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

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.

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