This is an exercise that helps to develop a "feel" for the reaction order. 
A-> products
Rate = k*(cA^n)
The key concept is that, everything else being equal, the reactant concentration decreases with time more SLOWLY as the reaction order INCREASES. Let's show this for the simplest case first, and let's plot simply cA/cA0 vs. time. We shall then plot the same function vs. the more appropriate dimensionless time. Note in Table 5.1 that the dimensionless time arises naturally in the reactor performance equations.

Clear[k, cA0, k1, k2, k3, kminus1, k0, 
      khalf]
cA0 = 1;
k = 1;
cAoverCA0minus1 = (1 - 
            2  k*time/
                cA0^2)^0.5   
cAoverCA0zeroth = 
      1 - k*time/cA0   
cAoverCA0half = (1 - 0.5  k*time/(cA0^0.5))^2  
cAoverCA01st = Exp[-k*time]  
cAoverCA02nd = 
      1/(1 + cA0*k*time)   
cAoverCA03rd = (1/(1 + 2  k*time*cA0^2))^0.5  
Plot[{cAoverCA0minus1, cAoverCA0zeroth, cAoverCA0half, cAoverCA01st, 
          cAoverCA02nd, cAoverCA03rd}, {time, 0, 0.5}, 
        PlotStyle -> {Thickness[0.002], Thickness[0.004], 
            Thickness[0.006], Thickness[0.008], Thickness[0.010], 
            Thickness[0.012]}, GridLines -> Automatic];

As the next step, let's replace t (time) with an expression (for time) that includes dimTime, the dimensionless time derived upon solving the corresponding rate equations (see column 3 of the handout). Let's also allow the possibility that the rate constants can have different values.

Clear[cA0, k, k1, k2, k3, k0, kminus1, khalf];

cAoverCA01st = 
      Exp[-k1*(dimTime/k1)]  
cAoverCA0zero = 
      1 - k0*(dimTime*cA0/k0)/
            cA0  
cAoverCA02nd = 
      1/(1 + cA0*k2*(dimTime/(cA0*k2)))   
cAoverCA0minus1 = (1 - 
            2  kminus1*(dimTime*cA0^2/kminus1)/
                cA0^2)^0.5  
cAoverCA03rd = (1/(1 + 
                2  k3*(dimTime/cA0^2/k3)*cA0^2))^0.5  
cAoverCA03half = (1 - 
            0.5  khalf*(dimTime/cA0^-0.5/
                    khalf)/(cA0^0.5))^2  
Plot[{cAoverCA0minus1, cAoverCA0zero, cAoverCA03half, cAoverCA01st, 
          cAoverCA02nd, cAoverCA03rd}, {dimTime, 0,  .5}, 
        PlotStyle -> {Thickness[0.002], Thickness[0.004], 
            Thickness[0.006], Thickness[0.008], Thickness[0.010], 
            Thickness[0.012]},  GridLines -> Automatic];

Note that we get the same plot as before, except that now the rate expressions are given in terms of dimensionless time, defined as (cA0^(n-1))(kt), and the abscissa is dimTime as well.

Let's now perform a parametric sensitivity analysis for the two most common cases of great practical significance: (a) 1st order vs. 2nd order; and (b) n=0 vs. n=1. Thus, for example, we saw in M-M kinetics that the reaction order is n=1 at low reactant concentrations and n=0 at high reactant concentrations.

Clear[cA0, k, k1, k2, k3, k0, kminus1, 
        khalf];
cA0 = 
      1.0;   
k1 = 
      1;
k2 = 1;   
cAoverCA01st = Exp[-k1*time];  
cAoverCA02nd = 1/(1 + cA0*k2*time);   
Plot[{cAoverCA01st, cAoverCA02nd}, {time, 0, 3}, 
        PlotStyle -> {Thickness[0.002], 
            Thickness[0.008]}];

Clear[cA0, k, k1, k2, k3, k0, kminus1, 
        khalf];
cA0 = 1;
k1 = 0.1;
k0 = 0.1;
cAoverCA01st = Exp[-k1*time];  
cAoverCA0zeroth = 1 - k0*time/cA0;  
Plot[{cAoverCA01st, cAoverCA0zeroth}, {time, 0, 10}, 
        PlotStyle -> {Thickness[0.002], Thickness[0.008]}, 
        GridLines -> Automatic];