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Question: The mass and charge of one mole of electrons, respectively is: (A) \(54.8 \times {10^{ - 7}}\)Kg, ...

The mass and charge of one mole of electrons, respectively is:
(A) 54.8×10−754.8 \times {10^{ - 7}}Kg, 9.65×1049.65 \times {10^4}C
(B) 5.48×10−75.48 \times {10^{ - 7}}Kg, 9.65×1039.65 \times {10^3}C
(C) 5.48×10−75.48 \times {10^{ - 7}}g, 9.65×1049.65 \times {10^4}C
(D) 5.48×10−75.48 \times {10^{ - 7}}Kg, 9.65×1049.65 \times {10^4}C

Explanation

Solution

We know that 1 mole of any substance will have 6.02×10236.02 \times {10^{23}} units (Avogadro number) of that substance. Also the charge of 1 electron is 1.6×10−191.6 \times {10^{ - 19}}C and the mass of 1 electron is 9.1×10−319.1 \times {10^{ - 31}}Kg. So, to find the charge and mass of 1 mole of electrons, find the product of the number of electrons present in 1 mole and the mass/charge of 1 electron.

Complete step by step answer:
-Let us start by just writing down the charge and mass of 1 electron.
The charge of 1 electron is 1.6×10−191.6 \times {10^{ - 19}}C and the mass of 1 electron is 9.1×10−319.1 \times {10^{ - 31}}Kg.
-We know that 1 mole of any substance has 6.02×10236.02 \times {10^{23}} units (Avogadro number) of that substance. Hence we can say that when we say 1 mole of electrons we are referring to 6.02×10236.02 \times {10^{23}} electrons.
-Now, we will calculate the mass of 1 mole of electrons.
Mass of 1 electron = 9.1×10−319.1 \times {10^{ - 31}}Kg
Number of electrons in 1 mole = 6.02×10236.02 \times {10^{23}}
Therefore the mass of 1 mole of electrons = 9.1×10−31×6.02×10239.1 \times {10^{ - 31}} \times 6.02 \times {10^{23}}Kg
= 5.48×10−75.48 \times {10^{ - 7}}Kg
Hence the mass of 1 mole electron of electrons is 5.48×10−75.48 \times {10^{ - 7}}Kg.
-Now, we will calculate the charge of 1 mole electrons.
Charge of 1 electron = 1.6×10−191.6 \times {10^{ - 19}}C
Number of electrons in 1 mole = 6.02×10236.02 \times {10^{23}}
Therefore the charge of 1 mole of electrons = 1.6×10−19×6.02×10231.6 \times {10^{ - 19}} \times 6.02 \times {10^{23}}C
= 9.65×1049.65 \times {10^4}C
Hence the charge of 1 mole of electrons will be 9.65×1049.65 \times {10^4}C.
So, the correct answer is “Option D”.

Note: We all know that there exist three types of particles which constitute an atom: electron, proton and neutron. A proton has a charge equal in magnitude with the electron but with opposite charge and is equal to = +1.6×10−19 + 1.6 \times {10^{ - 19}}C while the charge of an electron is = −1.6×10−19 - 1.6 \times {10^{ - 19}}C. A neutron is a neutral atom with 0 charge. Remember that this charge is always in units of Coulomb (C) and the mass we take here is in Kg (kilogram).