On dissolving 2.0 g of metal in sulphuric acid ,4.51 g of the metal sulphate was formed . The specific heat of the metal is 0.057 cal `g^(-1).^(@)C^(-1)`. What is the valency of metal ?

Explanation

Equivalent mass of `SO_(4)^(2-)` radical `= ("Ionic mass")/( "Valency")= ( 96)/( 2) = 48`
Mass of metal sulphate = 4.51 g
Mass of metal = 2.0 g
Mass of sulphate radical `= ( 4.51 - 2.0 ) = 2.51 g `
2.51 g of sulphate combine with 2.0g of metal.
So , 48g of sulphate will combine with `= ( 2 )/( 2.51) xx 48 = 38.24 g ` metal
Equivalent mass of metal `= 38.24`
According to Dulong and Petit's law,
Approximate atomic mass `= ( 6.4)/( "Specific heat") =( 6.4) /(0.057) = 112.5`
Valency `= ( "Approximate atomic mass")/( "Equivalent mass")`
` ( 112.5)/( 38.24) = 2.9 ~~3`
Exact atomic mass `= 38.24 xx 3 = 114.72`