Question

The carbonate of a metal is isomorphous (similar formula) with magnesium carbonate and contains 6.091 percent of carbon. The atomic weight of metal is
A.24
B.56
C.137
D.260

Answer 1

Here we will first assume and compare the structure of a metal carbonate which is isomorphous (similar formula) with magnesium carbonate and then we will calculate the atomic mass of the metal carbonate. After that, we can solve the problem easily.

Complete step by step solution:
Let the molecular formula of metal carbonate is $MC{O_3}$ as it is isomorphous with $MgC{O_3}$ magnesium carbonate.
Let the mass of the metal be m.
The molecular weight of carbonate ${\left( {C{O_3}} \right)^{2 - }}$

$$= 12 + \left( {3 \times 16} \right) \\\ = 12 + 48 \\\ = 60amu \\\$$

Hence, the molecular weight of metal carbonate= m+60
Now in the above question, the mass percentage of carbon in this compound =6.091%
Now by multiplying the mass percent of the carbon by the total mass of the given metal carbonate, we can find the mass of the carbon atom. Since we already know the mass of the carbon atom is12, we can find m from this equation.

$$\dfrac{{6.091}}{{100}} \times \left( {m + 60} \right) = 12 \\\ m + 60 = 12 \times 0.06091 \\\ m + 60 = 197 \\\ m = 137amu \\\$$

So the atomic weight of the metal $m$ is $137amu$.
The metal is barium whose atomic weight is 137amu and the metal carbonate is barium carbonate, $BaC{O_3}$.

Additional information:
In crystallography, crystals are described as isomorphous if they are closely similar in shape. In order to form isomorphous crystals, two substances must have the same chemical formulation. They must contain atoms which have corresponding chemical properties and the sizes of corresponding atoms should be similar. A carbonate is a salt of carbonic acid $({H_2}C{O_3})$ is characterized by the presence of the carbonate ion, a polyatomic ion with the formula of $C{O_3}^{2 - }$.
Metal carbonates such as calcium carbonate chalk react with acids to produce the gas carbon dioxide.

The correct answer is option C.

Note: In the question, remembering the atomic weight of every Atom in the periodic table is very important. Without this, we cannot solve this question easily using the periodic table of the element to find atomic weights, we can find that hydrogen has an atomic weight of 1 and oxygen is 16.