Expressions of the molar exergy and of the molar flow exergy of a pure chemical fuel are deduced rigorously from the basic principles of thermodynamics. It is shown that molar exergy and molar flow exergy coincide when the temperature T and the pressure p of the fuel are equal to the temperature T-B and the pressure p(B) of the environment; a general relation between exergy and flow exergy is proved as a consequence. The deduction of the expression of the molar exergy of a chemical fuel for non-standard values of T-B and p(B) is clarified. For hydrogen, carbon dioxide and several hydrocarbons, tables are reported to allow a simple calculation of the molar exergy of the fuel for any value of the temperature T-B and the relative humidity phi(B) of the environment, in the range 268.15 K <= T-B <= 313.15 K and 0.1 <= phi(B) <= 1, with reference to the standard atmospheric pressure. Additional tables are provided to evaluate the difference between the exergy or the flow exergy of the fuel in its given initial state and the exergy at T = T-B and p = p(B). In these tables, it is assumed that fuel and environment have the same temperature and that the fuel pressure varies in the range 1.01325 bar <= p <= 200 bar; the fuel may be gas or liquid. (C) 2009 Elsevier Ltd. All rights reserved.