Question

A current of 9.65 Ampere flowing for 10 minutes deposits 3 g of metal which is monovalent, the atomic mass of metal is a:
A.10
B.50
C.30
D.96.5

Answer 1

Hint: In order to calculate the atomic mass of a metal which is the mean weight possessed by an atom due to protons and neutrons in its nucleus, we will use formula of charge i.e. $q = I \times t$, here I is current, Q is charge and t is time and equivalent weight i.e. \[Eq.{\text{ }}wt.{\text{ }}of{\text{ }}metal\; = \dfrac{{Weight\;of\;metal}}{q} \times F\], F= faraday's constant.

Complete step by step answer:
According to the question the weight of metal deposited = \[3g\]
Amount of electricity passed through the metal will be; $q = I \times t.........(1)$
Here q represents charge, I represents current and t represents time.
 Current \[(I) = 9.65A\]
Time \[ = 10min\]
Conversion of minutes to second will take multiplication with 60.
$ \Rightarrow 10 \times 60 = 600sec$
Substituting the value of current and time in equation 1;
$q = I \times t$
\[q = 9.65 \times 600\]
\[q = 5790C\], C is the unit of charge i.e. coulomb
Therefore the charge is \[5790C\].
To find the atomic mass of the metal, the formula used is;
 \[Eq.{\text{ }}wt.{\text{ }}of{\text{ }}metal\; = \dfrac{{Weight\;of\;metal}}{q} \times F\], here F represents Faraday’s constant.
Faraday’s constant = \[96500\]
 So the, Equivalent weight of atom will be = \[57903{\text{ }} \times 96500\]
Equivalent weight of atom = $50gms$

In monovalent metals, the equivalent weight of metal will be equal to its atomic weight.
Thus, the Atomic mass of metal = 50g

So, the correct answer is “Option B”.


Note:
Atomic weight and equivalent weight are two different concepts; atomic weight is the sum total of the mass of atom whereas the equivalent weight is weight of an atom divided by its valency represented as $\dfrac{{weight{\text{ }} of {\text{ }}atom}}{{valency}}$.
1 coulomb: It is the SI unit of electricity, which is defined as equal to the quantity of electric charge transferred in one second across a conductor of one unit length in which a constant current of one ampere flows.