Question

The specific heat of a bivalent metal is 0.16. The approximate equivalent mass of the metal will be:
A.$40$
B.$20$
C.$80$
D.$10$

Answer 1

Hint: Equivalent mass of a metal is calculated by dividing its atomic mass by its valence. Atomic mass can be found out from specific heat using Dulong-Petit law.

Complete step by step answer:
Dulong-Petit law states that atoms of all elements have the same heat capacity. Therefore, the specific heat will be inversely proportional to the atomic mass of elements. Hence, the product of atomic mass and specific heat of an element in solid state will be constant, and its value is approximately equal to $6.4$.
i.e. atomic mass $ \times $ specific heat = $6.4$
We can find out the atomic mass of the element using the above equation.
Hence,
Atomic mass = $\dfrac{{6.4}}{\text{specific heat}}$
Given that, specific heat is equal to$0.16$. Let us substitute this value to the above equation.
Atomic mass = $\dfrac{{6.4}}{{0.16}} = 40$
i.e. the atomic mass of the element is $40$.
Given that the metal is bivalent. Therefore, its valency is $2$. We can find out the equivalent mass by dividing the atomic mass by $2$.
Equivalent mass = $\dfrac{\text{atomic mass}}{2}$
Equivalent mass = $\dfrac{{40}}{2} = 20$
Hence the approximate equivalent mass of the metal is $20$.
Additional information-
Dulong-Petit law can be applied to only elements which are in solid state. It cannot be applied to lighter elements having high boiling point. These are the limitations of the law. The product of atomic mass and specific heat of an element in solid state is called atomic heat of element.

Note:
Dulong-Petit law gives only the approximate atomic mass. Hence we can calculate only the approximate equivalent mass using this law.