Answer:
Arranged from the most efficient to the least efficient;
- Flame test
- AgNO3 precipitation test
- pH test
Explanation:
The pH test is the most efficient as it can identify 4 out of the 5 unknown solutions.
Starting with the Aluminium compound; Aluminium ion gives a silvery white colour in very high temperatures.
The Barium ion in Ba(NO3)2 gives a pale green/Apple green colour with flame test.
The Potasium ion in K2C2O4 gives Lilac colour with flame test.
And Sodium ion gives an intense yellow colour, usually invisible through Cobalt blue glass.
Only HCl would be left using flame test and that identifies HCl that way.
AgNO3 precipitation test would identify 3 out of the 5 unknown solutions as most Silver salts are usually insoluble, with different colours. Only AgNO3 and Ag(C2H3O2) are the soluble silver salts.
AgNO3 forms AgCl which is white and insoluble with HCl, forms yellowish, sometimes, grayish precipitate with Na2CO3 and Ag2C2O4 with K2C2O4, which is an insoluble white salt too, but it decomposes into Silver metal and CO2 with a little perturbation.
That's 3 unknown solutions, identified by the AgNO3 precipitation test.
The pH test can only outrightly identify HCl as having a pH less than 7.
It will also identify Na2CO3 because in solution, it is a basic solution. It might not be able to identify the rest of the unknown solutions.
Therefore, it is evident which tests are the most efficient to the least efficient.
Hope this Helps!!!