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The crystalized mixed salts from the zero liquid discharge process are a hazardous threat to the environment. In this study, we developed a novel electrodialysis (SBMED) method by assembling the monovalent selective anion-exchange membrane (MSAEM) into the bipolar membrane electrodialysis (BMED) stack. By taking the advantages of water splitting in the bipolar membrane and high perm-selectivity of MSAEM for the Cl− ions against the SO42− ions, this combination allows the concurrent separation of Cl−/SO42− and conversion of mixed salts into relatively high-purity monoprotic and diprotic acids. The current density has a significant impact on the acid purity. Both the monoprotic and diprotic acid purities were higher than 80% at a low current density of 10 mA/cm2. The purities of the monoprotic acids decreased with an increase in the current density, indicating that the perm-selectivity of MSAEM decreases with increasing current density. An increase in the ratio of monovalent to divalent anions in the feed was beneficial to increase the purity of monoprotic acids. High-purity monoprotic acids in the range of 93.9–96.1% were obtained using this novel SBMED stack for treating simulated seawater. Therefore, it is feasible for SBMED to valorize the mixed salts into relatively high-purity monoprotic and diprotic acids in one step.