# Relationship between temperature and rate constant

### Temperature dependence of rates of reactions

The rate constant, however, does vary with temperature. resembles the relationships seen in graphs of vapor pressure versus temperature. In conductivity, the barrier is the energy gap between the filled and empty bands. In , Svante Arrhenius suggested that rate constants very exponentially (This is a very strong dependence!) with the reciprocal of the absolute temperature. How is the collision theory and the rate of a chemical reaction related? Arrhenius equation tells us about the temperature dependence of a chemical reaction and it simultaneously considers other factors which determine the rate of a reaction. This equation equates the rate constant.

Set the two equal to each other and integrate it as follows: The first order rate law is a very important rate law, radioactive decay and many chemical reactions follow this rate law and some of the language of kinetics comes from this law.

The final Equation in the series above iis called an "exponential decay.

## In general, what is the relationship between temperature and the rate for a chemical reaction?

One of its consequences is that it gives rise to a concept called "half-life. For Example, if the initial concentration of a reactant A is 0.

In general, using the integrated form of the first order rate law we find that: Taking the logarithm of both sides gives: The half-life of a reaction depends on the reaction order. For a first order reaction the half-life depends only on the rate constant: Thus, the half-life of a first order reaction remains constant throughout the reaction, even though the concentration of the reactant is decreasing.

For a second order reaction of the form: Since the concentration of A is decreasing throughout the reaction, the half-life increases as the reaction progresses.

That is, it takes less time for the concentration to drop from 1M to 0.

Here is a graph of the two versions of the half life that shows how they differ from http: A first order reaction has a rate constant of 1. What is the half life of the reaction? Since the reaction is first order we need to use the equation: What is the rate constant?

In other words, the product, B, is at a lower energy level than the reactant, A.

Energetically, the reaction will proceed with a net release of energy i. The conversion appears to involve a swapping of the triple bond N-C group Conceptuallythe reaction may proceed through an intermediate state in which the triple-bond N-C portion of the molecule is sitting sideways denoted in brackets above In order for this group to rotate, the CH3-N bond must stretch and break.

## 14.5: Temperature and Rate

This will require the input of energy. This required input of energy is reflected in the activation energy barrier being higher than the energy level of methyl isonitrile The intermediate structure in brackets above is a high-energy intermediate called the transition state, or activated complex After the CH3-N bond is broken, the new C-C bond forms. This results in the release of energy. The formation of the C-C bond leading to the acetonitrile structure releases energy and thus the energy diagram decreases after the activation energy.

### Activation Energy

Acetonitrile is a lower energy structure than methyl isonitrile the C-C bond is a lower energy bond than C-N. The reaction is exothermic energy is released. What are the key properties of the above energy landscape for the conversion of methyl isonitrile to acetonitrile that determines the rate of the reaction?

The change in energy, DE, has no effect upon the rate of the reaction The rate depends upon the magnitude of the activation energy Ea Why doesn't B convert back into A? Note that for the backwards reaction, there are two issues: However, we have seen that entropic contributions can drive endothermic reactions in some cases. This is much greater in magnitude than Ea alone.

Arrhenius Equation Activation Energy and Rate Constant K Explained

Thus, not only is the reverse reaction energetically unfavored, the rate of the reverse reaction is much slower due to the larger activation energy "barrier". What fraction of molecules has enough kinetic energy to overcome the activation energy barrier, and how does temperature affect this?