The Effect of Temperature on Reaction Rates

These results are consistent with studies made in 1889 by the Swedish chemist Svante Arrhenius, who discovered a key relationship between T and k. In its modem form, the Arrhenius equation is 

We can calculate a ffoiri the Arrhenius equation by taking the natural logarithm of both sides and recasting the equation into one for a straight line  

Because the relationship between In k and 1 /T is linear, we can use a simpler method to find E if we know the rate constants at two temperatures, T2 and T  

When we subtract In from In k2, the term In A drops out and the other terms can be rearranged to give 

Plan We are given the rate constants, and 2. at two temperatures, T and T2, so we substitute into Equation 16.9 and solve for E.  

The rate of most chemical reactions increases rapidly with temperature slow reactions can be transformed into fast reactions by heat. The effect was first explained and quantified in terms of activation energy. Later on (Section 3.1.4), when discussing the transition state theory, we shall use the concept of free energy of activation instead, but for now let us see how the simpler concept of energy of activation accounts for the effect of temperature on reaction rates. 

From thermodynamic considerations we know that the equilibrium constant K is related to AHj  

FIGURE 3.1. Plot of potential energy along the reaction coordinate (collision theory). 

Agreement with observation is best when the constant J is given the value zero and with this adjustment Eq. (3.16) integrates to give the Arrhenius equation, generally as  

A is called the frequency or pre-exponential factor, and E is the activation energy. It follows that E in Eq. (3.17) is an experimentally determined quantity, derived from a plot of In [fe] against l/T. 

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Finally, there is an interesting article" that shows how to use Taylor s series to generate shortcut methods from established theory. Examples are given for developing a criterion for replacing log mean temperature differences with average differences and for estimating the effect of temperature on reaction rate. 

Activation energy the constant Ea in the exponential part of the Arrhenius equation associated with the minimum energy difference between the reactants and an activated complex (transition state), which has a structure intermediate to those of the reactants and the products, or with the minimum collision energy between molecules that is required to enable areaction to take place it is a constant that defines the effect of temperature on reaction rate. 

An everyday task in our laboratories is to make measurements of some property as a function of one or more parameters and to express our data graphically, or more compactly as an algebraic equation. To understand the relationships that we are exploring, it is useful to express our data as quantities that do not change when the units of measurement change. This immediately enables us to scale the response. Let us take as an example the effect of temperature on reaction rate. The well-known Arrhenius equation gives us the variation... 

FIG. 2.2 The effect of temperature on reaction rate. As the temperature of a chemical system is increased, the rate at which that system reacts to form products increases exponentially. 

Every time an item is placed in the refrigerator we depend on lower temperatures to slow reaction rates to prevent food spoilage. The effect of temperature on reaction rates is also illustrated by its impact on human survival. Normal body temperature is 37°C. An increase of body temperature of just a few degrees to produce a fever condition increases the metabolic rate, while lowering the body temperature slows down metabolic processes. The slowing of human... 

Figure 2 (38) shows that the effect of temperature on reaction rate was quite similar for phenyl and p-nitrophenyl phosphate and altogether different for /3-glycerophosphate. 

Bassam Z. Shakhashiri, "Light- sticks," Chemical Demonstrations, A Handbook for Teachers of Chemistry, Vol. 1 (The University of Wisconsin Press, Madison, 1983), pp. 146-152. Cyalume lightsticks are used to demonstrate the effect of temperature on reaction rates. 

A number of researchers have studied the effect of temperature on reaction rates of soil chemical phenomena (Burns and Barber, 1961 ... 

The effect of temperature on reaction rates can be demonstrated with two tablets of effervescent antacid, two cups, and tap water. Into one cup, place a half cup (120 milliliters) of cool tap water from the faucet. In the other cup, place an equal amount of hot tap water from the faucet. Drop one tablet into each cup at the same time. The fizzing action is clearly more vigorous in the hot water than in the cool water. In this case, the higher temperature helps in two ways. It forces more bubbles out of solution (which is the same reason you re cautious about opening a warm can of soda), and it increases the reaction rate because molecules at a higher temperature move around faster, find each other more often, and hit each other harder when they do. This effect and other principles concerning chemical kinetics is the subject of the following discussion. 

Explain why an increase in the frequency of collisions is not an adequate explanation of the effect of temperature on reaction rate. 

To generate an expression for the effect of pressure upon equilibria and extend it to reaction rates, this early work consisted of drawing an analogy with the effect of temperature on reaction rates embodied in the Arrhenius equation of the late 19th century.2 In the more coherent understanding since the development of transition state theory (TST),3 6 the difference between the partial molar volumes of the transition state and the reactant state is defined as the volume of activation, A V, for the forward reaction. A corresponding term A Vf applies for the reverse reaction. Throughout this contribution A V will be used and is assumed to refer to the forward reaction unless an equilibrium is under discussion. Thus ... 

Figure 3.37 Svante Arrhenius (1859-1927), who proposed the theory of electrolytic dissociations (1887), investigated the viscosity of solutions, the effect of temperature on reaction rates (1889), etc. (Published with permission from the Deutsches Museum, Munich.)...

Experiments have shown that chemical reaction rates increase with increasing temperatures. In many instances, the effect of temperature on reaction rate is related to its effect on the reaction rate constant. Arrhenius formulated the empirical rate law. 

Wood, J.A. (1989). Simulating the effect of temperature on reaction rates. Education in Chemistry, 26, 22-23. 

In Chapter 1, the effect of temperature on reaction rate was illustrated by means of the Arrhenius equation. In most cases, a reaction can be studied conveniendy over a rather narrow range of temperature, perhaps 30 to 40°C. Over a range of temperature of that magnitude, it is normal for a plot of In k versus 1/T to be linear. However, for a very wide range of temperature, such a plot will not be linear, as will now be shown. 

The effect of temperature on reaction rate was first observed over 100 years ago by Hood who noted that the relationship could be written as... 

Maintaining a near-constant temperature is one of the primary physiological functions of the human body. Normal body temperature generally ranges from 35.8 °C to 37.2 °C (96.5 °F to 99 °F). This very narrow range is essential to proper muscle function and to control of the rates of the biochemical reactions in the body. You will learn more about the effects of temperature on reaction rates in Chapter 14. 

The rates of most chemical reactions increase as the temperature rises. For example, dough rises faster at room temperature than when refrigerated, and plants grow more rapidly in warm weather than in cold. We can see the effect of temperature on reaction rate by observing a chemiluminescence reaction (one that produces light), such as that in Cyalume light sticks ( Figure 14.13). 

Kj and Ej are the rate constant and the activation energy, respectively. A is a constant, R is the universal gas constant, and T is the absolute temperature. Thus, the kinetic model as discussed above allows calculation of activation energy (E), using linear regression on data obtained at different temperatures. Typical plots showing the effect of temperature on reaction rate and conversion of free radically polymerised unsaturated polyester are shown in Figures 1.2a and 1.2b, respectively. 

The effect of temperature on reaction rates the Arrhenius relation... 

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