Question

How many moles of electrons weigh one kilogram?
A) $6.023 \times {10^{23}}moles$
B) $\dfrac{1}{{9.108}} \times {10^{31}}moles$
C) $\dfrac{{6.023}}{{9.108}} \times {10^{54}}moles$
D) $\dfrac{1}{{9.108 \times 6.023}} \times {10^8}moles$

Answer 1

Hint: To calculate number of moles of electrons in one kilogram, you should know these values.
Mass of an electron = $9.108 \times {10^{ - 31}} kg$ and, number of electrons in 1 mole = $6.023 \times {10^{23}} electrons$.
First, calculate the mass of one mole of electrons and then calculate the number of moles of electrons present in one kilogram by unitary method.

Complete step by step answer:
There are $6.023 \times {10^{23}} electrons$ (Avogadro number,${N_A}$ ) present in one mole of a substance and mass of one electron is $9.108 \times {10^{ - 31}}kg$.
Therefore, mass of one mole of electrons = mass of one electron $ \times $ number of electrons in one mole
$ \Rightarrow $ mass of one mole of electrons = $(9.108 \times {10^{ - 31}}) \times (6.022 \times {10^{23}})$ kg
We are asked to find the number of electrons present in one kilogram.
 Therefore, total mass given = 1 kilogram
$(9.108 \times {10^{ - 31}}) \times (6.022 \times {10^{23}})$ kg contains = 1 mole of electrons
1 kg will contain = $\dfrac{1}{{(9.108 \times {{10}^{ - 31}}) \times (6.022 \times {{10}^{23}})}}$ moles of electrons.
Or, 1 kg will contain = $\dfrac{1}{{9.108 \times 6.022}} \times {10^8}$ moles of electrons.
Thus, $\dfrac{1}{{9.108 \times 6.022}} \times {10^8}$ moles of electrons will weigh one kilogram.
So, the correct answer is “Option D”.

Additional Information:
The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in exactly 12 g (or 0.012 kg) of the carbon-12 isotope. Number of entities or electrons/atoms/molecules/ions present in one mole is equal to the Avogadro constant or Avogadro number (${N_A}$) which is $6.023 \times {10^{23}}particles/mol$.

Note: Always remember values of these physical constants:
Charge of an electron= $1.602 \times {10^{ - 19}}coulomb$ ,
Mass of an electron = $9.108 \times {10^{ - 31}}kg$ ,
Avogadro constant (${N_A}$) = $6.023 \times {10^{23}}particles/mol$,
Charge to mass ratio of an electron ($e/m$ )= $1.76 \times {10^{11}}coulomb/kg$ .