An equation which represents the swelling equilibrium of an ionic polymer network in a binary liquid mixture is introduced and evaluated numerically. Discontinuous volume changes are obtained with pertinent values of the parameters. From two types of dependence of the degree of ionic dissociation on the composition of a liquid mixture, two types of volume transitions of an ionic gel are illustrated. One is the transition typically seen in acrylamide gels, and the other is a re-entrant transition typical of isopropylacrylamide gels. The selective dissolution factor of two liquids into a swollen polymer network also becomes discontinuous in accordance with the discontinuous volume change. Transition points and the spinodal line are calculated from a generalized form of the free energy change of the swollen gel system.