The reactivity of chemically isolated lignocellulosic blocks, namely, alpha-cellulose, holocellulose, and lignin, has been rationalized on the basis of the dependence of the effective activation energy (E-alpha) upon conversion (alpha) determined via the popular isoconversional kinetic analysis, Friedman's method. First of all, a detailed procedure for the thermogravimetric data preparation, kinetic calculation, and uncertainty estimation was implemented. Resulting Ea dependencies obtained for the slow pyrolysis of the extractive-free Eucalyptus grandis isolated alpha-cellulose and holocellulose remained constant for 0.05 < alpha < 0.80 and equal to 173 +/- 10, 208 +/- 11, and 197 +/- 118 kJ/mol, thus confirming the single-step nature of pyrolysis. On the other hand, large and significant variations in Ea with a from 174 +/- 10 to 322 +/- 11 kJ/mol in the region of 0.05 and 0.79 were obtained for the Klason lignin and reported for the first time. The non-monotonic nature of weight loss at low and high conversions had a direct consequence on the confidence levels of Ea. The new experimental and calculation guidelines applied led to more accurate estimates of Ea values than those reported earlier. The increasing E-alpha dependency trend confirms that lignin is converted into a thermally more stable carbonaceous material.