• The?amount?of substance that is formed at an electrode during?electrolysis?is proportional to:
  • The amount of?time?where a constant current to passes
  • The?amount?of?electricity, in coulombs, that passes through the electrolyte (strength of electric?current)
  • The relationship between the current and time is:

Q = I x t

Q?= charge (coulombs, C)

I?= current (amperes, A)

t?= time, (seconds, s)

• The?amount?or the?quantity of electricity?can also be expressed by the?faraday?(F)?unit
  • One faraday is the amount of?electric charge?carried by 1 mole of electrons or 1 mole of singly charged ions
  • 1 faraday is 96 500 C mol^-1
• Thus, the relationship between the Faraday constant and the Avogadro constant (L) is:

F = L x e

F?= Faraday’s constant (96 500 C mol^-1)

L?= Avogadro’s constant (6.022 x 10²³?mol^-1)

e?= charge on an electron

Worked example: Determining the amount of electricity required

Answer

One Faraday is the amount of charge (96 500 C) carried by 1 mole of electrons

Answer 1

As there is?one mole?of electrons,?one faraday of electricity?(96 500 C) is needed to deposit one mole of sodium.

Answer 2

Now, there are?two moles?of electrons, therefore,?two faradays of electricity?(2 x 96 500 C) are required to deposit one mole of magnesium.

Answer 3

Two moles?of electrons are released, so it requires?two faradays of electricity?(2 x 96 500 C) to form one mole of fluorine gas.

Answer 4

Four moles?of electrons are released, therefore it requires?four faradays of electricity?(4 x 96 500 C) to form one mole of oxygen gas.

• The Avogadro’s constant (L) is the number of entities in?one mole
  • L?= 6.02 x 10²³?mol^-1
  • For example,?four moles?of water contains 2.41 x 10²⁴?(6.02 x 10²³?x 4) molecules of H₂O
• The value of?L?(6.02 x 10²³?mol^-1) can be?experimentally?determined by electrolysis using the following equation:

Finding?L?experimentally

• The charge on?one mole of electrons?is found by using a simple?electrolysis?experiment using copper electrodes

Apparatus set-up for finding the value of L experimentally

• Method
  • The pure copper?anode?and pure copper?cathode?are?weighed
  • A?variable?resistor?is kept at a constant current of about 0.17 A
  • An?electric?current?is then passed through for a certain time interval (e.g. 40 minutes)
  • The anode and cathode are then removed, washed with distilled water, dried with propanone, and then?reweighed
• Results
  • The?cathode?has?increased?in mass as copper is deposited
  • The?anode?has?decreased?in mass as the copper goes into solution as copper ions
  • Often, it is the decreased mass of the anode which is used in the calculation, as the solid copper formed at the cathode does not always stick to the cathode properly
  • Let’s say the amount of copper deposited in this experiment was 0.13 g
• Calculation:
  • The amount of charge passed can be calculated as follows:

Q = I x t

= 0.17 x (60 x 40)

= 408 C

• To deposit 0.13 g of copper (2.0 x 10^-3?mol), 408 C of electricity was needed
• The amount of electricity needed to deposit 1 mole of copper can therefore be calculated using simple proportion using the relative atomic mass of Cu

Calculating the amount of charge required to deposit one mole of copper table

• Therefore, 199 292 C of electricity is needed to deposit 1 mole of Cu
• The half-equation shows that?2 mol of electrons?are needed to deposit one mol of copper:

Cu²⁺(aq) +? 2e^-?→?? Cu(s)

• So, the charge on?1 mol?of electrons is:

= 99 646 C

• Given that the charge on?one electron?is 1.60 x 10^-19?C, then?L?equals:

= 6.23 x 10²³?mol^-1

• The?experimentally?determined?value for?L?of 6.23 x 10²³?mol^-1?is very close to the?theoretical?value of 6.02 x 10²³?mol^-1