In this paper we focus on the thermodynamical properties of the S = 1/2 Heisenberg chain with alternating antiferromagnetic and ferromagnetic exchange interactions, J(1) and J(2) In the first step, the magnetic and specific heat properties of this system have been calculated as function of alpha = J(2)/J(1) from a general numerical procedure based on closed spin chains of increasing length. A distinctive behavior characterized by a maximum in the chi T vs T plot is predicted when the ferromagnetic interaction is the dominant one (i.e., for alpha > 1). Conversely, antiferromagnetic-like behaviors are predicted when the antiferromagnetic interaction dominates (i.e., for alpha < 1). With respect to the magnetic specific heat, two rounded maxima can be distinguished in the C-p/R vs T plot for sufficiently different exchange values and dominant ferromagnetic exchange, which have been associated with the two kinds of exchange interactions. The magnetic susceptibility results derived from the model have been conveniently fitted to rational unified expressions. These expressions were used to describe the magnetic behaviors of two copper(II) complexes exhibiting alternating chain structures : The compound Cu(TIM)CuCl4 (TIM = 2,3,9,10-tetramethylcyclo-1,4,8,11-tetraazatetradecane-1,3,8,10-tetraene), which shows dominant ferromagnetic exchange (J(1)/k = -7.5 K; alpha = 3), and the compound [Cu(bpym)(OH)(2)(NO3)(2)].2H(2)O (bpym = 2,2’ bipyrimidine), which exhibits dominant antiferromagnetic exchange (J(1)/k = -200 K; alpha = 0.75).