Dear Sir. Concerning your issue about how to purify impure Alumina by an inexpensive method. Alumina can be purified by using activated carbon for 1.5 hr by stirring at 200 rpm at 82 oC . The purified AIP was obtained by the filtration and vacuum distillation at 10 mmHg and at ~ 140 oC. By using chelate reagent, the content of impurity element in a sample can be conveniently and highly accurately determined spectrophotometrically without being affected by any interfering substances. The activated carbon’s enormous capacity to absorb and retain significant quantities of many organic compounds has led to its use as a purifying medium. An anion is adsorbed onto the activated carbon, and the metal ion interacts with the anion, effectively being absorbed by an absorbate. Observation of the metal ion adsorption, displayed that complex organic agents and pre-absorbed anions can affect the amount of adsorption. I think the following below link and the attached file may help you in your analysis:

http://jcpr.kbs-lab.co.kr/file/JCPR_vol.15_2014/JCPR15-6/_272013-095_514-518.pdf

http://cn.agilent.com/cs/library/selectionguide/public/5990-8620EN_LO.pdf

Thanks

Thank you very much dear Dr. Isam Eldin Hussein Elgailani for your helpful information.

Thanks a lot dear Dr. Michael Päch. may you provide me the concentration of HCl and duration of ignition?

oh...  It was just a courteous statement for Islam's consideration and his time for my question (this is a part of our culture for finishing a conversation.)

Wash several times with distilled water that has been degassed, then filter and dry in hot vacuum oven. Na2O makes 2NaOH in water and washes away, while alumina does not.  

Use a strong acid cation resin in the H+ form. The sodium will load onto the resin. Try various ratios and contact times.

I may recommend multiple batch soaking in dilute acid such as acetic acid for long time. Then, rinse with water to pH 5.5-6 and dry at 120 then 800 degree celsius.