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: PA(1). B-1-M+ --> PA(2).B2M+ + (B-1 --> B-2)M+. Here PA(1) and PA(2) are two different states or structural forms of a polyanion, B-1 and B-2 are the number of M+ ions thermodynamically bound to the polyanions PA(1) and PA(2), 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, D-2(M1)M2/D-1(M1)M2. 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.