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# How many moles of electrons weigh one kilogram?(Mass of electron = ${\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ kg}}$; Avogadro number, = ${\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$(A) $\dfrac{1}{{{\text{9}}{\text{.108 x 6}}{\text{.023 }}}}{\text{x1}}{{\text{0}}^{\text{8}}}$(B) ${\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$(C) $\dfrac{1}{{{\text{9}}{\text{.108}}}}{\text{x 1}}{{\text{0}}^{{\text{31}}}}$(D) $\dfrac{{{\text{6}}{\text{.023}}}}{{{\text{9}}{\text{.108 }}}}{\text{x1}}{{\text{0}}^{54}}$

Hint: One mole of any substance has Avogadro number of atoms or molecules or ions. Avogadro number,${\text{\;}}{{\text{N}}_{\text{A}}}$= ${\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$

Complete step by step answer: It is given that mass of one electron = ${\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ kg}}$
We know that one mole of any substance has an Avogadro number of atoms or molecules or ions. Avogadro number,${\text{\;}}{{\text{N}}_{\text{A}}}$= ${\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$
⟹Mass of one mole of electrons = ${\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ x 6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$kg
Since in the options we can see that the numbers are not in simplified form so we do not perform the multiplication we can keep it as such till the end.
Now, we need to find the number of moles of electrons that weigh one kilogram(kg)
⟹ The number of mole of electrons that weigh one kilogram = $\dfrac{1}{{{\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ x 6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}}}$
Now let’s just simplify the power terms, by doing so we get,
⟹The number of mole of electrons that weigh one kilogram = $\dfrac{1}{{{\text{9}}{\text{.108 x 6}}{\text{.023 x 1}}{{\text{0}}^{ - 8}}{\text{ }}}}$
⟹The number of mole of electrons that weigh one kilogram =$\dfrac{1}{{{\text{9}}{\text{.108 x 6}}{\text{.023}}}}{\text{x 1}}{{\text{0}}^8}$

So, the correct option is A.

Additional information: A mole is the SI unit to measure the amount of substance. Avogadro number is defined as the number of atoms present in 12g of carbon-12. The value of Avogadro number is${\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$ molecules/atoms. It is denoted as ${\text{\;}}{{\text{N}}_{\text{A}}}$. Therefore, number of moles can also be calculated from the Avogadro number.
${\text{Number of moles = }}\dfrac{{{\text{Number of particles}}}}{{{\text{Avogadro Number}}}}$

Note: Mass of an electron can also be expressed in g since 1kg = ${\text{1}}{{\text{0}}^{\text{3}}}$g therefore mass of electron becomes ${\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 27}}}}{\text{g}}$ therefore proper unit conversion is necessary.