Chemical reaction rates are proportional to a rate constant k that changes with
ID: 3884850 • Letter: C
Question
Chemical reaction rates are proportional to a rate constant k that changes with temperature according to the Arrhenius equation
Using MatLab a function called reactionRates that inputs the baseline temperature k0 (min-1), the activation energy Q (cal/mol), and temperature T (K). In the function, use the universal gas constant with consistent units: R = 1.987 cal/ mol K.
For a certain reaction,
Q = 8000 cal/mol k0 = 1200 min-1
In your main homework script, define the values of k for temperatures from 100 K to 500 K, in 2 K increments. Use your user-defined function to calculate the reaction rate k. In your script, create a two-column matrix called ReactionRates, with temperature T in one column and corresponding values of k in the other.
Find the first temperature value, for which k is greater than 0.1 min-1.
Explanation / Answer
The rate of a simple, elementary reaction, say
A+B- > Products
can be represented as
rate=k[A][B]
Thus the temperature and concentration dependence of the rate can be effectively de-coupled.
The rate constant is obtained from the Arrhenius Equation:
k=Aexp(-E/RT)
where A is called a 'pre-exponential' , E is the activation energy, T is the system temperature and R is the gas constant.
It is common in practice to represent the rates of non-elementary reactions also with the above formulation. However, in those cases E is not exactly the activation energy in the strict sense. Activation energy has a very specific meaning in the above context, and this matter is worth probing further. Some of the theories for reactions that we consider later should clarify the concept of activation energy.
Clearly, a bit of mathematical manipulation indicates that, if the rate constant of a simple reaction can be measured as a function of temperature, plotting ln(k) vs. 1/T should give a straight line (what can we conclude if it is not a straight line?). The slope of this line gives us -E/R while the intercept gives ln(A). Thus with a few rate measurements, the pre-exponential and the activation energy can be evaluated (provided the order with respect to and the concentration of the reactants is known).
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