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Question: How many moles of electrons will weigh one kilogram? A. \[6.023\times {{10}^{23}}\] B. \[\dfrac{...

How many moles of electrons will weigh one kilogram?
A. 6.023×10236.023\times {{10}^{23}}
B. 19.108×1031\dfrac{1}{9.108}\times {{10}^{31}}
C. 6.0239.108×1054\dfrac{6.023}{9.108}\times {{10}^{54}}
D. 19.108×6.023×108\dfrac{1}{9.108\times 6.023}\times {{10}^{8}}

Explanation

Solution

To convert given mass to moles of that substance we know that we can get the number of moles of any substance by dividing the given mass by the molar mass of the substance. Molar mass is the mass of 1 mole or 6.023×10236.023\times {{10}^{23}} number of particles of that substance. We have to keep the mass in kilograms which is the SI unit of measurement for mass.

Complete answer: or Complete step by step answer:
So, we have to find the mass of 1 mole of electrons from the mass of the 1 electron.
Mass of one electron is given as = 9.108×10−319.108\times {{10}^{-31}}kg.

So the mass of one mole of electrons will be = 9.108×10−319.108\times {{10}^{-31}}× 6.023×10236.023\times {{10}^{23}}= 9.108 × 6.023 ×10−8{{10}^{-8}}kg.

The number of moles of electrons that weigh one kilogram will be given by = 19.108×6.023×10−8\dfrac{1}{9.108\times 6.023\times {{10}^{-8}}}​=19.108×6.023×108\dfrac{1}{9.108\times 6.023}\times {{10}^{8}}

So, the correct answer is Option D.

Note:
The mole is defined as the unit of measurement for the amount of substance in the International System of Units. A given mole of a substance or a mole of particles is defined as exactly 6.023×10236.023\times {{10}^{23}} particles, which may be atoms, molecules, ions, or electrons.
The electron is a subatomic particle, having electric charge which is negative one elementary charge. Electrons till now belong to the first generation of the particle family, and they are generally thought to be elementary particles as so far they have no known components or substructure constituting them.