Question

The specific heat of metal is $0.11{\text{ cal/g}}{{\text{ }}^\circ }{\text{C}}$ and its equivalent weight is $18.61$. Its exact atomic weight is-
A.$58.2$
B.$29.1$
C.$55.83$
D.$27.91$

Answer 1

Hint:We can use Dulong petit law which gives a relation between specific heat and approximate atomic mass. Put the given value to find approximate atomic mass which is given as-
Approximate atomic mass× specific heat=$6.4$
Then use the formula of valency which gives a relation between approximate atomic mass and equivalent weight which is given as-
$ \Rightarrow $ Valency=$\dfrac{{{\text{Approx}}{\text{. atomic mass}}}}{{{\text{Equivalent weight}}}}$
Then multiply the obtained valency with the given equivalent weight to find the exact atomic mass.

Complete step-by-step answer:Given, specific heat of a metal=$0.11{\text{ cal/g}}{{\text{ }}^\circ }{\text{C}}$
Its equivalent weight=$18.61$
We have to find its exact atomic weight.
From Dulong Petit law, we know that approximate atomic mass× specific heat=$6.4$
Then the approximate atomic mass of metal is given by-
$ \Rightarrow $ Approx. atomic mass=$\dfrac{{6.4}}{{{\text{specific heat}}}}$
On putting the given values in the above formula, we get-
$ \Rightarrow $ Approx. atomic mass=$\dfrac{{6.4}}{{{\text{0}}{\text{.11}}}}$
On solving, we get-
$ \Rightarrow $ Approx. atomic mass=$58.1$g
Now we know the formula of valency is given as-
$ \Rightarrow $ Valency=$\dfrac{{{\text{Approx}}{\text{. atomic mass}}}}{{{\text{Equivalent weight}}}}$
On putting the given values we get-
$ \Rightarrow $ Valency=$\dfrac{{{\text{58}}{\text{.1}}}}{{18.61}}$
On solving, we get-
$ \Rightarrow $ Valency=$3$
Now, we know that exact atomic mass= Equivalent mass× Valency
On putting the given values in the above formula, we get-
$ \Rightarrow $ Exact atomic mass=$3 \times 18.61$
So on multiplication of both terms, we get-
$ \Rightarrow $ Exact atomic mass=$55.83$g

The correct answer is option ‘C’.

Note:In this type of question we have to check the unit of specific heat first because if the unit of specific heat is in ${\text{J/gK}}$ then change it into ${\text{cal/g}}{{\text{ }}^\circ }{\text{C}}$ by multiplying $0.22$ in the given value.