Question

A certain metal $M$ forms an insoluble oxalate complex ${M_4}{O_3}{({C_2}{O_4})_3}.12{H_2}O$. If $3.2g$ of the complex is formed from $1g$ of oxalic acid, what is the atomic mass of $M?$

Answer 1

The molar mass is the mass of a given chemical element or chemical compound divided by the amount of substance. The molar mass of a compound can be calculated by adding the standard atomic masses of the constituent atoms. Molar mass serves as a bridge between the mass of a material and the number of moles since it is not possible to measure the number of moles directly.

Complete answer:
The characteristic molar mass of an element is simply the atomic mass in $\dfrac{g}{{mol}}$. However, molar mass can also be calculated by multiplying the atomic mass in $amu$ by the molar mass constant. To calculate the molar mass of a compound with multiple atoms, sum all the atomic mass of the constituent atoms.
The molar mass of a compound is equal to the sum of the atomic masses of its constituent atoms in $\dfrac{g}{{mol}}$.
Given weight of the complex is $3.2gm$
Molecular weight of complex $= 4M + 48 + 264 + 216$
$\Rightarrow 4M + 528$
Molar mass of oxalic acids $C{H_2}{C_2}{O_4} = 90m$
$\Rightarrow \dfrac{{3.2}}{{4M + 528}} \times 3 = \dfrac{1}{{90}}$
As there are $3$moles of oxalic acid is present in the complex
$\Rightarrow 9.6 \times 90 = 4M + 528$
$\Rightarrow 864 - 528 = 4M$
$\Rightarrow M = \dfrac{{336}}{4}$
$\Rightarrow 0084gm$

Note:
There is no physical way of measuring the number of moles of a compound, we can relate its mass to the number of moles by using the compound’s molar mass as a direct conversion factor. To convert between mass and number of moles, you can use the molar mass of the substance. Then, you can use Avogadro’s number to convert the number of moles to the number of atoms.