The specific heat capacity of a metal is $1 J / g -^{\circ} C$ and molar mass of its oxide is 102 , then valency of metal is
(Given : $1 cal = 4.2 J)$

Question

The specific heat capacity of a metal is 1 J / g − ∘ C and molar mass of its oxide is 102 , then valency of metal is (Given : 1 cal = 4.2 J )

TestHub · Accepted Answer

According to Dulong-Petit's Law, atomic weight $\times$ specific heat capacity (in cal/g-°C) $\approx$ 6.4.

Given specific heat capacity = 1 J/g-°C = $1/4.2$ cal/g-°C.

Atomic weight $\approx 6.4/ (1/4.2) = 6.4 \times 4.2 = 26.88$ .

Let the metal be M and its valency be $x$ . The oxide formula is M₂O $_{x}$ .

Molar mass of oxide = $2 \times$ Atomic weight of M + $x \times$ Atomic weight of O

$102 = 2 \times 26.88 + x \times 16$

$102 = 53.76 + 16 x$

$16 x = 102 - 53.76 = 48.24$

$x = 48.24/16 \approx 3$ .

Thus, the valency of the metal is 3.

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