Natural mineral carbonation can be accelerated using acid and alkali solutions to enhance atmospheric CO2 sequestration, but the production of these solutions needs to be carbon-neutral. A microbial reverse-electrodialysis electrolysis and chemical-production cell (MRECC) was developed to produce these solutions and H2 gas using only renewable energy sources (organic matter and salinity gradient). Using acetate (0.82 g/L) as a fuel for microorganisms to generate electricity in the anode chamber (liquid volume of 28 mL), 0.45 mmol of acid and 1.09 mmol of alkali were produced at production efficiencies of 35% and 86%, respectively, along with 10 mL of H2 gas. Serpentine dissolution was enhanced 17-87-fold using the acid solution, with approximately 9 mL of CO2 absorbed and 4 mg of CO2 fixed as magnesium or calcium carbonates. The operational costs, based on mineral digging and grinding, and water pumping, were estimated to be only $\$$25/metric ton of CO2 fixed as insoluble carbonates. Considering the additional economic benefits of H2 generation and possible wastewater treatment, this method may be a cost-effective and environmentally friendly method for CO2 sequestration.