# On dissolving 2.0g of metal in sulphuric acid 4.51g of the metal sulphate was formed.The specific heat of the metal is 0.057cal/g.What is the exact atomic mass of the metal?

$(a)\;120.72\qquad(b)\;114.72\qquad(c)\;112\qquad(d)\;121.02$

Step 1:
Equivalent mass of $SO_4^{2-}$ radical $=\large\frac{Ionic\;mass}{Valency}$
$\qquad\qquad\qquad\qquad\qquad\quad\;\;=\large\frac{96}{2}$
$\qquad\qquad\qquad\qquad\qquad\quad\;\;=48$
Mass of metal sulphate=4.51g
Mass of metal=2.0g
Mass of sulphate metal =4.51-2.0=2.51g
2.51g of sulphate combine with 2.0g of metal
So,48g of sulphate will combine with =$\large\frac{2}{2.51}$$\times 48$
$\Rightarrow 38.24g$ metal
Equivalent mass of metal=38.24
Step 2:
According to Dulong and Petit's law
Approximate atomic mass=$\large\frac{6.4}{specific\;heat}$
$\qquad\qquad\qquad\qquad\quad=\large\frac{6.4}{0.057}$
$\qquad\qquad\qquad\qquad\quad=112.5$
Valency =$\large\frac{(Approx)atomic\; mass}{Equivalent\;mass}$
$\qquad\;\;\;=\large\frac{112.5}{38.24}$
$\qquad\;\;\;=2.9$
$\qquad\;\;\;=3$(approx)
Step 3:
$\therefore$ Exact atomic mass=$38.24\times 3$
$\Rightarrow 114.72$
Hence (b) is the correct answer.

edited Jan 15