A \exp(-t/\tau)$
    2. Multi-step reactions may require multiple exponential terms
• Determine rate constants from relaxation time related to sum of forward and reverse rate constants ($k_f + k_r$)
  • $\tau = \frac{1}{k_f + k_r}$
  • Measure relaxation times at different temperatures or pressures to determine individual rate constants
• Analyze temperature dependence of rate constants using Arrhenius equation or Eyring equation
  • Arrhenius: $k = A \exp(-E_a/RT)$
  • Eyring: $k = \frac{k_B T}{h} \exp(-\Delta G^‡/RT)$
  • Plot $\ln k$ vs $1/T$ to determine activation energy ($E_a$) and pre-exponential factor ($A$)