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Postulates The theory for ideal gases makes the following assumptions: .... have 7 degrees of freedom, but the lighter gases act as if they have only 5. .... Introduction to the kinetic molecular theory of gases, from The Upper Canada ...

Transition state theory

Transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes.

TST is used primarily to understand qualitatively how chemical reactions take place. TST has been less successful in its original goal of calculating absolute reaction rate constants because the calculation of absolute reaction rates requires precise knowledge of potential energy surfaces, but it has been successful in calculating the standard enthalpy of activation (Î”â€¡Hâ¦µ), the standard entropy of activation (Î”â€¡Sâ¦µ), and the standard Gibbs energy of activation (Î”â€¡Gâ¦µ) for a particular reaction if its rate constant has been experimentally determined. (The â€¡ notation refers to the value of interest at the transition state.)

This theory was developed simultaneously in 1935 by Henry Eyring, then at Princeton University, and by Meredith Gwynne Evans and Michael Polanyi of the University of Manchester. TST is also referred to as â€œactivated-complex theory,â€� â€œabsolute-rate theory,â€� and â€œtheory of absolute reaction rates.â€�

Before the development of TST, the Arrhenius rate law was widely used to determine energies for the reaction barrier. The Arrhenius equation derives from empirical observations and ignores any mechanistic considerations, such as whether one or more reactive intermediates are involved in the conversion of a reactant to a product. Therefore, further development was necessary to understand the two parameters associated with this law, the pre-exponential factor (A) and the activation energy (Ea). TST, which led to the Eyring equation, successfully addresses these two issues; however, 46 years elapsed between the publication of the Arrhenius rate law, in 1889, and the Eyring equation derived from TST, in 1935. During that period, many scientists and researchers contributed significantly to the development of the theory.

## Theory

Basic ideas behind the transition state theory are as follows:

1. Rates of the reactions are studied by studying activated complexes which lie at the col (saddle point) of a potential energy surface. The details of how the complexes are formed are not important.

2. The activated complexes are in a special equilibrium (quasi-equilibrium) with the reactant molecules.

3. The activated complexes can convert into products which allows kinetic theory to calculate the rate of this conversion.

## Development

In the development of TST, three approaches were taken as summarized below

Thermodynamic Treatment

In 1884, Jacobus van't Hoff proposed the Van't Hoff equation describing the temperature dependence of the equilibrium constant for a reversible reaction:

A B
\frac{d\ln K}{dT} = \frac{\Delta U}{RT^{2}}

where Î”U is the change in internal energy, K is the equilibrium constant of the reaction, R is the universal gas constant, and T is thermodynamic temperature. Based on experimental work, in 1889, Svante Arrhenius proposed a similar expression for the rate constant of a reaction, given as follows:

\frac{d\ln k}{dT} = \frac{\Delta E}{RT^{2}}

Integration of this expression leads to the Arrhenius equation

k = Ae^{\frac{-E}{RT}}

A was referred to as the frequency factor (now called the pre-exponential coefficient), and E is regarded as the activation energy. By the early 20th century many had accepted the Arrhenius equation, but the physical interpretation of A and E remained vague. This led many researchers in chemical kinetics to offer different theories of how chemical reactions occurred in an attempt to relate A and E to the molecular dynamics directly responsible for chemical reactions.

In 1910, Rene Marcelin introduced the concept of standard Gibbs energy of activation. His equation can be written as

k\propto\exp\left(\frac{-\Delta^\ddagger G^\ominus}{RT}\right)

At about the same time as Marcelin was working on his formulation, Dutch chemists Philip Abraham Kohnstamm, Frans Eppo Cornelis Scheffer, and Wiedold Frans Brandsma introduced for the first time standard entropy of activation and the standard enthalpy of activation. They proposed the following rate constant equation

k\propto\exp\left(\frac{\Delta^\ddagger S^\ominus}{R}\right)\exp\left(\frac{-\Delta^\ddagger H^\ominus}{RT}\right)

However, the nature of the constant was still unclear.

Kinetic-Theory Treatment

In early 1900, Max Trautz and William Lewis studied the rate of the reaction using collision theory, based on the kinetic theory of gases. Collision theory treats reacting molecules as hard spheres colliding with one another; this theory neglects entropy changes.

Lewis applied his treatment to the following reaction and obtained good agreement with experimental result.

2HI â†’ H2 + I2

However, later when the same treatment was applied to other reactions, there were large discrepancies between theoretical and experimental results.

Statistical-Mechanical Treatment

Statistical mechanics played a significant role in the development of TST. However, the application of statistical mechanics to TST was developed very slowly given the fact that in mid-19th century, James Clerk Maxwell, Ludwig Boltzmann, and Leopol

Question:

Question:this is going to sound retarded, but at school we've just started a science unit on particles and such, but our teacher hasn't taught us anything about it, and now wants us to do a title page thats due very VERY soon. i need some help, FAST!! i understand most things, but now i have to write up an explanation of the particles in solids, liquids and gases. please help. they only have to be about 2 1/2 lines each, just cause i can make them look long as hell. please help me.

Answers:Three stages of matter: The easiest way to imagine particles is as small balls. These particles are in constant movement. The hotter they are, the faster they move. This explains freezing/melting, boiling/condensing and lots more. It is called the Kinetic Theory of Matter. Kinetic is something to do with movement. Solids: In solids, the particles are arranged in a regular pattern, touching each other. They attract each other with a strong force (because they are so small and so close). They cannot change places. The particles of matter are always moving. Since they cannot change places in a solid, they simply vibrate. Solids do not flow. The particles in a solid cannot change places so a solid will keep its shape (unless it is broken). Solids cannot be compressed. Since the particles of a solid are already touching each other, they cannot be squashed any closer. Solids can be quite strong because the particles are close which makes the forces holding each particle to its neighbour strong. It is not possible to pass through solids without breaking them because the particles are so tightly packed and cannot move out of the way. Liquids In liquids, the particles are still pretty close together but not necessarily touching each other. There is no pattern. They arranged randomly. They are moving about in all directions, changing places all of the time. The forces holding the particles together in a liquid are not as strong as those in a solid. The particles are moving all of the time. In a liquid it is possible for them to change places. Liquids can flow. This is because the particles can move past each other. Liquids will not keep any shape because the particles are always moving around and changing places. They will take up the shape of the container they are in. Liquids cannot be compressed because the particles are already very close together. Gases In gases, the particles are very spread out. They are moving very quickly in different directions. They are not arranged in any pattern. They are changing places all of the time. The forces holding the particles together are very small. They are so small that they can be ignored so there are no forces holding them together. Gases flow. The particles are always changing places with each other. Gases spread out to fill the container. They are moving very fast and there are no forces to stop them flying apart. They will be stopped by the solid walls of the container. Gases can be compressed. This is because the particles are so far apart. They can be squeezed together. Gases spring back when you stop compressing them. As soon as you stop squeezing, they fly apart again. It is easier to walk through air than through water. It is much easier to walk through water than through a wall.

Question:The particles in both gases and liquids are? A. consist only in atoms B. can change positions with other particles C. vibrate in fixed positions D. are packed closely together Which term best describes the process by which particles escape from the surface of a non boiling liquid and enter the gas state? A. vaporisation B. evaporation C. surface tension D. aeration Molecules at the surface of a liquid can enter the vapor phase only if? A. equilibrium has not been reached B. the concentration the vapor is zero C. their energy is high enough to overcome the attractive forces in the liquid D. condensation is not occurring The reaction Pb(NO3)2(aq)+ 2KI(aq) -> PbI2(s) + 2KNO3(aq) is a ? A. double replacment reaction B. synthesis reaction C. decomposition reaction D. combustion reaction What is the molar mass of magnesium chloride, MgCI2 ? A. 46 amu B. 59.763 amu C. 95.211 amu D. 106.354 amu The molar mass of NO2 is 46.01 g/mol. How many moles of No2 are present in114.95g? A. 0.4003 mol B. 1.000 mol C. 2.498 mol D. 114.95 mol The kinetic-molecular theory explains the properties of solids, liquids, gases in terms of the energy of the particles and? A. gravitational forces B. the forces that act between the particles C. diffusion D. the mass of the particles According to the kimetic-molecular theory, what is the most significant difference between gases and liquids? A. the shapes of the particles B. the mass of each particle C. the distance between the particle D. the type of collision that occurs between particles A solution can be diluted by adding more? A. solvent B. solute C. pressure D. temperature A saturated solution is one which ? A. chemical change has taken place B. no more solute will dissolve C. there is more solute than solvent D. all the liquid has evaporated Ions are formed from solute molecules by the action of the solvent in a process called A. ionization B. dissociation C. precipiation D. oxdation Which solute is present in aqueous solution mostly as molecules and only some ions? A. a weak electrolyte B. a strong electrolyte C. a nonelectrolyte D. a covalent electrolyte Which of the following is a strong electrolyte? A. CH3COOH B. HBr C. HF D.NH3 Which of the following is at equilibrium when undissolved solute is visible? A. a saturated solution B. an unsaturated solution C. a supersaturated D. all of the above If the amount of solute presents on a solution at a given temperature is less than the maximum amount that can dissolve at that tempature, the solution is said to be? A. a saturated solution B. an unsaturated solution C. a supersaturated D. concentrated If the amount of dissolved solute in a solution at a given tempature is greater than the amount that can permanently remain in solution at the tempature, the solution is said to be? A. a saturated solution B. an unsaturated solution C. a supersaturated D. diluted which of the following is an example of a polar solvent? A. carbon tetrachloride B. benzene C. water D.gasoline The soulibility gases in liquids? A. always increases with increasing pressure B.sometimes increases with increasing pressure C. always decreases with ncreasing pressure D. does not depend on pressure