Temperature and Rate

The rates of most chemical reactions increase at the temperature rises

• Rate expressions describe reaction rates in terms of concentrations and rate constants (k)

Rate = k[A], or Rate = k[A]², or Rate = k[A][B], etc.

• Temperature changes do not affect concentrations
• Therefore, the observed effects of temperature upon reaction rates must be due to changes in the value of the rate constant k. In particular, k increases with increasing temperature

Overall reaction rates can be increased by:

• Increasing the concentration of reactants
• Increasing the temperature
• The underlying physical interpretation for these two observations is the Collision Model of chemical kinetics
• The main point of the Collision Model is that

1. molecules must physically collide in order to react
2. The more collisions that occur over a given period of time, the faster the reaction rate

• Increasing concentration (i.e. the number of molecules in a given volume) will increase the number of collisions and result in a faster reaction rate
• What about increasing temperature?

The Kinetic Molecular Theory of Gases and the effect of temperature upon rates:

• Increasing temperature results in an increase in the velocity of molecules
• As molecules mover faster, there are more collisions per unit of time
• Not only are there 1) more collisions, but 2) the collisions are harder (i.e. the impacts involve greater energy levels)

Does every collision result in a reaction?

• Only a small fraction of collisions (~1 in every 10¹³ collisions!) results in a reaction.

1888 Swedish chemist Svante Arrhenius proposed:

• The available energy is related to the kinetic energy of the molecular collision
• The kinetic energy of impact can be used to stretch, bend and break covalent bonds, resulting in chemical reactions (recall that in a typical chemical reaction some bond is broken and a new bond is formed)
• If molecules are moving too slowly, they collide with insufficient energy, and just bounce off each other instead of reacting

The minimum energy needed to cause a particular chemical reaction is called the Activation Energy

• Activation Energy is symbolized by E_a
• The value of E_a is dependent upon the particular reaction in question (it is a different value for different reactions)
• Although a reaction may be energetically favorable overall (i.e. DEnergy = DH_rxn = a negative value) the rate of reaction depends upon the magnitude of the activation energy; the higher the activation energy, the slower the reaction

In the above energy diagram for the reaction A® B we have the following features:

1. Overall, the reaction is energetically favorable. 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.e. goes downhill energetically as it goes from A à B)
2. However, for the reaction to proceed, there is an activation energy barrier that molecule A will have to overcome

The conversion of methyl isonitrile (H₃CNC) to acetonitrile (H₃CCN):

• The conversion appears to involve a swapping of the triple bond N-C group
• Conceptually, the 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. 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.
• 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 E_a

Why doesn't B convert back into A? Note that for the backwards reaction, there are two issues:

1. The reaction of B->A is energetically unfavorable (i.e. is endothermic, and requires the input of energy. However, we have seen that entropic contributions can drive endothermic reactions in some cases.
2. Note that the activation energy for the reverse reaction is equal to E_a + DE. This is much greater in magnitude than E_a alone. 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".

• The kinetic energy (speed) distribution of gas molecules at two different temperatures:

• Increasing the temperature increases the fraction of molecules with higher speeds
• If the activation energy is the minimum needed for the reaction to proceed (i.e. to overcome the activation energy barrier) then at higher temperatures more molecules will have that amount of energy.
• The reaction rate will be proportional to the number of molecules that have the minimum required activation energy (i.e. the area of the curves to the right of the minimum activation energy line).

• In addition to the activation energy requirement collisions between molecules may need a correct orientation for the chemical reaction to occur
• The particular reactive atoms may need to collide in the appropriate geometry or juxtaposition
• For example in the reaction Cl + NOCl -> NO + Cl₂ the O-Cl bond is broken and a Cl-Cl bond is formed. In this case, it may be essential for the incoming Cl atom to collide in the correct orientation with the Cl atom of NOCl (all other collisions being unproductive despite having appropriate kinetic energy)

Arrhenius studied the relationship between the increase in reaction rate and increasing temperature:

• The increase in reaction rate (k) is not linear with temperature
• The relationship between the reaction rate and temperature was found by Arrhenius to be:

• k is the rate constant, E_a is the activation energy, R is the gas constant (8.314 J/mol K), and T is the temperature (Kelvin)
• The term A is the frequency factor.
• It is related to the frequency of collisions and the probability that the collisions are productive (i.e. correctly oriented)
• It is specific for the particular reaction

• If we take the natural log of both sides of the Arrhenius equation we get:

• Thus, this will have the form of a linear equation if we plot lnk vs. 1/T. The slope of this line will be equal to (-E_a/R) and the y intercept will be lnA

• Thus, for this data, -E_a/R = -6014, and E_a therefore equals 50,000 J/mol. lnA = 9.210, therefore, A = 10,000 s^-1

If we know the reaction rate at two different temperatures, T₁ and T₂ we can calculate the activation energy, E_a, without knowing the value for the frequency factor, A

Subtracting the equation for lnk₂ from lnk₁ gives: