Question

Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of $10.0 g$. Silver has $47$ electrons per atom, and its molar mass is $107.87gmol^{-1}$.
A. ${\text{2}}{\text{.62}} \times {\text{1}}{{\text{0}}^{{\text{24}}}}$
B. ${\text{5}}{\text{.24}} \times {\text{1}}{{\text{0}}^{{\text{24}}}}$
C. ${\text{7}}{\text{.62}} \times {\text{1}}{{\text{0}}^{{\text{24}}}}$
D. ${\text{1}}{\text{.62}} \times {\text{1}}{{\text{0}}^{{\text{24}}}}$

Answer 1

Firstly, find the number of moles in 10 g of silver by dividing the given mass by atomic mass of silver. After that on multiplying Avogadro constant find the total number of atoms that a mass of 10 gm of silver contain and then according to property of silver calculate the total number of electrons by multiplying the total number of atom with 47 as one neutral atom contain 47 electrons in it.

Complete step by step answer:
According to initial data we have,
Mass of silver pin (m) = 10.0 g
Number of electrons per atom = 4
Molar mass of a silver atom = $107.87gmol^{-1}$

Now, by using the formula of moles
$n = \dfrac{m}{M}$
Where
n= number of moles
m= given mass of silver pin
M= Molar mass of silver
On putting values in equation we have
$n = \dfrac{{10g}}{{108.7gmo{l^{ - 1}}}}$

$n = \dfrac{{10}}{{108.7}}mole$

Now, using the formula of the number of atoms per mol.
$N = n \times {N_A}$
Where
n=moles
N= number of atoms
$N_A$= Avogadro constant which is equal to 6.023 $\times$ 10$^{23}$

Putting values in above equation
$N = \dfrac{{{\text{10}}}}{{{\text{107}}{\text{.87}}}} \times {\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}$

On solving we get
$N = 5.58 \times 10^{22}$

Total number of electrons = (number of electrons per atom) $\times$ (number of atoms)
Total number of electron = $47 \times N$

On putting the values we get
Total number of electrons $=47 \times 5.58\times 10^{22}$

On further solving we get
Total number of electrons = $2.62 \times 10^{24}$

Therefore Option (A) is correct.

Note: Be careful while calculating number of moles and atoms from moles. One mole of a substance is equal to ${\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}$ units of that substance (such as atoms, molecules, or ions).
The number ${\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}$ is known as Avogadro's number or Avogadro's constant. The concept of the mole can be used to convert between mass and number of particles.