Chemical Kinetics Kinetics – how fast does a reaction proceed? Chemical dynamics Reaction rate Rate Law Change of concentration with time Rate and temperature Reaction mechanism Catalysis

Chemical Dynamics The study of how individual molecules react is called chemical dynamics. It provides answers to the question of if two molecules collide what is the probability of a reaction taking place…(and what is the reaction…)..

Reaction Barrier In a chemical reaction, the first thing we have to do is to break a bond, that costs energy, and then we make a new bond. On a simple energy diagram this is Cl + H + Br Cl + HBr HCl + Br DHrxn At first we invest energy into breaking the HBr bond, and then get the energy back when the new HCl bond is formed. For the EXOTHERMIC reaction, the enthalpies of formation of Cl + HBr lies above those of HCl + Br. The reaction produces energy. Conversely if it were endothermic, the reactants would have enthalpies of formation that were lower than those of the products. In that case you would have to put energy in to get the reaction to go

Over the hill Forward reaction   Reverse reaction https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory In either case, the reaction has to get over that hill, it needs a push to get going, which requires energy. Where can it get energy from?

Both Ways Now The enthalpy of the reaction can be either exo or endothermic

Sometimes you need more energy For example, if you took hydrogen and nitrogen and put them in a container and nothing would happen. You could put it on your shelf and it would sit there forever. But if you press real hard on it and heat it way up you would make ammonia. That won’t happen until you provide enough energy to break the nitrogen bond and break the hydrogen bond so the atoms they can recombine into ammonia. Sometimes you need less energy On the other hand assume that there is a really small barrier ABC A + BC AB + C So small that even at room temperature there is enough energy in the average collision to get over the barrier.

Maxwell Boltzmann Distribution The Boltzmann curve gives the probability of a collision having a certain energy. https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/The_Collision_Theory_1 In this case, we can imagine that if the dotted line were the energy needed to get over the barrier, all of the collisions with higher energies could lead to reaction.

Maxwell Boltzmann Distribution James Maxwell developed a distribution for the speed of molecules in an ideal gas From Wikipedia The k here, just to confuse everybody is Boltzmann’s constant Nak = R. Most often Boltzmann’s constant is written as kB to try and avoid this confusion. The exponential is the ratio of the kinetic energy of the molecule, ½ mv2 to the thermal energy kT. https://upload.wikimedia.org/wikipedia/commons/5/57/James_Clerk_Maxwell.png https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/09%3A_Gases/9.5%3A_The_Kinetic-Molecular_Theory From LibreTexts

Maxwell Boltzmann Distribution The most probably speed is The most probably speed is https://upload.wikimedia.org/wikipedia/commons/c/c3/Boltzmann_age31.jpg https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/09%3A_Gases/9.5%3A_The_Kinetic-Molecular_Theory Ludwig Boltzmann extended Maxwell’s work to handle real gases and liquids

Effect of Mass https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/09%3A_Gases/9.5%3A_The_Kinetic-Molecular_Theory At a given temperature, all gases have the same KEavg for their molecules. Gases composed of lighter molecules have more high-speed particles and a higher urms, with a speed distribution that peaks at relatively higher velocities. Gases consisting of heavier molecules have more low-speed particles, a lower urms, and a speed distribution that peaks at relatively lower velocities.

Effect of Temperature https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/09%3A_Gases/9.5%3A_The_Kinetic-Molecular_Theory

Effect of Temperature If we increase the temperature, a higher percentage of the collisions have enough energy to react. But, if the energy needed to react is very high, very few collisions lead to reaction, and if it is very, very high, the molecules will not react at all. https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/The_Collision_Theory_1 How to make a reaction go faster? Heat the reactants up. That almost always works. Why do I need to provide heat even if the reaction is exothermic? To get over the reaction barrier. http://www.chemguide.co.uk/physical/basicrates/temperature.html http://www.science.uwaterloo.ca/~cchieh/cact/c123/maxwell.html

There is always something else Of course, the probability of reaction also depends on the angle of approach, as well as the energy involved in the collision and a whole other host of other issues. A good way of representing such a reaction is a potential energy surface. Here are two and three dimensional models for AB + C  A + BC reactions https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/11%3A_Molecules/Potential_Energy_Surface

Collision Theory https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry%3A_The_Central_Science_(Brown_et_al.)/14%3A_Chemical_Kinetics/14.5%3A_Temperature_and_Rate The Maxwell-Boltzmann distribution tells us the probability of a reaction exceeding this limit.

Collision Theory For a reaction to occur at a minimum the collision between molecules has to have enough energy to get over the reaction barrier. There may be steric factors and other issues, but the collisions exceeding activation energy is key. The Maxwell-Boltzmann distribution tells us the probability of a reaction exceeding this limit. https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory

Activated Complex The transition state is sometimes called an activated complex https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory

Collision Theory The rate of a reaction is proportional to the rate of reactant collisions The reacting species must collide in an orientation that allows contact between the atoms that will become bonded together in the product. The collision must occur with adequate energy to permit mutual penetration of the reacting species’ valence shells so that the electrons can rearrange and form new bonds (and new chemical species). https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory

Arrhenius Law k = A e-EA/RT The Arrhenius rate law summarizes both experiment and collision theory It allows us to figure out how rate constants change with temperature k = A e-EA/RT https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory

Using the Arrhenius Law k = A e-EA/RT In the Arrhenius Law A is called the pre-exponential factor. It includes all of the dynamics. The exponential term tells us how many of the collisions have enough energy to reach the transition state. Both the activation energy and the pre-exponential factor can be determined by experiment (and theory).

Using the Arrhenius Law k = A e-EA/RT Taking the logarithm of both sides of the equation we find ln k = ln A – EA/RT ln k = ln A – EA/RT Intercept =ln A Slope = – EA/R This is a straight line plotting the natural log of the rate constant against the inverse of temperature https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory

More Confusion Do not confuse the graphical solutions for the Arrhenius plot to determine how the rate constant changes with temperature ln k = ln A – EA/RT With the graphical solution to find the rate constant of a first order reaction where A is the reactant. https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry_(OpenSTAX)/12%3A_Kinetics/12.5%3A_Collision_Theory https://chem.libretexts.org/@api/deki/files/15967/Ex_9_A.jpg?revision=1 Ln [A(t)] = ln Ao – kt

An Example For the reaction 2HI(g)  H2(g) + I2(g) T (K) k (L/mol/s) 555 3.52 × 10−7 575 1.22 × 10−6 645 8.59 × 10−5 700 1.16 × 10−3 781 3.95 × 10−2

Steps Convert the temperatures to inverse temperatures Calculate ln k Plot ln k vs 1/T Determine the slope (-EA/R) and the intercept (A)

More Math Given two measurements of the rate constant, k1 and k2 at two different temperatures T1 and T2 we can calculate activation energy.   Subtracting