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

Explanation

Step I. Calculation of empirical formula:

The simplest atomic ratio of K : Al: S : O is 1: 1: 2 : 8. The empirical formula of the anhydrous salt is : `KAlS_(2)O_(2)`.
Step II. To calculate the empirical formula mass of anhydrous salt Empirical formula mass of anhydrous salt = 39 + 27 + 64 + 128 = 258.
Step III: To calculate the amount of water associated with 258 parts by weight of compound
Let the weight of hydrated salt be 100 g
The weight of water lost = 45.6 g The weight of anhydrous salt = 100 - 45.6 g = 54.4 g
If the weight of anhydrous salt is 54.4 gm, the weight of water in the crystalline salt = 45.6 gm.
If the weight of anhydrous salt in 258 gm, the weight of water in the crystalline salt = `=(45.6)/(54.4) xx 258 =216.2`g
54.4
Step IV. 7b calculate the number of molecules of water of crystallisation
It is clear from the above calculations that 216.2 parts by weight of water are present in combination with 258 parts be weight of the salt.
The number of molecules of water of crystallisation corresponding to 216.2 parts by weight of water
`=(216.2)/18 = 12`
`therefore` The simplest formula of crystalline salt is `KAlS_(2)O_(3).12H_(2)O`.