Question

A metal M (specific heat 0.16) forms a metal chloride with \[\approx \] 65% chlorine present in it. The formula of the metal chloride will be
(A) $MCl$
(B) $MC{{l}_{2}}$
(C) $MC{{l}_{3}}$
(D) $MC{{l}_{4}}$

Answer 1

Hint: According to Dulong-Petit law which is a thermodynamic law, the law states the classical expression for the molar specific heat capacity of certain chemical elements. The formula for calculating the approximate mass of the metal using Dulog-Petit law is-
The approximate atomic mass of the metal \[=\dfrac{6.4}{\text{specific heat}}\]

Complete step by step solution:
-In 1819, two French physicists named Pierre Louis Dulong and Alexis Therese Petit proposed Dulong-Petit law which stated that the gram-atomic heat capacity (specific heat times atomic weight) of an element is constant; that is, it is the same for all solid elements.
-Dulong Petit law says that if the specific heat of an element is measured, then the atomic weight of the element can be calculated using the empirical law.
-Specific heat is the amount of heat required to raise the temperature of one mole of an element from 287.5 K to 288.5 K. The SI unit of specific heat is J/mol/K.
-Atomic heat of the element is the product of atomic mass and specific heat of the element.
-Dulong-Petit law in simple words said that the product of specific heat and the atomic mass of an element is the solid-state is approximately equal to 6.4 or we can say that the atomic heat of a solid element is nearly equal to 6.4.
-Let the formula of the metal chloride be $MC{{l}_{x}}$.
According to Dulong –Petite law,
The approximate atomic mass of the metal $=\dfrac{6.4}{\text{specific heat}}$
According to the question, the specific heat of metal is 0.16.
Therefore, the approximate atomic mass of the metal $=\dfrac{6.4}{0.16}=40$
-Let us consider the weight of metal chloride to be 100g.
 % of chlorine present is $\approx $ 65% that is 65 g of chlorine is present.
Therefore the % of metal present = 100 – 65 = 35% , that is 35 g
% of metal present in the salt $=\dfrac{x\times 35.5}{40+x\times 35.5}\times 100$
$\therefore 65=\dfrac{x\times 3550}{40+35.5x}\Rightarrow x=2.09255\approx 2$
So, $MC{{l}_{x}}=MC{{l}_{2}}$

Therefore, the correct answer is option B.

Note: Dulong-Petit law has some limitations too. This law applies to only those elements which are in solid-state. Dulong-Petit law is only applicable to the heavier elements and does not apply to lighter elements having a high melting point. This law gives the approximate value of atomic mass which sometimes deviates from the real values.