Question

If a single helium atom has a mass of $ 6.65\times {{10}^{-27}}kg $ . What is the mass of a mole of helium atoms?

Answer 1

Hint: We know that when dealing with particles at atomic level, even one gram of pure element consists of a huge number of atoms and thus, we use mole which is a count of very large number of particles and number of particles or atoms of any substance in one mole is called Avogadro’s number which is equal to $ 6.023\times {{10}^{23}} $ .

Complete answer:
As per question, it is given that mass of one atom of helium is equal to $ 6.65\times {{10}^{-27}}kg $ and we need to calculate mass of one mole of helium i.e., molar mass of helium atom.
The molar mass of a chemical element is defined as the ratio given mass of the chemical substance and the amount of substance i.e., the number of moles of that substance. Mathematically, it is represented as follows:
Molar mass $ =\dfrac{\text{given mass}}{\text{number of moles}} $
As the mass is given for one helium atom, so we need to convert given mass from atoms to number of moles as per following relation:
1 mole $ =6.023\times {{10}^{23}} $ atoms
Since, mass of 1 atom of helium $ =6.65\times {{10}^{-27}}kg $
Therefore, the mass of 1 mole of helium $ =6.65\times {{10}^{-27}}\times 6.023\times {{10}^{23}} $
Hence, the molar mass for one mole of helium can be expressed as follows:
 $ M=\dfrac{6.65\times {{10}^{-27}}\times 6.023\times {{10}^{23}}}{1} $
 $ \Rightarrow M=40.05\times {{10}^{-4}}kgmo{{l}^{-1}} $
In terms of grams, the molar mass of helium will be as follows:
 $ \Rightarrow M=40.05\times {{10}^{-4}}\times {{10}^{3}}\ \ \ \ \left[ \because 1kg={{10}^{3}}g \right] $
 $ \Rightarrow M=4.0gmo{{l}^{-1}} $
Thus, we can conclude that the mass of a mole of helium atoms is $ 4.0gmo{{l}^{-1}} $ .

Note:
Remember that the characteristic molar mass of an element is simply its atomic mass expressed in $ gmo{{l}^{-1}} $ and the molar mass of any substance serve as a bridge between the mass of a material and number of moles as it is not possible to calculate the number of moles directly for any element or compound.