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Question

What is meant by reaction co-ordinate in the statement:
"The energy required to form this intermediate, called the activated complex is known as activation energy. Figure 4.7 is obtained by plotting potential energy versus reaction co-ordinate. Reaction co-ordinate represents the profile of energy change when reactants change into products"
Please explain the meaning of the sentence and the term reaction coordinate in an easy way.
(Chemistry part 1, Class 12, NCERT, Chapter: Chemical Kinetics Page: 112)

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Solution

The reaction coordinate is the progress of a reaction from reactants to products with various intermediates and transition states in between. It is an abstraction. It has no relation to time. Rather it is the progress of bond-forming and bond-breaking reaction steps. The free energy change of partially formed and partially broken bonds cannot be measured. The free energies of transition states (local maxima) cannot be directly measured. These states are transient and cannot be directly observed. For a simple reaction with few mechanistic steps, the activation energy (transition state energy) can be calculated from kinetics measurements. The free energy of intermediates can often be determined directly or indirectly if they are long-lived. Most of these diagrams are assembled from a few measured data points and either extrapolation or theoretical computation.

If two reaction coordinate axes are presented, this often means that there are two separate pathways the reaction can take, and each pathway is presented on one of the two reaction coordinate axes. Perhaps the reaction involves two different steps, but those steps need not happen in the same order every time. As a generic example, consider nucleophilic substitution reactions in organic chemistry: A generic nucleophile (Nu-) reacts with an organic molecule R-X, where X is a leaving group, and R is the rest of the molecule (which is unchanged or nearly unchanged). The overall reaction would be

Nu- + R-X --> Nu-R + X-

This process involves two steps: forming the bond between Nu and R, and breaking the bond between R and X. These two steps can happen in three different orders: 1) the R-X bond breaks first and the R-Nu bond forms second (this is the dissociative or SN1 mechanism); 2) The R-Nu bond forms first and the R-X bond breaks second (this is the associative or SNAc mechanism); and 3) The R-X bond breaks and the R-Nu bond forms at the same time (this is the intermediate or SN2 mechanism). All three of these cases occur in reactions that are covered in any undergraduate organic chemistry text. These three processes would look like the following. The items in parentheses are transition states with partially formed/broken bonds (---).

Dissociative:
Step 1: Nu- + R-X --> (Nu- + R---X) --> Nu- + R+ + X-
Step 2: Nu- + R+ + X- --> (Nu---R + X-) --> Nu-R + X-

Associative:
Step 1: Nu- + R-X --> (Nu---R-X) --> [Nu-R-X]-
Step 2: [Nu-R-X]- --> (Nu-R---X) --> Nu-R + X-

Intermediate:
Only step: Nu- + R-X --> (Nu---R---X) --> Nu-R + X-

A reaction coordinate energy diagram for a substitution process could then be graphed over two different reaction coordinates: breaking the R-X bond and forming the R-Nu bond. For ease of two dimensional representation, these are often presented as contour diagrams.


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