Question

The total charge on 0.28 g of \[F{e^{n + }}\] is 1448 coulombs. What is the charge on iron? (Given atomic mass of iron=56 amu)
A.+3
B.+2
C.+4
D.+1

Answer 1

Hint: One coulomb is defined as the amount of charge from a current of one ampere flowing for one second. We know that the charge of one electron is \[1.6 \times {10^{ - 19}}\] C. According to quantisation of energy we can say that:
\[ \Rightarrow Q = ne\]
Where Q is the total charge
n is the number of elementary charged particle
e is charge of one electron which is \[1.6 \times {10^{ - 19}}\] C

Complete answer:
It is given to us that 0.28g of the given sample is 1448 Coulombs. Thus we can find out the number of moles of the sample. This is done by using the mole concept.
\[ \Rightarrow {\text{Moles of F}}{{\text{e}}^{n + }}{\text{ = }}\dfrac{{{\text{0}}{\text{.28}}}}{{56}} = \dfrac{1}{{200}}\]
Thus the total number of \[F{e^{n + }}\] in the sample can be calculated as
Number of Particles = Number of moles \[ \times \] Avogadro number
Since the total charge of this is n
\[ \Rightarrow {\text{Number of charged particles}} = {\text{ }}n \times \dfrac{1}{{200}} \times 6.022 \times {10^{23}}\]
We can say that the above value is equal to the total charge of the system which is 1448 coulombs.
Thus we can write the equation as:
\[ \Rightarrow n = \dfrac{{1448 \times 200}}{{1.6 \times {{10}^{ - 19}} \times 6.022 \times {{10}^{23}}}}\]
\[ \Rightarrow n = \dfrac{{289600}}{{9.6352 \times {{10}^4}}}\]
\[ \Rightarrow n = 30056.459 \times {10^{ - 4}}\]
\[ \Rightarrow n \approx 3\]
Thus we can say that the charge of the given Fe sample is +3
The correct option is (A).

Note:
An atomic unit of mass or amu is defined as accurately one-twelfth the mass of a carbon-12 atom. A carbon-12 atom has six neutrons and six protons in its nucleus. The masses of all other elements in the periodic table are based on this standard. To calculate the atomic mass of a single atom of any given element, we need to add up the mass of protons and neutrons.