steady state approximation

Examples of steady state approximation in the following topics:

• Steady-State Approximation

  • The steady state approximation can be used to determine the overall rate law when the rate-determining step is unknown.
  • Both cases can be addressed by using what is known as the steady state approximation.
  • With the steady state assumption, we can write the following:
  • We had no knowledge of the rate-determining step, so we used the steady state approximation for our reaction intermediate, N2O2.
  • Simplify overall rate laws using the steady state approximation for reactions with various or unknown rate-limiting steps, explainting the steady state approximation and when it is valid

• Alkene Isomerization

  • A photochemical reaction occurs when internal conversion and relaxation of an excited state leads to a ground state isomer of the initial substrate molecule, or when an excited state undergoes an intermolecular addition to another reactant molecule in the ground state.
  • Non-radiative internal conversion of this S1 twisted state leads to the transition state region of S0, which decays equally to the ground states of the cis and trans isomers.
  • Molecules occupying this new excited state then relax to either DHP or cis-stilbene ground states.
  • This energetic state then serves to activate a substrate molecule to a lower energy triplet state by collisional exothermic energy and spin exchange, returning the sensitizer to its ground state.
  • The unexpected change in steady state isomer distribution with the triplet energy of the sensitizer could not be rationalized as a single classical energy transfer.

• Mercury Battery

  • Mercury batteries have the advantages of a long shelf life of up to 10 years and steady voltage output.
  • Although these batteries were very common in the mid-20th century, the Mercury-Containing and Rechargeable Battery Management Act (the Battery Act) passed in 1996 in the United States has largely phased out mercury batteries due to environmental concerns.
  • In 1996, the Mercury-Containing and Rechargeable Battery Management Act (the Battery Act; Public law 104-142) was signed into law in the United States.

• Mechanistic Background

  • Both the ground (lowest energy electronic state) and excited states are shown as energy profiles populated by vibrational energy states (green lines) as well as rotational states (not shown).
  • This consequence of the Born-Oppenheimer approximation led James Franck and R.
  • Overall bonding in an excited state is usually lower than in the ground state.
  • Each electronic state will have a group of vibrational (and rotational) states, depicted by light blue lines above each state marker.
  • The approximate timescales for these transitions are given in the following table.

• Introduction

  • In the presence of an external magnetic field (B0), two spin states exist, +1/2 and -1/2.
  • The magnetic moment of the lower energy +1/2 state is aligned with the external field, but that of the higher energy -1/2 spin state is opposed to the external field.
  • The earth's magnetic field is not constant, but is approximately 10-4 T at ground level.
  • Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2 spin state.
  • The following diagram gives the approximate frequencies that correspond to the spin state energy separations for each of these nuclei in an external magnetic field of 2.35 T.

• Avogadro's Law: Volume and Amount

  • Avogadro's Law states that at the same temperature and pressure, equal volumes of different gases contain an equal number of particles.
  • Avogadro's Law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) is a gas law; it states that under the same pressure and temperature conditions, equal volumes of all gases contain the same number of molecules.
  • In practice, real gases show small deviations from the ideal behavior and do not adhere to the law perfectly; the law is still a useful approximation for scientists, however.

• Acid-Base Indicators

  • An indicator is a weak acid (or a weak base) that has different colors in its dissociated and undissociated states.
  • The eye is sensitive to color changes over a range of concentration ratios of approximately 100 or over two pH units.
  • Below pH 2.8, a solution containing methyl orange is red; above approximately 4.8, it is clearly yellow.
  • Note that this color change occurs over the pH range from approximately 3-4.

• Real Gases

  • This law sufficiently approximates gas behavior in many calculations; real gases exhibit complex behaviors that deviate from the ideal model, however, as shown by the isotherms in the graph below.
  • For most applications, the ideal gas approximation is reasonably accurate; the ideal gas model tends to fail at lower temperatures and higher pressures, however, when intermolecular forces and the excluded volume of gas particles become significant.
  • At a certain point of combined low temperature and high pressure, real gases undergo a phase transition from the gaseous state into the liquid or solid state.
  • The ideal gas model, however, does not describe or allow for phase transitions; these must be modeled by more complex equations of state.
  • Notice that the higher isotherms on the graph, which represent the gas' state at higher temperature, show the typical, concave decreasing curve of an inverse relationship.

• The Uncertainty Principle

  • Roughly, the uncertainty in the position of a particle is approximately equal to its wavelength (λ).
  • Therefore, to a first approximation the Heisenberg Uncertainty Principle gives that the product of these two uncertainties is on the order of Planck's constant (h).
  • The uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology.

• Effect of a Common Ion on Solubility

  • This is because Le Chatelier's principle states the reaction will shift toward the left (toward the reactants) to relieve the stress of the excess product.
  • Therefore, the approximation that s is small compared to 0.10 M was reasonable.
  • This approximation is also valid, since only 0.0019 percent as much CaF2 will dissolve in 0.10 M NaF as in pure water.