Subject: Physics

#### Overview

According to Faraday's first law of electrolysis, the mass of a substance liberated or deposited on an electrode during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte.

First Law

The mass of a substance liberated or deposited on an electrode during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte.

If m is the mass of the substance deposited on the cathode when an electric charge Q is passed through the electrolyte, then

\begin{align*} m &\propto Q \\ \text {or,} \: m &= ZQ \\ \text {or,} \: m &= Zit \\ \end{align*}

where Z is a proportionality constant called electrochemical equivalent of the substance.

Second Law

If the same amount of electric charge passed through different electrolytes, the masses of the substances liberated or deposited are proportional to their chemical equivalents.

Let m1 , m2, and m3 be the masses of the substances liberated in three different voltameters when the same current is passed through them and E1, E2 and E3 be their respective chemical equivalents. Then

\begin{align*} \frac {m_1}{E_1} =& \frac {m_2}{E_2} = \frac {m_3}{E_3} \\ \text {or,} \: \frac mE &= \text {constant} \\\end{align*}

#### Experimental Verification of Faraday’s Law of electrolysis

##### Verification of the First Law

A copper voltameter is taken in the arrangement. Cathode plate is washed, dried, weighted and placed inside the voltameter. Then appropriate current is passed through the electrolyte for a suitable time, t1 by adjusting rheostat. The cathode plate is again weighted to determine the mass, m1 of copper deposited.

This experiment is repeated in different interval of time t2 and with different mass m2 deposited on the cathode plate is determined. It is found that

\begin{align*} \frac {m_1}{m_2} &= \frac {t_1}{t_2} \\ \text {or,} \: m \propto t \dots (i) \\ \end{align*}

If m1 and m2 be the masses of copper deposited on the cathode when current I1 and I2 passed through the electrolyte, than it would be found that

\begin{align*} \frac {m_1}{m_2} &= \frac {I_1}{I_2} \\ \text {or,} \: m \propto I \dots (ii) \\ \text {From } \: (i) \: \text {and} \: (ii),\: \text {we get} \\ m \propto It \\ \text {or,} \: m \propto Q \\ \dots (iii) \\ \end{align*}

This is Farady’s first law. This is the mass of ion deposited is directly proportional to the amount of charge that liberate it.

##### Verification of Second Law

Three voltameters such as copper voltameter, silver voltameter, and water voltameter are connected in series as in figure and the same current is passed through them for the same interval of time. The mass of ions liberated or deposited on respective cathodes is determined. If m1, m2 and m3 be the mass of copper, silver and hydrogen deposited on the cathodes, then it is found that

$$\frac {m_1}{E_1} =\frac {m_2}{E_2} = \frac {m_3}{E_3}$$

where, E1, E2, and E3 are the chemical equivalents of copper silver and hydrogen.

#### Electrochemical Equivalent and its Experimental Determination

From Faraday’s first law of electrolysis,

$$m = ZIt$$

If Q = 1 coulomb, then Z = m

Electrochemical equivalent (z) of a substance is defined as the mass of the substance liberated or deposited in electrolysis by the passage of 1 coulomb of charge. Its SI unit is kg/C. its value for copper is 3.29 × 10-7 kg/C, for silver 1.118 × 10-6 kg/C, for hydrogen 1.05 × 10-11 kg/C.

The experimental arrangement for determination of E.C.E of copper is shown in the figure.

Cathode plate is washed, dried, weighed and placed inside the voltameter. Then the appropriate current is passed through the voltameter for a known interval of time, t. The cathode plate is taken out and then washed, dried and weighted again to determine the mass, m of the copper deposited. From Faraday’s first law,

\begin{align*} m &= ZIt \\ \text {or,} \: Z &= \frac {m}{It} \\ \end{align*}

The value of Z is determined by knowing the value of m, I and t.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, et al.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

##### Things to remember

According to Faraday's first law of electrolysis, the mass of a substance liberated or deposited on an electrode during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte.

According to Faraday's second law of electrolysis, if the same amount of electric charge passed through different electrolytes, the masses of the substances liberated or deposited are proportional to their chemical equivalents.

Electrochemical equivalent (z) of a substance is defined as the mass of the substance liberated or deposited in electrolysis by the passage of 1 coulomb of charge.

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