Chemical Forums
Chemistry Forums for Students => High School Chemistry Forum => Topic started by: Tom on June 09, 2004, 08:40:11 AM

True: If a reaction follows Arrheius' theory, a plot of the logarithm of the rate constant, 1n(k), vs. the absolute temperature, T, is a straight line.

is this a question? I'll add my two cents in anyways.
Yes, by taking the natural log of the Arrhenius equation: k=Ae^{Ea/RT}, where A is a prefactor, Ea is the activation energy, and R is the Boltzmann constant... we get:
ln(k)=ln(A)Ea/RT
So, if we can plot k over several temperatures, we get the prefactor and the activation energy for free. The prefactor is generally the frequency with which the event tries to happen, like how often gas molecules have to hit each other. ln(A) is the yintercept and after multiplying the slope by RT we get the activation energy.
What, you might say, is the use of prefactors? Well, there are a few equations that use prefactors to get other information. For example, in terms of surface diffusion, the movement of molecules on the surface, by getting the prefactors for diffusion and hopping rate, which both have Arrhenius behavior, we can put it into the equation:
D_{0}=L^{2}*h_{0}/2, where L is the mean jump length, D_{0} is the diffusion prefactor, and h_{0} is the hopping rate prefactor
and from that we can get the mean jump length. However, there is a problem with deriving data from prefactors due to the uncertainty usually associated with them, so there's some fancy math or methods being investigated to avoid the high uncertainty.

Thankyou for explaining that to me in detail. I appreciate it.