`A` crystalline hydrated salt on being rendered anhydrous, loses `45.6%` of its weight. The percentage composition of anhydrous salt is `:Al=10.5%, K=15.1%, S=24.8%` and `O=49.6%`. Find the empirical formula of the anhydrous and crystalline salt :

Answer

`KAIS_(2)O_(8),KAIS_(2)O_(8).12H_(2)O`

Explanation

Empirical formula
`KAlS_(2)O_(8){{:(Al,K,S,O,"Elements",),(10.5,15.1,24.8,49.6,"Mass percentage",),(0.388,0.387,0.775,3.1,"Mole ratio",),(1,1,2,8,"Simple ratio",):}`
Empirical formula weight `= 258`
From weight loss information `:54.4 g` anhydrous
salt `-= 45.6 g H_(2)O`
` implies 258g` anhydrous salt `-=216.26 g = 12` mol `H_(2)O`
implies Empirical formula of hydrated salt `=KAlS_(2)O_(8).12H_(2)O`