Question

What weight of substance is deposited if x ampere of current is flown through its salt solution for 10s? (The equivalent weight of substance is $\dfrac{M}{y}$ )
(1) $w = \dfrac{{My}}{{10x}}$
(2) $w = \dfrac{{10Mx}}{{yF}}$
(3) $w = \dfrac{{yF}}{{10Mx}}$
(4) $w = \dfrac{{yF10x}}{M}$

Answer 1

To answer this question, you must remember the concepts of Electrochemistry. Recall all the formulae one by one and then select and use the correct formula to calculate the answer. You must remember the formula for weight of substance deposition, enlist the formula and all its requirements and then put the correct value by taking care of the units. And you will finally reach the correct answer.
Formula used: $w =$ $Z \times i \times t$ ; where Z = chemical equivalent of element, i is value of current, and t is time.

Complete step-by-step solution:
Step 1: Enlist all the given quantities:
Amount of current passed = x amperes
Time = 10 seconds
Equivalent Weight of Substance = E = $\dfrac{M}{y}$

Step 2: Enlist the correct formula for finding the amount of deposited substance and that is:
$w =$ $Z \times i \times t$ ; where Z = chemical equivalent of element, i is value of current, and t is time.
$Z\, = \,\dfrac{E}{F}\, = \,\dfrac{{\dfrac{M}{y}}}{F}\, = \,\dfrac{M}{{yF}}$ ; F = 96500 Coulomb

Step 3: Calculate the deposited weight:
$w =$ $d\frac{M}{{yF}} \times x \times 10 =$ $\dfrac{{10Mx}}{{yF}}$ units
Here, in the weight we do not have written any standard unit because we do not know the unit in which the equivalent weight is provided, so it will not be a good approach to use any general unit without having any confirmation. But most probably the unit will be in grams, but it will be better to write units here.
So, we got the value of the deposited weight of the substance is $\dfrac{{10Mx}}{{yF}}$ units.

Hence, the correct answer is option 2.

Note: Faraday's first electrolysis Law states that the quantity of reaction taking place in terms of mass of ions formed or discharged from an electrolyte is proportional to the amount of electric current passed. Since electric current (ampere) is the number of coulombs (Q) flowing in one second, Mass of the ions formed or reacted (m) α electric current α Q, or m α Q. The proportionality constant is equal to the mass of the substance involved in the reaction. Z is the electrochemical equivalent mass of one coulomb charge.