This Mathematica notebook illustrates the temperature dependence of reaction rates. Here is first an illustration of Table 2.1, p. 28, in slightly simplified form.

gasConst = 8.314    ;
deltaTemp = (1/temp1 - Log[2]/(Eact/gasConst))^-1 - 
          temp1;
deltaTemp1 = (1/673 - Log[2]/(160000/gasConst))^-1 - 
        673   
plot = 
        Plot[{deltaTemp /. temp1 -> 300, deltaTemp /. temp1 -> 700, 
            deltaTemp /. temp1 -> 1300}, {Eact, 15000, 300000}, 
          Background -> GrayLevel[0.9], Frame -> True, 
          FrameLabel -> {"Activation energy", "Rate-doubling \
temperature rise"}, GridLines -> Automatic, 
          PlotStyle -> {Thickness[0.004], Thickness[0.006], 
              Thickness[0.008]}];

What follows next is an illustration of Figure 2.2, p. 28. By varying the pre-exponential factor and the activation energies, you should get a feel for the temperature sensitivity of reaction rates.

kzero1 = 10^12;
kzero2 = 10^14;
k1 = kzero1 Exp[-10000*recipTemp];
k2 = kzero2 Exp[-40000*recipTemp];
Plot[{Log[k1], Log[k2]}, {recipTemp, 0.00002, 0.002}, 
        PlotRange -> {0, 35}];

You might ask: "What is a realistic value for the pre-exponential factor?" Remember your PChem?! For an elementary reaction, the pre-exponential factor is called the frequency factor and its upper bound can be estimated from collision theory (kinetic theory of gases), as follows (for a bimolecular reaction, in units of m^3/mol/s)... Please check the units!

nA = 
        6.022 10^23;   
kB = 
        1.38 10^-23;   
rA = 5 10^-10;   
rB = 
        5 10^-10;  
mu = 10^-25;   
t = 300;   
preExpFactor = nA*(rA + rB)^2*Sqrt[8  Pi*kB*t/mu]

These are typical values (ca. 10^11 L/mol/s), but they are typically much higher (see below) than the values determined experimentally. This disagreement between theory and experiment is accounted for by a "steric factor" (molecules have to be in the right geometric orientation for reaction to occur). A more useful theoretical approach (than collision theory) is the activated complex (or transition state) theory, because it relies on statistical thermodynamics. According to this theory, the frequency factor can be estimated as follows (in units of s^-1). Again, check the units!

h = 
        6.63 10^-34;  
freqFactor = kB*t/h

Finally, here are a few examples of calculations of the activation energy and the pre-exponential factor from measurements of the temperature dependence of the reaction rate.
(a) Problem 3.1 in Hill, "Chemical Engineering Kinetics & Reactor Design," (Subscript[N, 2])(Subscript[O, 5]) --> (Subscript[N, 2])(Subscript[O, 4]) + 0.5  (Subscript[O, 2]),1st order reaction:

x[1] = 1/288.1;   
y[1] = 
        Log[1.04 10^-5];   
x[2] = 1/298.1;
y[2] = Log[3.38 10^-5];
x[3] = 1/313.1;
y[3] = Log[2.47 10^-4];
x[4] = 1/323.1;
y[4] = Log[7.59 10^-4];
x[5] = 1/338.1;
y[5] = Log[4.87 10^-3];
data1 = Table[{x[i], y[i]}, {i, 1, 5}]
dataPlot1 = 
        ListPlot[data1,  PlotStyle -> PointSize[0.015], 
          AxesOrigin -> Automatic];

Fit[data1, {1, x}, x]

Exp[30.0207]   
11988.8*8.314/
        1000

(b) Example 3-1 in Fogler, "Elements of Chemical Reaction Engineering," for the decomposition of benzene diazonium chloride (1st order reaction):

u[1] = 1/313 // N;   
v[1] = 
        Log[43 10^-5] // 
          N;   
u[2] = 1/319 // N;
v[2] = Log[103 10^-5] // N;
u[3] = 1/323 // N;
v[3] = Log[18 10^-4] // N;
u[4] = 1/328 // N;
v[4] = Log[35.5 10^-4] // N;
u[5] = 1/333 // N;
v[5] = Log[7.17 10^-3] // N;
data2 = Table[{u[i], v[i]}, {i, 1, 5}]
dataPlot2 = 
        ListPlot[data2,  PlotStyle -> PointSize[0.015], 
          AxesOrigin -> Automatic];

Fit[data2, {1, x}, x]

Exp[38.9246]   
14611.7*8.314/
        1000

(c) Example 4-8 in Missen et al., "Chemical Reaction Engineering and Kinetics," for the 2nd order  reaction (Subscript[C, 2]) (Subscript[H, 4])  +  (Subscript[C, 4]) (Subscript[H, 6])  ->  (Subscript[C, 6]) 
          (Subscript[H, 10])(Disc. Faraday Soc., 10, 198, 1951):

x[1] = 1/760;   
y[1] = 
        Log[0.384];   
x[2] = 1/780;
y[2] = Log[0.560];
x[3] = 1/803;
y[3] = Log[0.938];
x[4] = 1/832;
y[4] = Log[1.565];
x[5] = 1/822;
y[5] = Log[1.34];
x[6] = 1/823;
y[6] = Log[1.23];
x[7] = 1/826;
y[7] = Log[1.59];
x[8] = 1/863;
y[8] = Log[3.12];
x[9] = 1/866;
y[9] = Log[4.05];
x[10] = 1/867;
y[10] = Log[3.47];
x[11] = 1/876;
y[11] = Log[3.74];
x[12] = 1/894;
y[12] = Log[5.62];
x[13] = 1/921;
y[13] = Log[8.20];
data3 = Table[{x[i], y[i]}, {i, 1, 13}]
dataPlot3 = 
        ListPlot[data3,  PlotStyle -> PointSize[0.015], 
          AxesOrigin -> Automatic];

Fit[data3, {1, x}, x]

Exp[17.1728]   
13839*8.314/
        1000

(d) Problem 1.1 in Froment and Bischoff, "Chemical Reactor Analysis and Design," for the 1st order thermal cracking of ethane:

x[1] = 1/702;   
y[1] = Log[0.15];   
x[2] = 1/725;
y[2] = Log[0.273];
x[3] = 1/734;
y[3] = Log[0.333];
x[4] = 1/754;
y[4] = Log[0.595];
x[5] = 1/773;
y[5] = Log[0.923];
x[6] = 1/789;
y[6] = Log[1.492];
x[7] = 1/803;
y[7] = Log[2.138];
x[8] = 1/810;
y[8] = Log[2.718];
x[9] = 1/827;
y[9] = Log[4.137];
x[10] = 1/837;
y[10] = Log[4.665];
data4 = Table[{x[i], y[i]}, {i, 1, 10}]
dataPlot4 = 
        ListPlot[data4,  PlotStyle -> PointSize[0.015], 
          AxesOrigin -> Automatic];

Fit[data4, {1, x}, x]

Exp[20.0399]   
15472.5*8.314/
        1000

Note that the pre-exponential factors vary "all over the place," from 10^7 to 10^17 1/s, and some are in apparent conflict with theory. To explore this issue further would be going beyond the scope of ChE 414... So let's conclude by making the following points: (a) Theoretical analyses are applicable to elementary reactions.  (The reactions analyzed above may be a complex combination of elementary reactions.) If we want to combine experiments with theory (it is often said that one day spent in the library can save us one year spent in the lab or pilot plant), we need to talk to our friends the "kineticists", who are often chemists or even physicists. (b) For reactor design, engineers need the temperature sensitivity of the reaction rate, for which the Arrhenius expression is good enough (as long as we verify it experimentally and do not assign too much physical significance to the absolute value of the pre-exponential factor (and even of the activation energy).