To distinguish sodium carbonate and sodium hydrogencarbonate, we cannot add water as both of them dissolve. We will heat the solid and the one remains stable is sodium carbonate while the one decompose on heating to release a colourless gas which can turn lime water milky is sodium hydrogencarbonate.
2NaHCO3(s) --> Na2CO3 +H2O + CO2
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To distinguish sulphate and sulphite solution, we can add acidified barium nitrate solution. The one which forms white precipitate is sodium sulphate while the solution which does not show observable change is sodium sulphite.
*barium sulphite is insoluble in water but redissolve in dilute nitric acid.
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To test for the presence of silver ions, add excess ammonia solution to see whether colourless solution form.
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