electrochemistry

1. ‫قولى‬ ‫يفقهوا‬ ‫لصانى‬ ‫من‬ ‫عقدة‬ ‫واحلل‬ ‫امرى‬ ‫ويسرلى‬ ‫صدرى‬ ‫لى‬ ‫اشرح‬ ‫رب‬
রাব্বিস রাহলি ছদলর ওয়া ইয়াছলছরলি আমলর ওয়াহ্িুি
উকদাতাম লমি লিছালি ইয়াফ কাহু কাউলি
অর্ থ
ঃ “ হহ আমার প্রভু! আমার হৃদয় প্রশস্ত করর লদি, আমার
কাজ সহজ করর লদি, আর আমার ব্বজহ্বা হর্রক জড়তা দূর করর
লদি, যারত হিাক আমার কর্া বুঝরত পারর এবং আমার জিয
একজি সহায়ক লিযুক্ত করর লদি আমার পলরবার পলরজি
হর্রক” (সূরা-ত্বাহা, আয়াত-২৫-২৮)।

2. Voltaic cell: Influence of anolyte and catholyte concentrations
Q1. How EMF changes with the concentration
of catholyte or anolyte in case of voltaic cell?
Q2. How can you experimentally determine
𝐸𝑐𝑒𝑙𝑙
𝑜
of a reversible cell?
Q3. How can you experimentally determine
the number of ET in case of a cell reaction
taking place in a reversible cell?

3. )
(
|
)
100
.
0
(
||
)
10
0
.
1
(
|
)
( 2
5
2
s
Cu
M
Cu
M
Zn
s
Zn +
−
+

⇌
Cell reaction: )
s
(
Cu
)
aq
(
Zn
)
aq
(
Cu
)
s
(
Zn 2
2
+
+ +
+
]
[
]
[
log
0592
.
0
log
0592
.
0
2
2
+
+
−
=
−
=
Cu
Zn
n
E
E
Q
n
E
E
o
cell
cell
o
cell
cell
Voltaic cell: Influence of anolyte and catholyte concentrations
logQ
𝑬𝒄𝒆𝒍𝒍
Slope=+
2.303𝑅𝑇
𝑛𝐹
Slope=−
2.303𝑅𝑇
𝑛𝐹
𝐸𝑐𝑒𝑙𝑙
𝑜
= 1.10V, where Q=1
[Variation of Cu2+]
Variation of [Zn2+]
1) 𝑬𝒄𝒆𝒍𝒍 increases as catholyte conc. increases
2) 𝑬𝒄𝒆𝒍𝒍 decreases anolyte conc. increases
3) number of ET can be determined from the slopes
4) 𝐸𝑐𝑒𝑙𝑙
𝑜
can be obtained from the intercept
0.0

4. Kinds of electrodes
• Zeroth kind
• First kind
• Second kind
• Third kind
Zeroth kind: Electrodes where an inert
metal is dipped in a solution of redox
couple: Example Pt/Fe2+, Fe3+
Anode: Fe2+ ⟶ Fe3++𝑒−
Cathode: Fe3++𝑒− ⟶ Fe2+
Q4. Is the standard potential of Pt/Fe2+, Fe3+ electrode is same in 0.1M HCl, 10M HCl or in 0.1M
H2SO4 solution? Why?

5. Formal potential:
Standard potential is estimated under 1M electrolytic condition of analyte but, there
may present other electrolytes in the solution too. Hence, it may be difficult to get
standard potential. In such a case, consideration of formal potential is meaningful.
Fe3+ ++𝑒− ⇌ Fe2 (1)
𝐸 = 𝐸𝑜 −
𝑅𝑇
𝑛𝐹
ln
𝑎𝐹𝑒2+
𝑎𝐹𝑒3+
= [𝐸𝑜−
𝑅𝑇
𝑛𝐹
ln
𝐹𝑒2+
𝐹𝑒3+
] −
𝑅𝑇
𝑛𝐹
ln
[𝐹𝑒2+]
[𝐹𝑒3+]
(2)
𝑜𝑟, 𝐸 = 𝐸𝑜′
−
𝑅𝑇
𝑛𝐹
ln
𝐹𝑒2+
𝐹𝑒3+
3
where 𝐸𝑜′
= 𝐸𝑜 −
𝑹𝑻
𝒏𝑭
𝒍𝒏
𝑭𝒆𝟐+
𝑭𝒆𝟑+
(4)
If
𝐹𝑒2+
𝐹𝑒3+ = 1, the electrode potential is known as formal potential (𝐸𝑜′
). The value of 𝐸𝑜′
varies medium to medium as the
activity coefficient is dependent on ionic strength as we know from DH limiting law. For example, standard reduction potential (eq.
𝐸𝑜=0.77V but formal reduction potential (eq.1) 𝐸𝑜′ = 0.70V, 0.53V, 0.68V in 1M HCl, 10M HCl and 1M H2SO4, respectively.

6. Electrodes of first kind
Electrode of the first kind is a simple metal electrode immersed in a solution containing its own ion
(e.g., silver immersed in a silver nitrate solution). The equilibrium potential of this electrode is a
function of the concentration (more correctly of activity) of the cation of the electrode metal in the
solution
Example: Zn⎹ Zn2+ (aq)
Cu ⎹ Cu2+ (aq)
𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛: 𝐸 = 𝐸𝑜
−
𝑅𝑇
𝑛𝐹
ln
1
[𝑀𝑛+]
= 𝐸𝑜
+
𝑅𝑇
𝑛𝐹
ln[𝑀𝑛+
]
𝑂𝑥𝑖𝑑𝑎𝑡𝑖𝑜𝑛: 𝐸 = 𝐸𝑜
−
𝑅𝑇
𝑛𝐹
ln[𝑀𝑛+
]
−
+
+
→ e
aq
Zn
s
Zn
ox 2
)
(
)
(
: 2
)
(
2
)
(
: 2
s
Cu
e
aq
Cu
red →
+ −
+ If the electrodes of this kind is used for a longer period,
the M⇌ 𝑀𝑛+𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑖𝑠 𝑙𝑜𝑠𝑡 𝑎𝑛𝑑 𝑎 𝑛𝑒𝑤 𝑠𝑡𝑎𝑡𝑒 𝑜𝑓
𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑖𝑠 𝑒𝑠𝑡𝑎𝑏𝑙𝑖𝑠𝑒𝑑 𝑟𝑒𝑝𝑒𝑎𝑡𝑒𝑑𝑙𝑦, hence this types of
electrodes don’t have any fixed potential.

7. Second kind electrodes
Electrodes of the second kind are metal electrodes assembly with the equilibrium potential being a function
of the concentration of an anion in the solution. In this case, a metal is combined with its sparingly soluble
salt and a strong electrolyte having common anion.
Typical examples are Ag/ AgCl, 1M KCl, Hg/Hg2Cl2, 1M KCl

8. Ag/ AgCl, 1M KCl electrode
Anode: Ag (s)+𝐶𝑙− ⇌ 𝐴𝑔𝐶𝑙 𝑠 + 𝑒− (1)
Cathode: 𝐴𝑔𝐶𝑙 𝑠 + 𝑒− ⇄ 𝐴𝑔(𝑠) + 𝐶𝑙− (2)
𝑂𝑥𝑖𝑑𝑎𝑡𝑖𝑜𝑛: 𝐸𝑜𝑥 = 𝐸𝑜 −
𝑅𝑇
𝐹
ln
1
[𝐶𝑙−]
= 𝐸𝑜 +
𝑅𝑇
𝐹
ln 𝐶𝑙− = 0.197𝑉 + 0 = 0.197𝑉 (3)
𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛: 𝐸𝑟𝑒𝑑 = 𝐸𝑜
−
𝑅𝑇
𝐹
ln 𝐶𝑙−
= 0.197𝑉 − 0 = 0.197𝑉 (4)
It can be seen that the equilibrium is dependent only on the concentration of Cl- ions.
Since the electrode contains sufficiently large amount of KCl (aq), hence the potential of
this electrode remains constant even after application of longer period. Hence, this
electrode is highly used as reference electrode.

9. Q5. Explain why Ag/ AgCl, 1M KCl and calomel electrode are (Hg/Hg2Cl2, 1M KCl) used as reference electrodes.
Calomel electrode are (Hg/Hg2Cl2, 1M KCl)
𝑬𝟎
= 𝟎. 𝟐𝟖𝑽 vs. SHE

10. Electrode of the third kind is a metal electrode assembly with the equilibrium potential being a function of the
concentration of a cation, other than the cation of the electrode metal, in the solution.
3rd electrodes
Pb(s)⎹PbC2O4 (s), CaC2O4 (s), Ca(NO3)2 (aq)
𝑃𝑏(𝑠) + CaC2O4 (s) ⇄ PbC2O4 (s) + 𝐶𝑎2+(𝑎𝑞) + 2𝑒−
The equilibrium is not destroyed as it depends on soluble calcium ions, hence, potential
remains constant.
𝐸 = 𝐸𝑜
−
𝑅𝑇
𝑛𝐹
ln[𝐶𝑎2+
]

11. Potentiometric determination of pH using
quinhydrone electrode system
H2Q Q

12. Potentiometric determination of pH using quinhydrone
electrode system coupled with calomel electrode
(Pt) Hg, Hg2Cl2⎹saturated KCl⎹⎹ H+ solution (unknown pH) +Quinhydrone⎹⎹Pt
Anode: 2Hg (s) +2𝐶𝑙−
(aq) ⇄ 𝐻𝑔2𝐶𝑙2 𝑠 + 2𝑒−
, 𝐸𝑐𝑎𝑙
𝑜
= −0.241 𝑉
Cathode: 𝑄 + 2𝐻+ 𝑎𝑞 + 2𝑒− ⇄ 𝐻2𝑄, 𝐸𝑆𝐶𝐸
𝑜
= 0.699 𝑉
Cell: 𝑄 + 2𝐻+
𝑎𝑞 + 2Hg (s) +2𝐶𝑙−
(aq) ⇄ 𝐻2𝑄 + 𝐻𝑔2𝐶𝑙2 𝑠 𝐸𝑐𝑒𝑙𝑙
𝑜
= −0.241 𝑉 + 0.699 𝑉= 0.458V
𝑁𝑜𝑤, 𝐸𝑐𝑒𝑙𝑙 = 𝐸𝑜 −
𝑅𝑇
𝑛𝐹
ln
1
𝐻+ 2 = 0.458V +
𝑅𝑇
2𝐹
ln 𝐻+ 2 = 0.458V +
2.303𝑅𝑇
𝐹
l𝑜𝑔 𝐻+ = 0.458𝑉 + 0.059𝑙𝑜𝑔 𝐻+
𝑜𝑟, 𝐸𝑐𝑒𝑙𝑙 = 0.458𝑉 − 0.059𝑝𝐻
𝑝𝐻=
0.458𝑉−𝐸𝑐𝑒𝑙𝑙
0.059

13. Potentiometric determination of pH using quinhydrone
electrode system coupled with calomel electrode

14. Potentiometric determination of pH using glass electrode

15. In the glass-electrode method, the known pH of a
reference solution is determined by using two electrodes,
a glass electrode and a reference electrode, and
measuring the voltage (difference in potential) generated
between the two electrodes. The difference in pH between
solutions inside and outside the thin glass membrane
creates electromotive force in proportion to this difference
in pH.
The liquid inside the glass electrode usually has a pH of 7.
Thus, if one measures the electromotive force generated
at the electrode membrane, the pH of the sample can be
found by calculation.
A second electrode is necessary when measuring the
electromotive force generated at the electrode membrane
of a glass electrode. This other electrode, paired with the
glass electrode, is called the reference electrode. The
reference electrode must have extremely stable potential.
Therefore, it is provided with a pinhole or a ceramic
material at the liquid junction.

16. • The glass electrode used to measure
pH is the most common ion-selective
electrode.
• A typical pH combination electrode,
incorporating both glass and reference
electrodes in one body.
• Glass combination electrode with a
silver-silver chloride reference
electrode. The glass electrode is
immersed in a solution of unknown pH
so that the porous plug on the lower
right is below the surface of the liquid.
The two silver electrodes measure the
voltage across the glass membrane.
Potentiometric determination of pH using glass electrode

17. • The potential difference between inner and outer silver-silver chloride
electrodes depends on the chloride concentration in each electrode
compartment and on the potential difference across the glass membrane.
• Because [Cl−] is fixed in each compartment and because [H+] is fixed on the
inside of the glass membrane, the only variable is the pH of analyte
solution outside the glass membrane.
• The voltage of the ideal pH electrode changes by 59.16 mV for every pH-unit
change of analyte activity at 25°C.
Potentiometric determination of pH using glass electrode

18. • 𝐸𝑐𝑒𝑙𝑙 = 𝐸𝑜𝑢𝑡𝑒𝑟.𝑟𝑒𝑓 + 𝐸𝑡𝑒𝑠𝑡
= 𝐸𝐴𝑔,𝐴𝑔𝐶𝑙+(𝐸𝑔𝑙𝑎𝑠𝑠−0.0591𝑝𝐻)
• 𝑝𝐻 =
𝐸𝑐𝑒𝑙𝑙−(𝐸𝑜𝑢𝑡𝑒𝑟.𝑟𝑒𝑓 + 𝐸𝑡𝑒𝑠𝑡)
0.0591
Potentiometric determination of pH using glass electrode
Q6. Explain how pH is determined using (i) Quinhydrone and (ii) Glass electrodes.

19. Enthalpy of reversible cells
𝐺 = 𝐻 − 𝑇𝑆 (1)
𝐺 = 𝐻 − 𝑇𝑆 (2)
𝑑𝐺 = 𝑉𝑑𝑃 − 𝑆𝑑𝑇 (3)
𝑆 = −
𝜕𝐺
𝜕𝑇 𝑃
(4)
∆𝑆 = −
𝜕(∆𝐺)
𝜕𝑇 𝑃
(5)
𝑇ℎ𝑢𝑠, 𝑓𝑟𝑜𝑚 2 𝑏𝑦 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑛𝑔 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓∆𝑆
𝐺 = 𝐻 + 𝑇
𝜕(∆𝐺)
𝜕𝑇 𝑃
(6)
Now, substituting ∆𝐺 = −𝑛𝐸𝐹
−𝑛𝐸𝐹 = 𝐻 − 𝑛𝐹𝑇
𝜕𝐸
𝜕𝑇 𝑃
𝑜𝑟, 𝐻 = −𝑛𝐹𝑇 + 𝑛𝐹𝑇
𝜕𝐸
𝜕𝑇 𝑃
(7)
𝑤ℎ𝑒𝑟𝑒,
𝜕𝐸
𝜕𝑇 𝑃
is known as temperature coefficient
NB: If emf and temperature coefficient of a reversible cell is
know, then using it is possible evaluate heat change of a
revisable electrochemical process using eq.(7).

20. Q7. Deduce an equation to show how enthalpy of a reversible cell changes under constant T &P.
𝑄8. 𝐶𝑜𝑛𝑠𝑖𝑑𝑒𝑟 𝑎𝑛 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑐ℎ𝑒𝑚𝑖𝑐𝑎𝑙 𝑐𝑒𝑙𝑙 Zn⎹ZnCl2(0.01M)⎹⎹AgCl (s), sat. KCl⎹Ag. (i) Write cell reaction
(ii) Calculate emf and free energy change(iii) Calculate equilibrium constant
(iv) If temperature coefficient is −4.0210−4
V𝐾−1
, calculate heat change.
Q9. Evaluate formal potential of Cu2+⎹Cu+ in (i) 0.01M and (ii) 0.5 M HNO3 solutions. Consider that concentrations of copper
salts are negligible compared to the concentration of supporting electrolytes.
Q10. Write down the kinds of electrodes giving examples.