`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 1. To calculate the empirical formula of the anhydrous salt

Thus, the empirical formula of the anhydrous salt is K Al `S_(2)O_(8)`
Step 2. To calcualte the empirical formula mass of the anhydrous salt.
Empirical formula mass of the anhydrous salt `(KAlS_(2)O_(8))=1xx39.0+1xx27.0+2xx32.0+8xx16.0`
`=258.0u.`
Step 3. To calculate the empirical formula mass of the hydrated salt.
Let the empirical formula mass of the hydrated salt = 100.0 u.
Loss of weight due to dehydration = `45.6%`
`therefore` Empirical formula mass of the anhydrous salt `=100-45.6=54.5u.`
Now, if the empirical formula mass of the anhydrous salt is 54.4, then that of hydrated salt = 100
`therefore `If the empirical formula mass of the anhydrous salt is 258,, that of hydrated salt `=(100)/(54.4)xx258=474.3u.`
Step 4. To calculate the number of molecules of water in the hydrate salt.
Total loss in mass due to dehydration =`474.3-258.0=216.3u`
Loss in mass due to one molecule of water = 18.0 u
`therefore" No. of molecules of water in the hydrated sample"=(216.3)/(18)=12`
Step 5. To calcualte the empirical formula of the hydrated salt.
Empirical formula of the anhydrous salt `=KAlS_(2)O_(8)`
No. of molecules of water of crystallization = 12
`"Empirical formula of the anhydrated salt "=KAlS_(2)O_(8).12H_(2)O`