Even though both compounds do not contain H+ and OH- ions, Arrhenius concept in these cases can be applied from the point that adding Na2CO3 to water increases the concentration of OH- ions, and AlCl3 increases the concentration of H+.
For Na2CO3:
CO32- + H2O <-> HCO3- + OH- => the solution is basic.
AlCl3 partially hydrolyzes forming HCl:
AlCl3 + 3H2O <-> Al(OH)3 + 3HCl.
HCl as a strong acid, in its turn, dissociates forming H+ ions:
HCl --> H+ + Cl- => the solution is acidic.
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