A crystalline salt when heated becomes anhydrous and losses 51.2%

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#1

A crystalline salt when heated becomes anhydrous and losses 51.2% of its weight. The anhydrous salt on analysis gave the percentage composition as Mg= 20.0%, S= 26.66% and 0=53.33%.


#2

The empirical formula of the anhydrous salt comes out to be $MgSO_{4}$. Empirical formula mass = 120.
Molecular mass = 120.
Hence, molecular formula = $MgSO_{4}$.
As crystalline salt on becoming anhydrous loses 51.2% by mass, this means 48.8 g of anhydrous salt contains $H _{ 2 }O$ = 51.2 g. Therefore, 120 g of anhydrous salt contains
51.2 / 48.8 x 120 g = 126 g = 126/18 molecules = 7 $H _{ 2 }O$ molecules

Hence, molecular formula of crystalline salt = $MgSO_{4}$ • 7$H _{ 2 }O$