Question

The Avogadro's number is $6 \times 10^{23}$ per gm mole and the electronic charge is $1.6 \times 10^{-19} \mathrm{C}$. The Faraday's number is
A. $6 \times 10^{23} \times 1.6 \times 10^{-19}$
B. $\dfrac{6 \times 10^{23}}{1.6 \times 10^{-19}}$
B. $1.6 \times 10^{-19}$
C. $6 \times 10^{23} \times 1.6 \times 10^{-19}$
D. $\dfrac{1.6 \times 10^{-19}}{6 \times 10^{23}}$

Answer 1

Hint: Avogadro number gives the number of particles present in one mole of substance. Faraday's number gives the amount of electric charge that one mole of substance carries.
We can use the standard relation connecting Avogadro number and electronic charge to find Faraday's number.

Formula used: Faraday's number, $F=N e$
$\mathrm{N}$ is Avogadro's number and e is the electric charge.

Complete Step by Step Answer:
Avogadro number gives the information about the number of particles present in one mole of a substance. This number helps to calculate even large numbers. $6 \times 10^{23}$ is the Avogadro number. Mainly it helps to compare different atoms of a particular substance with the same number of atoms. Generally, it is represented by $\mathrm{N}$ or $N_{A}$.

In the above equation ' $e$ ' represents the electric charge. It helps in determining how electric field and magnetic field rule within a particle. It is the property of a matter. Generally electric charge is represented by e or q. It can have both positive or negative value. The value of electric charge is also constant, that is $1.6 \times 10^{-19} \mathrm{C}$. The Charge S.I unit is Coulomb, represented by ' $C$'.

Faraday's number gives the amount of electric charge that one mole of substance carries. This number is explained on the basis of Avogadro number and electric charge. These two quantities are constant hence Faraday's number is also a constant. Its unit is coulombs per mole. It can be easily derived from the above equation. Here we are asked to find out Faraday's number simply we need to multiply Avogadro number and charge.

That is, $F=N e$
$\mathrm{N}=6 \times 10^{23}$
$\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$
Therefore $\mathrm{F}=6 \times 10^{23} \times 1.6 \times 10^{-19} \mathrm{Cmol}^{-1}$
Therefore, the answer is option A.

Note: Possible mistakes occurred in solving this problem by forgetting to put units. Some of us may have confusion in taking power of charge.