Question

One gm metal ${M^{3 + }}$ was discharged by the passage of $1.81 \times {10^{23}}$ electrons. What is the atomic mass of the metal?
A) $8g/mol$
B) $9g/mol$
C) $10g/mol$
D) None of these

Answer 1

The reaction is ${M^{3 + }} + 3{e^ - } \to M$. The charge on a single electron is $1.6 \times {10^{ - 19}}C$ and the value of $1F$ is $96500C$. Also, we are given that the number of electrons is $1.81 \times {10^{23}}$.

Complete answer:
When we discharge one gm of ${M^{3 + }}$ , the reaction is
${M^{3 + }} + 3{e^ - } \to M$
So, here, we can see that one mole of metal is deposited by $3$ electrons, which means $3F$.
So, one mole of metal is deposited by $3 \times 96500C = 289500C$
Now, the charge on a single electron is $1.6 \times {10^{ - 19}}C$
So, the charge on $1.81 \times {10^{23}}$ electrons is $\left( {1.6 \times {{10}^{ - 19}} \times 1.81 \times {{10}^{23}}} \right) = 2.9 \times {10^4}C$
So, $289500C$ deposit $1$ mole of metal
So, $2.9 \times {10^4}C$ will deposit $\dfrac{{2.9 \times {{10}^4}}}{{289500}} = \dfrac{{29000}}{{289500}} = 0.100$ moles of metal.
So, it is now clear that $0.100$ moles metal is equal to $1$ gm metal
So, atomic mass of the metal is $10$ gm/mol
Hence option C is correct .

Additional information: The atomic mass of a single atom is defined simply as its total mass. It is generally expressed in “amu” (atomic mass units). For example, an atom of carbon, which has six neutrons (carbon-12), has an atomic mass of 12 amu. For any given isotope or atom or molecule, the sum of the numbers of protons and the number of neutrons in the nucleus is called the mass number of that isotope or atom or molecule. The reason behind it is that each proton and each neutron weigh one amu. So, one can calculate the mass of an atom only by adding together the number of protons and neutrons and then multiplying by 1 amu.

Note:
Here, $F$ is the unit, Faraday. It is used to measure the electricity, which is required to break down a compound by electrolysis and also the value of $1F$ is $96500C$ [Where, $C$ is the unit, Coulomb]. The charge carried by one mole of electrons is about $96500$ coulombs per mole.