Rate Laws

Introduction:

Origin of Rate Laws:

The Basics:

Thermodynamics versus Kinetics

Thermodynamics is all about the “if” of a reaction, such as whether the process can occur.  Kinetics is all about “how”, such as whether the reaction occurs fast or slow.  The kinetics of the process is how to overcome the energy barrier from the reactants to the products, while the thermodynamics ensures that the reaction is a favorable transformation.
For a process to occur, it must overcome the energy maximum, usually denoted E (activation energy).  The larger the barrier (Ea), which is the difference between the energy maximum and initial minimum, the more difficult the process to occur, which thus results in a slower rate.  For a reaction to occur, not only must the thermodynamically favored with a -ΔG (which could be referred to as the driving force), it must also be fast enough, which results from a small Ea.  
If a reaction is thermodynamically favored, that means that the products are in the lowest possible energy state.  If a reaction is kinetically favored, that means that the reaction went through the easiest possible direction, that is, it went in the direction with the lowest activation energy.  Given inifite amount of time, all reactions would proceed to the thermodynamically favored products.  However, if the reaction was only given a short time to proceed, some kinetically favored products would be in solution, however it is unlikely any thermodyamically favored products would, assuming the activation energy of the thermodynamically favored products is higher than that of the kinetically favored products.  The diagram below describes a possible reaction that is helpful in the understanding of thermodynamics versus kinetics. 

If you started with B and were asked what would be created, C or A, if the reaction was thermodynamically favored, the answer would be C.  Why?  C is at a lower, more stable energy than A, therefore, given infinite amount of time, all of B would eventually form C.  If you started with C and went in the reverse reaction, what would the rate determining step be? As stated before, the rate determining step is the one with the highest activation energy.  Therefore, the rate determining step would be from B to A, because that is the biggest energy “hump” to get over.

Below is another energy diagram that can be studied to help better understand the relationship, and difference, between kinetics and thermodynamics.   

Given the reactant D, what is the kinetically favored product, E or F?  The answer is E, but why?  Does that mean F is the thermodynamically favored product?  To answer the latter, E is the kinetically favored product because it has a lower activation energy i.e. the “hump” is smaller and easier to get over.  To answer the last question, F is not then, by process of elimination, the thermodynamically favored product.  Both products E and F have the same energy, therefore one product is not energetically favored versus the other.  However, if F was lower energy than E, even though the activation energy is higher than that of D to E, then F would be the thermodynamically favored product. 

Handling Multi-step Reactions

Multi-step reactions can be handled by first finding the rate-determining step, which is the slowest elementary step, and then setting it to equilibrium. 

Temperature Increases Reaction Rates

As temperature increases, reaction rates, k, increase extremely rapidly.  Svante Arrhenius suggested that the reaction rate is exponential to the inverse of temperature.

(k = A e^(-Ea/RT).

 Where E_a is a constant with dimensions of energy and A is a constant with the same dimensions as k.  

If E_a is the critical relative collision energy required for a pair of molecules to react, then only a fraction of the molecules will have the amount of energy needed to react. This fraction is represented by the area under the Maxwell-Boltzmann distribution curve.  

The average speed, ū,  is related to temperature by:

Kinetic Energy  = ½ mŪ²= 3/2 k_BT

Thus, as temperature increases, the average speed of molecule increases. Thus, the distribution function spreads out to include molecules with higher speeds or energies that will surpass the E_a and allow more molecules to react. This shows that temperature increases reaction rates.

Pressure Increases Reaction Rates

Along with temperature, pressure can also increase reaction rates. Increasing the pressure, while keeping the other variables (n,T) in the ideal gas law, PV=nRT, constant means that if pressure is increasing, volume is shrinking. This means that there will be more molecules/unit volume, therefore, there is less space for the molecules to spread out, and it would take less time before it collides with the wall or other molecules. This means that more molecules will collide in a given time. Since a reaction occurs by molecules colliding, we can say that as pressure increases, reaction rate increases

Questions:

1. Kinetically favored reactions:

     a. have a comparitively high activiation energy

     b. have a comparitvely low activation energy

     c. are the lowest possible energy product

     d. a and c

     e. b and c

Answers: 1. b