A general thermodynamic analysis is presented, describing how counterion species of different nature, but the same valency, influence polyelectrolyte transformations and reactions of the general form: PA1.B1-M(+)-->PA2.B2M+ + (B1 - B2)M+. Here PA1 and PA2 are two different states or structural forms of a polyanion, B1 and B2 are the number of M+ ions thermodynamically bound to the polyanions PA1 and PA2, respectively. The specific effects of the two counterions, M1+ and M2+, on this equilibrium can be simply related to the quotient of their selectivity constants, D2M2M1/D1M2M1, for the polyion states 1 and 2. We analyze how different monovalent counterions (particularly, sodium and potassium) affect polyelectrolyte reactions and transformations such as, e.g., the DNA helix-coil transition. Previous experimental results on the competition between DNA and the synthetic polyanion, poly(methacrylic acid), for binding to the synthetic polycation, poly(N-ethylvinylpyridinium), has been investigated with respect to sodium and potassium ion specificity, using our model. We also discuss the DNA-histone disassembly/assembly reaction modeled as a competition of two polyanions for binding to a polycation.