Dear Ahmed S. Aadli many thanks for asking this interesting technical question on RG. It is not quite clear to me what you mean by "reversible reaction", but the amphoteric behavior of Al(OH)3 is basic knowledge in aluminum chemistry. It also forms the foundation of industrial aluminum manufacture. It just means that Al(OH)3 is soluble in both acids and bases. White Al(OH)3 precipitates when you add e.g. alkali metal hydroxides (NaOH, KOH) to aluminum salts in water. Upon addition of excess hydroxide the precipitate redissolves again, and a clear, colorless solution is obtained which contains the tetrahydroxo complexes M[Al(OH)4] (M = Na, K). This is indeed a reversible reaction. When you add one equivalent of acid (HCl, HNO3) to the solution of the tetrahydroxo complexes, Al(OH)3 will precipitate again. This can be repeated many times.
Good luck with your work and best wishes, Frank Edelmann
Thank you dear @Frank T. Edelmann for your illustration. I mean during digestion of bauxite in Bayer process and formation of sodium aluminate then converted to aluminium hydroxide with the presence of excess of sodium hydroxide, the reaction between sodium hydroxide and aluminium hydroxide occurs to give sodium aluminate again?
Dear Ahmed S. Aadli thank you for your kind response and question. Yes, what is commonly called sodium aluminate is in solution primarily sodium tetrahydroxoaluminate, Na[Al(OH)4]. Thus the reaction between sodium hydroxide and aluminium hydroxide occurs readily and gives sodium aluminate again. In this context you might also want to watch the following instructive YouTube video:
Preparation of Sodium aluminate
https://www.youtube.com/watch?v=kOORqbP0s1w
Please stay safe and healthy! With best wishes, Frank Edelmann
Dear Ahmed S. Aadli attached please find a good overview of the Bayer process. Please note that when talking about "sodium aluminate" it is often not clearly distinguished between the compounds NaAlO2 and Na[Al(OH)4]. The latter is mostly present in solution and in the presence of excess NaOH. When you compare the two formulas you will see that the difference is just two H2O molecules.
Dear Ahmed S. Aadli many thanks for your kind response and explanation. This is actually a question that goes beyond my fields of expertise. Here you should consult handbooks about the Bayer process or specialized research articles. For a potentially useful paper in which this question has been addressed please have a look at the following study:
Carbonation of Sodium Aluminate/Sodium Carbonate Solutions for Precipitation of Alumina Hydrates—Avoiding Dawsonite Formation
The article has been published Open Access and you can freely download it as pdf file (please see attached pdf file).