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Question: The molar mass of an electron is: A.\[\text{6}\text{.023 }\times \text{ 1}{{\text{0}}^{-23}}g/mol\...

The molar mass of an electron is:
A.6.023 × 10−23g/mol\text{6}\text{.023 }\times \text{ 1}{{\text{0}}^{-23}}g/mol
B.5.486 × 10−4g/mol\text{5}\text{.486 }\times \text{ 1}{{\text{0}}^{-4}}g/mol
C.9.108 × 10−28kg/mol\text{9}\text{.108 }\times \text{ 1}{{\text{0}}^{-28}}kg/mol
D.9.108 × 10−24g/mol\text{9}\text{.108 }\times \text{ 1}{{\text{0}}^{-24}}g/mol

Explanation

Solution

Hint: Molar mass of an electron is the mass of one mole of electrons.
According to J.J Thomson’s experiment , the mass of an electron is about 1/1837{}^{1}/{}_{1837} times the mass of a proton.
Value of the Avogadro's number (NA{{N}_{A}}) = 6.023 × 1023\text{6}\text{.023 }\times \text{ 1}{{\text{0}}^{23}}.

Complete step by step answer:
Molar mass of an electron is the mass of one electron multiplied by the Avogadro's number (NA{{N}_{A}}) .
The mass of one electron is 9.1083×10−319.1083\times {{10}^{-31}}kg.
So, the molar mass of an electron = mass of one electron ×\times Avogadro's number (NA{{N}_{A}})
= 9.1083×10−31×6.023 × 10239.1083\times {{10}^{-31}}\times \text{6}\text{.023 }\times \text{ 1}{{\text{0}}^{23}}
= 54.6 × 10−854.6\text{ }\times \text{ 1}{{\text{0}}^{-8}}kg/mol
= 54.6 × 10−8 × 10354.6\text{ }\times \text{ 1}{{\text{0}}^{-8}}\text{ }\times \text{ 1}{{\text{0}}^{3}}g/mol = 54.6 × 10−554.6\text{ }\times \text{ 1}{{\text{0}}^{-5}}g/mol
= 5.486 × 10−4g/mol\text{5}\text{.486 }\times \text{ 1}{{\text{0}}^{-4}}g/mol
So, the correct option is B.
Alternative way:
The mass of one electron is 9.1083×10−319.1083\times {{10}^{-31}}kg
Let, the weight of one mole of electrons is X kg.
Number of particle in one mole of electron is the Avogadro's number (NA{{N}_{A}}) that is 6.023 × 1023\text{6}\text{.023 }\times \text{ 1}{{\text{0}}^{23}}.
So, X = 9.1083×10−316.023 × 1023\dfrac{9.1083\times {{10}^{-31}}}{\text{6}\text{.023 }\times \text{ 1}{{\text{0}}^{23}}} = 5.48×10−75.48\times {{10}^{-7}}kg/mol = 5.48×10−45.48\times {{10}^{-4}}g/mol

Additional Information:
1.Electrons are much smaller than the nucleus of an atom.
2.Protons are the positively charged particles of an atom.
3.Neutrons are chargeless particles and mass equal to the rest mass.
4.Protons and electrons are of the same masses and equal and opposite charges. Protons and neutrons are together called nucleons. The number of protons in the nucleus is called the atomic number. The total number of protons and neutrons is called mass number.

Note: Do not confuse between molar mass of an electron and mass of one electron. The concept of the Avogadro's number should be applied properly.