Re: CCL:rotational barrier: experiment and theory

From: "Peter Shenkin" <shenkin ^at^ still3.chem.columbia.edu>
Subject: Re: CCL:rotational barrier: experiment and theory
Date: Thu, 29 May 1997 13:16:54 -0400
 On May 29,  3:16am, Jorge Seminario wrote:
 > Subject: CCL:rotational barrier: experiment and theory
 > Hello dear members:
 >
 > I wonder if you could help me to clear up some problems to interpret my
 > colleagues' experiment by using our computational tools. The molecule
 > consists in two benzene rings connected by two carbon atoms.
 > The experiment on Ph-C-C-Ph (where the central C-C bond is triple and
 > the adjacents are single) indicates that a sudden rotation of one of
 > the benzene rings with respect to the other is initiated when the
 > temperature reaches 30 K.
 What is meant by "sudden"?  All your other arguments seem to argue
 for an activated process, which would imply Arrhenius-type behavior;
 this is not usually called "sudden", though in colloquial sense
 I suppose it is.
 > ...  The calculations
 > yield a barrier of about 0.5 kcal/mol for the rotation of the benzene
 > rings. The argument against this theoretical barrier is that
 > at 30K, the kT (or RT) available for this mode is only 0.06 kcal/mol and
 > therefore, the rotation of the phenyl groups is not possible because the
 > barrier is almost ten times bigger than the available energy.
 Sorry, but this argument isn't right.  RT= ca. 2.5 kJ at 300K, yet
 most chemical reactions of everyday interest have activation energies
 many times greater than this.  For instance, we're told in school
 that "typical" room-temperature reactions double in rate when the
 temperature is raised by 10 K.  A typical exam question is to compute
 the activation energy of such a reaction.  The answer is about
 53 kJ/mol, or more than 20 RT.
 The action proceeds because the "pre-exponential factor" is enormously
 high at room temperature.  We now turn to the back of the proverbial
 envelope.
 Using Eyring formalism to estimate the pre-exponential factor,
 kT/h_bar is equal to about 4x10^13/s at 300 K;  at 30 K, we get
 4x10^12/s, which is still huge.
 The Boltzmann factor comes out to about 2x10^-4 for your reaction
 at 30 K, but multiplying this by the corresponding pre-exponential
 factor gives a rate constant of about 8x10^8/sec, which is pretty
 darn fast.
 	-P.
 --
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