Question

I did a back titration with an unknown carbonate and using the average % carbonate (by mass) which I found to be 27.40% and appropriate calculation decided where the unknown is an alkali metal carbonate or an alkaline earth metal carbonate. I have no idea how to tell the difference between to two using the percentage.

Answer 1

I think it would be Mg but I am still unsure as to what calculations to use

Answer 2

I'm not sure from your description exactly what you've done; however, one way you can check it is to calculate % carbonate in the few alkali and alkaline earth metal carbonates.
Li2CO3 - = (60/73.9)*100 = 81.2
Na2CO3= (60/106)* 100 = 56.6
K2CO3 = (60/138.3)*100 = 43.4%
MgCO3 is (60/84.3)*100 = 71.1
CaCO3 = (60/100)^100 = 60%
You aren't likely to have Rb2CO3 or Cs2CO3 but Rb2CO3 is (60/230.9)*100 = 26%
MgCO3 isn't soluble in water. Was your sample soluble in water? How much confidence to you have in the 27.4.

Answer 3

It was in HCl, the 27.4% was obtained through the lab