Question

The carbonate of a metal is isomorphous with $\text{MgC}{{\text{O}}_{3}}$ and contains \[6\cdot 091%\] of carbon. Atomic weight of the metal is nearly:
(A) 48
(B) $68\cdot 5$
(C) 137
(D) 120

Answer 1

Hint: Isomorphous substances are those substances which usually have similar chemical formulas and the polarizability and ratio of anion and cation radii are also generally comparable. Atomic weight of a metal can be defined as the total weight of the atom.

Complete Step by step solution:
The atomic weight is calculated by adding the mass of each isotope multiplied by its fractional abundance.
Atomic weight = Mass$\times $Fractional abundance
$\text{Mass Percentage = }\dfrac{\text{Component Mass}}{\text{Total mass}}\times 100%$
Given that, the metal is isomorphous with $\text{MgC}{{\text{O}}_{3}}$ therefore the molecular formula of metal carbonate is$\text{MC}{{\text{O}}_{3}}$.
Let the mass of metal be $\text{M}$.
Now, the molecular weight of the metal carbonate$=\left( \text{M}+12+48 \right)$
Given, the mass percentage of carbon in the metal carbonate $\text{= 6}\cdot \text{091 }\!\!%\!\!\text{ }$
Now,
$\text{Mass percentage of carbon }\times \text{ Mass percentage of MC}{{\text{O}}_{3}}=\text{ Atomic weight of carbon}$
The atomic weight or mass of carbon is $12\text{ a}\text{.m}\text{.u}$
Thus,
$\begin{align}
& \Rightarrow \dfrac{6.091}{100}\times \left( \text{M + 12 + 48} \right)=12 \\
& \Rightarrow \text{M = }\dfrac{12\times 100}{6.091}-60 \\
& \Rightarrow \text{M = 137 a}\text{.m}\text{.u}\text{.} \\
\end{align}$
Atomic weight of the element $137\cdot 01$a.m.u
, which is Barium and the mental carbonate is $\text{BaC}{{\text{O}}_{3}}$.

Hence, the option-C is the right answer.

Additional Information:
Atomic weight: Atomic weight also known as atomic mass can be defined as the number of protons and neutrons present in an atom. In addition to this, each proton and neutron has a mass of approximately 1 a.m.u . The electrons within an atom are so minute as compared to the neutrons and protons that their mass is negligible.

Note: The isomorphous substances have the same shape, structure, and polarizability. The isomorphous substances are almost identical in every way. The conceptual knowledge about various concepts such as atomic mass, mass percentage, isomorphous substances and its characteristics is required by the student.