Question

If the mass of an electron is $\text{ }9\times {{10}^{-28}}\text{ }$ grams, the weight of one mole of the electron is:
(A) $\text{ }9\times {{10}^{-28}}\text{ }$
(B) $\text{ }6\times {{10}^{-28}}\text{ }$
(C) $\text{ }1.008g\text{ }$
(D) $\text{ 0}.00054g\text{ }$

Answer 1

Hint: A mole can be defined as a unit or measure containing the same number of atoms or molecules. One mole of atoms or molecules has $\text{ }6.022\times {{10}^{23}}\text{ }$ electrons and these electrons have their mass. So, if the mass of a single electron is given, the mass of 1 mole of electrons can be easily calculated.

Complete Solution :
To understand the mole concept, one needs to know the difference between atomic mass, molecular mass, and molar mass.
Atomic mass can be defined as the mass of a single atom given in amu (atomic mass unit)
For example, the atomic mass of a single carbon atom $\text{ (C)=12amu }$
Similarly, the atomic mass of oxygen $\text{ (O)=16amu }$

- A molecule is formed by a combination of two or more atoms. Therefore, a molecular mass can be defined as the total mass of all the elements involved in forming a molecule.
One such example of a molecule is $\text{ }{{\text{H}}_{\text{2}}}\text{O }$ .
$\begin{align}
  & \text{ Molecular mass of }{{\text{H}}_{\text{2}}}\text{O=2 }\!\!\times\!\!\text{ }\left( \text{mass of H atom} \right)+1\text{ }\!\!\times\!\!\text{ }\left( \text{mass of O atom} \right) \\
 & \Rightarrow \text{Molecular mass of }{{\text{H}}_{\text{2}}}\text{O=2 }\!\!\times\!\!\text{ }\left( \text{1} \right)+1\text{ }\!\!\times\!\!\text{ }\left( \text{16} \right) \\
 & \therefore \text{Molecular mass of }{{\text{H}}_{\text{2}}}\text{O=}18\text{ amu } \\
\end{align}$

- Molar mass is defined as the total mass present in one mole of a substance. It is determined in gram per mole ($\text{ g/mol }$ ).
$\text{ Molar mass=}\dfrac{\text{Mass of substance (in grams)}}{\text{no}\text{.of moles}}\text{ }$
For example, one mole of $\text{ NaCl }$ has mass $\text{ }58g\text{ }$. Therefore, the Molar mass of $\text{ NaCl }$ is
$\text{ mole of NaCl = }\dfrac{58}{1}=58\text{ g/mol }$
A single mole of an atom contains $\text{ }6.022\times {{10}^{23}}\text{ }$ electrons
For example, $\text{ }14g\text{ }$ of Nitrogen forms 1 mole, and this $\text{ }14g\text{ }$ of Nitrogen consists of $\text{ }6.022\times {{10}^{23}}\text{ }$ electrons.
Similarly, $\text{ 1g }$ of Hydrogen forms 1 mole i.e., it consists of$\text{ }6.022\times {{10}^{23}}\text{ }$electrons.
These $\text{ }6.022\times {{10}^{23}}\text{ }$ electrons present in 1 mole of substance have their mass
Therefore,
If the mass of a single electron is $\text{ }9\times {{10}^{-28}}\text{ g }$ and Electrons in 1 mole of a substance contains $\text{ }6.022\times {{10}^{23}}\text{ }$electrons
$\begin{align}
  & \therefore \text{ weight of one mole electrons = }6.022\times {{10}^{23}}\times \text{ mass of single electrons} \\
 & \Rightarrow \text{weight of one mole electrons = }6.022\times {{10}^{23}}\times \text{ 9}\text{.0}\times {{10}^{-28}} \\
 & \therefore \text{weight of one mole electrons = }54\times {{10}^{-5}}=0.00054\text{ g } \\
\end{align}$
Therefore, the answer is $\text{ }0.00054\text{ g }$ .
So, the correct answer is “Option D”.

Note: While the atomic mass and molar mass are numerically equivalent, it is to be kept in mind that they are very different in terms of scale. Note that Avogadro's number is a proportionality constant which relates the number of particles and amount of substance.