On dissolving 2.0 g of a metal in sulphuric acid, 4.51 grams of the metal sulphate was formed. The specific heat of the metal is 0.057 cal/g. What is the valency of the metal and its exact atomic weight?

Explanation

Let the formula of the metal sulphate be `M_(2)(SO_(4))_(x)` ( x being the valency of the metal M)
`:. X xx` moles of M = `2xx ` moles of `SO_(4)^(-2)`
or `x xx "(wt.of M")/("atomic weight of M ") = 2 xx ("wt. of sulphate ion ")/(" ionic wt. of "SO_(4)^(2-))`
`x xx (2)/(112) = 2 xx((4.51-2))/(96)`
`x= 2.85 =3`
{ at wt. of M = `(6.4)/(0.057) =112 ` (approx).}
The valency is, therefore, 3.
Now, substitute the valency of x as 3 in eqn. (1) again to calculate the accurate value of the atomic weight of the metal.