Question

The $1gram$ of a carbonate $\left( {{M_2}C{O_3}} \right)$ on treatment with excess $HCl$ produces $0.01186$ mole of $C{O_2}$ the molar mass of ${M_2}C{O_3}$ in $g mol{e^{ - 1}}$ is:
$A.$ $1186$
$B.$ $84.3$
$C.$ $118.6$
$D.$ $11.86$

Answer 1

The molar mass of carbonate $\left( {{M_2}C{O_3}} \right)$ can be calculated by finding a relation between numbers of mole, mass and molar mass. We know the number of moles of substance is equal to the given mass of substance divided by its molar mass.
Formula used
$n = \dfrac{m}{M}$
Where, $n$ is the number of moles of substance, $m$ is the given mass of substance and $M$ is the molar mass of substance.

Complete step by step solution
In the question it is given that $1gram$ of a carbonate $\left( {{M_2}C{O_3}} \right)$ on treatment with excess $HCl$ produces $0.01186$ mole of $C{O_2}$ , we have to calculate the molar mass of carbonate $\left( {{M_2}C{O_3}} \right)$ .
This is the reaction, according to the given question,
${M_2}C{O_3} + 2HCl \to 2MCl + {H_2}O + C{O_2}$
Now, from the reaction we may conclude that moles of $C{O_2}$ is equal to moles of ${M_2}C{O_3}$ that is equal to $1gram$ of ${M_2}C{O_3}$ .
i.e. $0.01186$ moles of $C{O_2}$ $= 0.01186$ moles of ${M_2}C{O_3}$ $=$ $1g$ ${M_2}C{O_3}$
Hence, we know the relation between numbers of moles, mass and molar mass.
$n = \dfrac{m}{M}$
By putting the value of the number of moles of ${M_2}C{O_3}$ and its mass, we can calculate the molar mass of ${M_2}C{O_3}$ in the above equation.
$0.01186 = \dfrac{1}{M}$
$\Rightarrow$ $M = \dfrac{1}{{0.01186}}$
$M = 84.3gmol{e^{ - 1}}$
Therefore, the molar mass of carbonate is found to be $84.3gmol{e^{ - 1}}$ . Thus, the correct option is $A.$

Additional information
Molar mass: it is the total mass of all the atoms in a molecule, it is denoted by atomic mass unit $\left( {amu} \right)$ . Its unit is $g/mole$

Note
It is to be noted that mole represent $6.022 \times {10^{23}}$ atoms, molecules or ions of a substance or the amount of substance is equal to its gram atomic mass or molecular mass and a definite number of atoms, molecules or ions of a substance.