Lecture 18: Biophysical Chemistry

Lecture 18: Biophysical Chemistry

Overview for Quarter II

Chemical Kinetics

Today:

Kinetics: Dynamic process of transforming a physical-chemical-biochemical property.

• Rate law
• Order of Reaction
• Stoichiometry versus mechanism of reaction
• Analyzing experimental data
• Zero order reactions
• Example: Ethanol to acetaldehyde conversion
• First order reactions
• Radioactivity
• Activity of Penicillin
• Concept of half life
• Second Order reaction
• Oxidation of Fe
• Renaturation of DNA

Rate Laws

In kinetics we are concerned with the timescale and precise sequence of events that lead to transformation of reactants to products. To develop a better quantitative framework we define few common terms used in the chemical kinetics.

Velocity/rate of reactions: It is defined as:

where c is a concentration of the reactant. This rate depends on the concentration of the reactant as well as nature of the solvent/environment. To simplify the problem, we might better define the system by specifying not only the concentrations, but also the precise conditions under which takes place. These auxiliary conditions can be fixed, for example temperature, pressure etc. Under such conditions, we write for a general reaction as:

The overall reaction is then said to be or order n+m+p. It is also common to define the order with respect to a component, e.g., m th order with B etc. Also note we have divided individual component rate by the corresponding number particles that are involved in the reactionSimplifications

The above outlined approach, in general, is complex and even worse mathematically intractable. As one can imagine biological reactions are very complex involving multiple steps and different intermediates. If we had to know the concentration of each of these species our analysis will be exceedingly difficult if not impossible. Therefore over the years several strategies have to developed to simplify the complex problem.

1.For reaction involving many components it is usually possible to consider only those components whose concentration changes significantly. For example in the case of water formation reaction, if the concentration of O2 were to be much much greater than hydrogen we could ignore it’s effect on the reaction rate.

2.Component that act as catalysts, i.e., whose concentration does not vary with time, can be ignored. However this does not mean they do not affect the rate constant.

3.Molecular collisions are important in chemical reactions. However probabilities of collisions between three and more molecules become exceedingly low. Thus higher order reactions are generally uncommon. But there are exceptions.

4.Cases involving multiple steps, we can generally identify “rate determining step”. Then we focus on the kinetics of the rate-determining step.Reaction Mechanism versus Stoichiometry

Consider again a simple reaction of hydrogen with oxygen to form water. Stoichiometrically we can write:

Although chemically balanced, these reaction schemes do not actually tell us about the mechanism of formation of the water. It could be for example:

Notice each of these reactions is stoichiometrically balanced and involves one or at the most two particles to undergo a chemical transformation. We can write rate equation for each of these equations and the overall kinetics could be far more complex than the simple reaction stoichiometry. Some examples are shown below

Oth order reaction

Consider oxidation of alcohol brought about the liver enzyme dehydrogenase to produce acetaldehyde. If we were to monitor either disappearance of alcohol or formation of aldehyde using an analytical technique we may find results as shown in the figure below.

Since the plots are linear, the rate (dC/dt) is constant. Which we may write for aldehyde production as:

Note that for the 0th order reaction can not remain 0th order forever, since that would lead to infinite concentration of product and negative concentration of reactant!

First Order Reaction

Note the ideas of chemical kinetics are sufficiently powerful that we can even apply them to other physical properties such as remaining activity of Penicillin.

In this case as the activity does not decrease linearly but seem to decay exponentially. This is shown in the right figure, where log-linear plot clearly reveals the exponential dependence of activity.

Such behavior results from following rate equation.

More commonly we define first order reactions by the half lives, that is time needed for the concentration/activity to fall by half it’s starting value, it is given by ln(2)/k.

Radioactive Carbon Dating

In upper atmosphere Nitrogen is converted to radioactive Carbon by absorption of neutrons from Cosmic rays:

Radioactive carbon decays to normal carbon by a very slow first order kinetics given by

The beta particles are simply electrons emitted by the Carbon nucleus. These can be easily determined from variety of detectors.

In nature, the radioactive carbon gets is assimilated in plant kingdom during the photosynthesis process. Since carnivores eat herbivores, this radioactive carbon finds it’s way in all living things. However, the decay product is not readily converted back to 14C since neutrons from cosmic ray do not readily reach the surface of the earth.

Thus, this carbon clock is an extremely valuable in studies of plants, archeology etc. The half-life of the radioactive carbon is 5770 years! Thus the first order process allows us to determine the age of living/dead objects of biological origin as far as millions of years.

Second order reactions

These types of reactions have been further subdivided into two categories

Examples:

Examples

Renaturation of DNA

More Complex Case