Question

A new element $E$ forms a compound with chlorine which contains $1.455g$ of $Cl$ per $g$ of $E$. The specific heat of E was found to be $0.05cal/g$. If eq. weight of element is $24$, then the value of $x$ in $EC{l_x}$ is:

Answer 1

Hint:First we can find the atomic mass of the element from its specific heat, using the Dulong-Petit Law. We are given the proportion of chlorine present per gram of the element in the compound. From our knowledge of the atomic mass of chlorine, we can find the number of atoms present in the compound.
Formulas used:Atomic mass $ \times $ specific heat in $cal$ $ = 6.4$

Complete answer:
We can use the Dulong-Petit Law to find the atomic mass of the element, which states that the product of an element’s atomic mass and its specific heat is approximately equal to $6.4$. Hence, we have:
Atomic mass $ \times $ specific heat in $cal$ $ = 6.4$
Specific heat is given as $0.05cal/g$. Substituting this, we get:
Atomic mass $ = \dfrac{{6.4}}{{0.05}} = 128g$
It is given that the compound contains $1.455g$ of $Cl$ per $g$ of $E$. Therefore, to find the amount of chlorine present in the compound, we just have to multiply the atomic mass of the element with the amount of chlorine present per gram of the element, which is $1.455g$.
Hence, total mass of chlorine present in the compound $ = 1.455 \times 128 = 186.24g$
We know that the molar mass of chlorine is $35.5g/mol$. Hence, to find the number of atoms of chlorine in this compound ($x$), we divide the total mass of chlorine in the compound with the molar mass of one chlorine atom.
Therefore, the number of atoms present $ = \dfrac{{186.24}}{{35.5}} = 5.24$
As we have used an approximation law, we round off the answer to the nearest integer to get the actual number of atoms of chlorine.
Hence, the number of atoms of chlorine in the compound, $x = 5$.

Note:
The Dulong-Petit Law was formed as an approximation law based on experiments conducted by both these scientists. It is an empirical law and does not have any proof. However, the justification for this law came many years later from the kinetic theory of gases, which said that the product of specific heat and molar mass of most solid elements is a constant at a given temperature, and is equal to the $3R$, where $R$ is the universal gas constant. Note that the equivalent weight given in the question is for the case if we don’t know the atomic mass of chlorine (equivalent weight multiplied by the value $1.455g$ would also give us the atomic mass of chlorine).