Quantitative electrolysis Electrochemistry
Objectives A10.4 Quantitative electrolysis
By the end of this topic you will
The volumes of gases and masses of substances produced during electrolysis
be able to:
can be calculated using t he mole concept t hat you studied in Unit 7. Michael
Faraday (1791–1867) was t he rst person to propose t hat t he mass of a
● dene the Faraday constant
substance produced at an electrode during electrolysis is directly propor tional
● calculate the volumes of gases
to t he quantity of electricity passing t hrough t he electrolytic cell.
and masses of substances
produced during electrolysis.
The quantity of electricity, or quantity of electrical charge, is given t he
symbol Q and is measured in units called coulombs, C. During electrolysis,
electrons ow from t he anode to t he cat hode t hrough electrical wires.
Each electron owing t hrough t hese wires has an electrical charge which is
Did you know?
? extremely small. n fact, t he electrical charge on one electron is so small t hat
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when 1 C of electrical charge ows t hrough a circuit, 6.25 10 electrons
The electrical charge on one
have owed.
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electron is 1.6 10 C. This
means that 1 C of electrical charge
The quantity of electricity or electrical charge owing t hrough an electrolytic
1
___________
is equivalent to cell during electrolysis depends on two factors.
19
1.6 10
electrons.
● The rate of ow of the electrical charge, i.e. the current, which is given
the symbol I and is measured in units called amperes (also known as
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amps), A. A current of 1 amp is equivalent to 1 C, or 6.25 10 electrons,
owing for 1 s.
● The lengt h of time, t, t hat t he current ows for, measured in seconds, s
The quantity of electricity or electrical charge can t hen be calculated using
t he following formula:
quantity of electrical charge (C) current (A) time (s)
i.e. Q I t
Example
Calculate t he quantity of electrical charge t hat ows when a current of 2.0 A
ows in a circuit for 20 min.
Current 2.0 A
Time in seconds 20 60 1200 s
∴ quantity of electrical charge owing 2 1200 C 2400 C
We can relate t his to moles if we consider t he electrical charge which 1 mol
of electrons has. You will recall t hat 1 mol of electrons is equivalent to
Key fact
!
23 19
6.0 10 electrons. The charge on one electron is 1.6 10 C, t herefore,
The Faraday constant is the size
if we have 1 mol of electrons, t hese electrons would have a total charge of
of the electrical charge on one mole
96 500 C. This value is known as t he Farad ay constant
of electrons, i.e. 96 500 C mol .
Dur ing electrolysis, a cation wit h a single positive charge, i.e. M , is
discharged at t he cat hode according to t he following equation:
M e M
This shows t hat 1 mol of electrons is required to discharge 1 mol of M ions
and form 1 mol of M or, applying t he Faraday constant, 96 500 C is required
to discharge 1 mol of M ions and form 1 mol of M. This also applies when
discharging 1 mole of anions wit h a single negative charge at t he anode, i.e.
96 500 C is required.
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Electrochemistry Quantitative electrolysis
The following examples will show how we can use t he Faraday constant
to calculate t he volumes of gases and masses of substances formed during
electrolysis. You will recall t he following quantities t hat relate moles to mass
and volumes of gases.
Molar mass, M mass of 1 mol of a substance.
Molar volume, V volume of 1 mol of a gas.
m
3 3
At stp, V 22.4 dm , at r tp, V 24.0 dm
m m
Examples
1 Calculate t he mass of lead produced at t he cat hode when a current
of 5.0 A ows t hrough molten lead(II) bromide for 16 minutes and
5 seconds.
Determine t he quantity of electricity t hat ows:
Current 5.0 A
Time in seconds (16 60) 5 965 s
∴ quantity of electricity (5.0 965) C 4825 C
Write t he equation for t he reaction at t he cat hode:
2
Pb (l) 2e Pb(l)
From t he equation:
2 mol of electrons are required to form 1 mol Pb.
∴ 2 96 500 C form 1 mol Pb
i.e. 193 000 C form 1 mol Pb
1
________
∴ 1 C forms mol Pb
193 000
1
________
∴ 4825 C forms 4825 mol Pb
193 000
0.025 mol Pb
M(Pb) 207 g mol
i.e. mass of 1 mol Pb 207 g
∴ mass of 0.025 mol Pb 0.025 207 g 5.175 g
2 f an electric current of 2.5 A is passed t hrough dilute sulfuric acid for
2 hours 34 minutes and 24 seconds, calculate t he volume of oxygen
produced at t he anode at r tp.
Determine t he quantity of electricity t hat ows:
Current 2.5 A
Time in seconds (2 60 60) (34 60) 24 9264 s
∴ quantity of electricity (2.5 9264) C 23 160 C
Equation for t he reaction at t he anode:
4OH (aq) 2H O(aq) O (g) 4e
2 2
189
Quantitative electrolysis Electrochemistry
From t he equation:
4 mol electrons are lost in forming 1 mol O
2
∴ 4 96 500 C form 1 mol O
2
i.e. 386 000 C form 1 mol O
2
1
________
∴ 1 C forms mol O
2
386 000
1
________
∴ 23 160 C forms 23 160 mol O
2
386 000
0.06 mol O
2
Volume of 1 mol O at r tp 24.0 dm
2
3 3
∴ volume of 0.06 mol O 0.06 24.0 dm 1.44 dm
2
3 A solution of copper(II) sulfate is electrolysed using copper electrodes.
Determine t he decrease in mass of t he anode if a current of 4.0 A passes
t hrough t he solution for 32 minutes and 10 seconds.
Determine t he quantity of electricity t hat ows:
Current 4.0 A
Time in seconds (32 60) 10 1930 s
∴ quantity of electricity 4.0 1930 C 7720 C
Equation for t he reaction at t he anode:
2
Cu(s) Cu (aq) 2e
From t he equation:
2
2 mol electrons are lost in forming 1 mol Cu ions.
2
∴ 2 96 500 C form 1 mol Cu ions
2
i.e. 193 000 C form 1 mol Cu ions
1
________ 2
∴ 1 C forms mol Cu ions
193 000
1
________ 2
∴ 7720 C forms 7720 mol Cu ions
193 000
21
0.04 mol Cu ions
2 1
M(Cu ) 64 g mol
2
i.e. mass of 1 mol Cu ions 64 g
2
∴ mass of 0.04 mol Cu ions 0.04 64 g 2.56 g
Therefore, decrease in mass of t he anode 2.56 g
4 A steel spoon needs to be electroplated wit h 13 g of chromium.
Calculate the length of time that a current of 15 A would have to ow to
electroplate the spoon when placed as the cathode of the electrolytic cell.
Calculate t he number of moles of chromium which need to be
produced:
M(Cr) 52 g mol
i.e. mass of 1 mol Cr 52 g
13
___
∴ number of moles in 13.0 g mol 0.25 mol
52
190
Electrochemistry Industrial applications of electrolysis
Equation for t he reaction at t he cat hode:
3
Cr (aq) 3e Cr(s)
From t he equation:
3 mol electrons form 1 mol Cr.
∴ 3 96 500 C form 1 mol Cr
i.e. 289 500 C form 1 mol Cr.
∴ 0.25 289 500 C form 0.25 mol Cr 72 375 C
Therefore, t he quantity of electricity required 72 375 C
Calculate t he time taken for 72 375 C to ow using a current of 15 A:
quantity of electricity (C) current (A) time (s)
72 375 C 15 A time (s)
72 375
______
∴ time s
15
4825 s
1 hour 20 minutes 25 seconds
t would take 1 hour 20 minutes 25 seconds to electroplate the spoon.
Summary questions
1 Dene the Faraday constant.
2 Calculate the mass of magnesium that would be deposited on the
cathode when a current of 5.0 A ows through molten magnesium
chloride for 2 hours 40 minutes and 50 seconds.
3 Determine the volume of chlorine that would be produced at the anode
at rtp when a current of 2.5 A ows through concentrated sodium
chloride solution for 51 minutes and 28 seconds.
4 How long must a current of 10.0 A ow through a solution of copper( II)
sulfate to produce 25.6 g of copper at the cathode?
A10.5 Industrial applications of electrolysis Objectives
By the end of this topic you will
Electrolysis is used in many ways in industr y including:
be able to:
● extracting metals from t heir ores
● describe how electrolysis can
● purifying metals, i.e. electrorening
be used to extract metals from
● plating one metal wit h anot her, i.e. electroplating
their ores
● coating a metal wit h its oxide, i.e. anodising.
● describe how electrolysis can
be used to purify metals
We will now look at each of t hese in more detail.
● describe the process of
electroplating
Extraction of metals
● describe the process of
Ver y few metals are found in t heir free state in t he Ear t h’s cr ust. Most are
anodising.
found bonded to ot her elements in ionic compounds known as minerals.
Minerals from which metals can be extracted are known as ores. The process
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