How do describe the process to prepare disodium phosphate given a solution of phosphoric a id, 0.500 molar and a solution of sodium hydroxide base, 0.500 molar?

1. H3PO4(aq) + 2NaOH(aq) = 2Na+ + PO4- - - + H+ + 2H2O(l) balanced reaction
2. Add one part phosphoric acid 0.500M to two parts sodium hydroxide 0.500M with stirring and cooling, if possible. This will be an exothermic reaction.
3. A solution of acidified NaHPO4 is attained.

Phosphoric acid reacts with NaOH in stages :

H3PO4 + NaOH → NaH2PO4 + H2O The product is monosodium phosphate

H3PO4 + 2 NaOH → Na2HPO4 + 2H2O - The product is disodium phosphate which is what you want

Therefore you have to react 1 molar quantity of H3PO4 with 2 molar quantity of NaOH

Because your two solutions have identical molarity :

Measure out a convenient volume of the 0.500 M H3PO4 solution - say 100 mL

Measure out exactly double this volume of 0.500 NaOH solution - in this case 200 mL

Slowly add the NaOH solutiion to the H3PO4 solution . The reaction is exothermic so work slowly and allow to cool before adding further NaOH solution

When all the NaOH has been added, you will have a solution of Na2HPO4.