Question

Calculate the number of gram atoms in $4.6$ grams of sodium.

Answer 1

Hint:
We know that the number of gram atoms can be determined or identified with the help of two masses. One is given mass or weight and the other one is molecular mass or molecular weight of that given species.

Complete step by step solution
Given, the mass of sodium is $4.6$ g.
As we all know, the value of the molar mass of sodium is ${\rm{23}}\;{\rm{g/mol}}$ and the molecular weight of sodium atom is ${\rm{23}}\;{\rm{g/g}}\;{\rm{atom}}$.

The law of definite proportion says that the formation of a chemical compound occurs by taking the accurate similar proportions of elements by mass. In other words, the composition of the substance depends on how many kinds of atoms have been formed. The chemical formula of most compounds will always have the same number and types of atoms.

The number of gram atoms that is also derived as the number of moles of the sodium can be calculated or determined by using the formula as shown below.
${\rm{Number}}\;{\rm{of}}\;{\rm{gram}}\;{\rm{atoms}} = \dfrac{{\rm{W}}}{{{\rm{MW}}}}$
Where, W is the mass or weight of sodium atom and MW is the molecular weight of sodium.

Substitute all the respective values in the above equation. We get,
$
{\rm{Number}}\;{\rm{of}}\;{\rm{gram}}\;{\rm{atoms}} = \dfrac{{{\rm{4}}{\rm{.6}}\;{\rm{g}}}}{{{\rm{23}}\;{\rm{g/g}}\;{\rm{atom}}}}\\
 = 0.2\;{\rm{g}}\;{\rm{atoms}}
$
Hence, the number of grams of sodium is $0.2$.

Therefore, the number of gram atoms in $4.6$ grams of the sodium is $0.2$.

Note:
The mass, molar mass or molecular mass and the number of grams all together comes in the same category that is physical quantity. The mass is usually measured in kilograms and grams. The kilogram is the highest unit which is used to measure or denotes the value of mass of the species.