what is conventional representation

A-level Chemistry/AQA/Module 5/Redox equilibria

• 1 OXIDATION AND REDUCTION
• 2.1 Electrode potentials
• 2.2 Creating an emf
• 2.3 Designing electrochemical cells
• 2.4 Standard conditions
• 2.5 Reference electrodes
• 2.6 Conventional Representation of Cells
• 3 THE ELECTROCHEMICAL SERIES
• 4.1 Oxidising agents and reducing agents
• 4.2.1 Displacement reactions
• 4.2.2 Disproportionation
• 4.3 Non-standard conditions
• 4.4 Kinetic stability

OXIDATION AND REDUCTION [ edit | edit source ]

Redox reactions were studied extensively at AS-level. The key points are summarized here:

• The gain and loss of electrons can be shown by means of full equations;

• Oxidation is the loss of electrons. When a species loses electrons it is said to be oxidised. E.g. Fe 2+ à Fe 3+ + e -

• Reduction is the gain of electrons. When a species gains electrons it is said to be reduced. E.g. MnO 4 - + 8H + + 5e - à Mn 2+ + 4H 2 O

• Electrons can in fact never be created or destroyed; they can only be transferred from one species to another. Reactions which involve the transfer of electrons are known as redox reactions.

• Overall redox equations can be created by combining the half-equations for the oxidation process and reduction processes, after multiplying all the coefficients of the species in one of the half-equations by a factor which ensures that the number of electrons gained is equal to the number of electrons lost. E.g. Fe 2+ à Fe 3+ + e - oxidation MnO 4 - + 8H + + 5e - à Mn 2+ + 4H 2 O reduction Multiplying all coefficients in the oxidation reaction by 5: 5Fe 2+ à 5Fe 3+ + 5e - means that 5 electrons are gained and five are lost overall equation: MnO 4 - + 8H + + 5Fe 2+ à Mn 2+ + 4H 2 O + 5Fe 3+

• A species which can accept electrons from another species is an oxidising agent. Oxidising agents are reduced during redox reactions. E.g. MnO 4 - is the oxidizing agent in the above reaction.

• A species which can donate electrons to another species is a reducing agent. Reducing agents are oxidised during redox reactions. E.g. Fe 2+ is the reducing agent in the above reaction.

• The oxidation number of an atom is the charge that would exist on the atom if the bonding were completely ionic.

In simple ions, the oxidation number of the atom is the charge on the ion: Na + , K + , H + all have an oxidation number of +1. O 2- , S 2- all have an oxidation number of -2.

In molecules or compounds, the sum of the oxidation numbers on the atoms is zero: E.g. SO 3 ; oxidation number of S = +6, oxidation number of O = -2. +6 + 3(-2) = 0

In complex ions, the sum of the oxidation numbers on the atoms is equal to the overall charge on the ion. E.g. MnO 4 - ; oxidation number of Mn = +7, oxidation number of O = -2. +7 + 4(-2) = -1 E.g. Cr 2 O 7 2- ; oxidation number of Cr = +6, oxidation number of O = -2. 2(+6) + 7(-2) = -2 E.g. VO 2 + ; oxidation number of V = +5, oxidation number of O = -2. +5 + 2(-2) = +1

In elements in their standard states, the oxidation number of each atom is zero: In Cl 2 , S, Na and O 2 all atoms have an oxidation number of zero.

Many atoms, including most d-block atoms, exist in different oxidation numbers. In complex ions or molecules, the oxidation number of these atoms can be calculated by assuming that the oxidation number of the other atom in the species is fixed.

• Oxidation numbers are useful for writing half-equations:

The number of electrons gained or lost can be deduced from the formula: No of electrons gained/lost = change in oxidation number x number of atoms changing oxidation number

The oxygen atoms are balanced by placing an appropriate number of water molecules on one side.

The hydrogen atoms are balanced by placing an appropriate number of H + ions on one side.

• Disproportionation is the simultaneous oxidation and reduction of the same species. There are many d-block species which readily undergo both oxidation and reduction, and which can therefore behave as both oxidising agents and reducing agents. Cu + , Mn 3+ and MnO 4 2- are all examples:

E.g. Cu + à Cu 2+ + e - oxidation Cu+ + e à Cu reduction

E.g. Mn 3+ + 2H 2 O à MnO 2 + 4H + + e - oxidation Mn 3+ + e - à Mn 2+ reduction

E.g. MnO 4 2- à MnO 4 - + e - oxidation MnO 4 2- + 2H + + 2e - à MnO 2 + 2H 2 O reduction

Species such as these are capable of undergoing oxidation and reduction simultaneously. Disproportionation reactions are special examples of redox reactions.

ELECTROCHEMICAL CELLS [ edit | edit source ]

Electrode potentials [ edit | edit source ].

Consider a zinc rod immersed in a solution containing Zn²⁺ ions (e.g. ZnSO4):

The Zn atoms on the rod can deposit two electrons on the rod and move into solution as Zn²⁺ ions: Zn(s) == Zn²⁺(aq) + 2e This process would result in an accumulation of negative charge on the zinc rod. Alternatively, the Zn²⁺ ions in solution would accept two electrons from the rod and move onto the rod to become Zn atoms: Zn²⁺(aq) + 2e == Zn(s) This process would result in an accumulation of positive charge on the zinc rod.

In both cases, a potential difference is set up between the rod and the solution. This is known as an electrode potential.

A similar electrode potential is set up if a copper rod is immersed in a solution containing copper ions (e.g. CuSO4), due to the following processes: Cu²⁺(aq) + 2e == Cu(s) - reduction (rod becomes positive) Cu(s) == Cu²⁺(aq) + 2e - oxidation (rod becomes negative)

Note that a chemical reaction is not taking place - there is simply a potential difference between the rod and the solution. The potential difference will depend on the nature of the ions in solution, the concentration of the ions in solution, the type of electrode used the temperature.

Creating an emf [ edit | edit source ]

If two different electrodes are connected, the potential difference between the two electrodes will cause a current to flow between them. Thus an electromotive force (emf) is established and the system can generate electrical energy.

The circuit must be completed by allowing ions to flow from one solution to the other. This is achieved by means of a salt bridge - often a piece of filter paper saturated with a solution of an inert electrolyte such as KNO3(aq).

The e.m.f can be measured using a voltmeter. Voltmeters have a high resistance so that they do not divert much current from the main circuit.

The combination of two electrodes in this way is known as an electrochemical cell, and can be used to generate electricity. The two components which make up the cell are known as half-cells.

A typical electrochemical cell can be made by combining a zinc electrode in a solution of zinc sulphate with a copper electrode in a solution of copper sulphate.

The positive electrode is the one which most favours reduction. In this case it is the copper electrode which is positive.

The negative electrode is the one which most favours oxidation. In this case it is the zinc electrode which is negative.

Thus electrons flow from the zinc electrode to the copper electrode. Reduction thus takes place at the copper electrode: Cu²⁺(aq) + 2e à Cu(s) Oxidation thus takes place at the zinc electrode: Zn(s) à Zn²⁺(aq) + 2e

The overall cell reaction is as follows: Zn(s) + Cu²⁺(aq) à Zn²⁺(aq) + Cu(s)

The sulphate ions flow through the salt bridge from the Cu2+(aq) solution to the Zn²⁺(aq) solution, to complete the circuit and compensate for the reduced Cu2+ concentration and increased Zn2+ concentration. The cell reaction including spectator ions can thus be written as follows: CuSO4(aq) + Zn(s) à Cu(s) + ZnSO4(aq).

The external connection must be made of a metallic wire in order to allow electrons to flow. The salt bridge must be made of an aqueous electrolyte to allow ions to flow.

By allowing two chemical reagents to be connected electrically, but not chemically, a reaction can only take place if the electrons flow externally. The chemical energy is thus converted into electrical energy.

Designing electrochemical cells [ edit | edit source ]

Half-cells do not necessarily have to consist of a metal immersed in a solution of its ions. Any half-reaction can be used to create a half-cell.

If the half-reaction does not contain a metal in its elemental state, an inert electrode must be used. Platinum is generally used in this case, as it is an extremely inert metal. If a gas is involved, it must be bubbled through the solution in such a way that it is in contact with the electrode.

A few examples are shown below:

a) Fe3+(aq) + e == Fe2+(aq) A platinum electrode is used, immersed in a solution containing both Fe2+ and Fe3+ ions:

b) Cr2O72-(aq) + 14H+(aq) + 6e == 2Cr3+(aq) + 7H2O(l) A platinum electrode is used, immersed in a solution containing Cr2O72-, H+ and Cr3+ ions:

c) Cl2(g) + 2e == 2Cl-(aq) A platinum electrode is used, immersed in a solution containing Cl- ions. Chlorine gas is bubbled through the solution, in contact with the electrode:

d) 2H+(aq) + 2e == H2(g) A platinum electrode is used, immersed in a solution containing H+ ions. Hydrogen gas is bubbled through the solution, in contact with the electrode:

In addition to making electricity, half-cells provide important information on the relative ability of a half-reaction to undergo oxidation or reduction. The more positive the electrode, the greater the tendency to undergo reduction, and the more negative the electrode, the greater the tendency to undergo oxidation.

Standard conditions [ edit | edit source ]

The electrode potential depends on the conditions used, including temperature, pressure and concentration of reactants.

It is therefore necessary to specify the conditions used when measuring electrode potentials. These conditions are normally set at a temperature of 298 K, a pressure of 1 atm and with all species in solution having a concentration of 1.0 moldm-3. Electrode potentials measured under these conditions are known as standard electrode potentials. They are denoted by the symbol Eo.

It is possible to predict how the electrode potential will vary if non-standard conditions are used by using Le Chatelier’s Principle.

If the oxidizing agent has a concentration greater than 1.0 moldm-3, it is more likely to favour reduction and the electrode potential will be more positive than the standard electrode potential. If it has a concentration of less than 1.0 moldm-3, it is more likely to favour oxidation and the electrode potential will be more negative than the standard electrode potential. For reducing agents, the reverse is true.

E.g.: Fe2+(aq) + 2e == Fe(s) Standard electrode potential = -0.44 V If [Fe2+] = 0.1 moldm-3 the electrode potential = -0.50 V The concentration is lower than standard so reduction is less likely to take place, and hence the electrode potential is more negative than expected.

If the temperature is higher than 298 K, then the system will move in the endothermic direction and the electrode potential will change accordingly.

If the pressure is greater than 1 atm, then the system will move to decrease the pressure and the electrode potential will change accordingly.

In general, a change which favours the reduction direction will make the electrode potential more positive, and a change which favours the oxidation direction will make the electrode potential more negative.

Reference electrodes [ edit | edit source ]

The emf of electrochemical cells is easy to measure, but the individual electrode potentials themselves cannot actually be measured at all; it is only possible to measure the potential difference between two electrodes. Even if another electrode were inserted into the solution, it would set up its own electrode potential and it would only be possible to measure the difference between the two electrodes.

It is therefore only possible to assign a value to a half-cell if one half-cell is arbitrarily allocated a value and all other electrodes are measured relative to it. An electrode used for this purpose is known as a reference electrode. The electrode conventionally used for this purpose is the standard hydrogen electrode.

The gas pressure is fixed at 1 atm, the temperature is 25oC and the H+ ions have a concentration of 1.0 moldm-3.

This electrode is arbitrarily assigned a value of 0.00V.

Using this electrode, it is possible to assign an electrode potential to all other half-cells.

Voltmeters measure potential on the right-hand side of the cell and substract it from the potential on the left-hand side of the cell:

Emf = ERHS - ELHS

If the standard hydrogen electrode is placed on the left-hand side of the voltmeter, therefore, the ELHS will be zero and the emf of the cell will be the electrode potential on the right-hand electrode:

E.g. if the standard Zn2+(aq) + 2e == Zn(s) electrode is connected to the standard hydrogen electrode and the standard hydrogen electrode is placed on the left, the emf of the cell is

The Zn2+(aq) + 2e == Zn(s) half-cell thus has an electrode potential of -0.76V.

E.g. if the Cu2+(aq) + 2e == Cu(s) electrode is connected to the standard hydrogen electrode and the standard hydrogen electrode is placed on the left, the emf of the cell is +0.34V. The Cu2+(aq) + 2e == Cu(s) half-cell thus has an electrode potential of +0.34V.

The standard electrode potential of a half-reaction can be defined as follows:

"The standard electrode potential of a half-reaction is the emf of a cell where the left-hand electrode is the standard hydrogen electrode and the right-hand electrode is the standard electrode in question".

The equation emf = ERHS - ELHS can be applied to electrochemical cells in two ways:

a) If the RHS and LHS electrode are specified, and the emf of the cell measured accordingly, then if the Eo of one electrode is known then the other can be deduced.

E.g. If the standard copper electrode (+0.34V) is placed on the left, and the standard silver electrode is placed on the right, the emf of the cell is +0.46V. Calculate the standard electrode potential at the silver electrode.

Emf = ERHS - ELHS +0.46 = E - (+0.34V) E = 0.46 + 0.34 = +0.80V

b) If both SEP's are known, the emf of the cell formed can be calculated if the right-hand electrode and left-hand electrode are specified.

E.g. If RHS = silver electrode (+0.80V) and LHS is copper electrode (+0.34V), then emf = +0.80 - 0.34 = +0.46V

In fact, the hydrogen electrode is rarely used in practice for a number of reasons: - the electrode reaction is slow - the electrodes are not easily portable - it is difficult to maintain a constant pressure

Once one standard electrode potential has been measured relative to the standard hydrogen electrode, it is not necessary to use the standard hydrogen electrode again. Any electrode whose electrode potential is known could be used to measure standard electrode potentials. Such electrodes are known as secondary standard electrodes. A useful example is the calomel electrode.

Conventional Representation of Cells [ edit | edit source ]

As it is cumbersome and time-consuming to draw out every electrochemical cell in full, a system of notation is used which describes the cell in full, but does not require it to be drawn.

Half-cells are written as follows:

- the electrode is placed on one side of a vertical line. - the species in solution, whether solid, liquid, aqueous or gaseous, are placed together on the other side of the vertical line. - if there is more than one species in solution, and the species are on different sides of the half-equation, the different species are separated by a comma.

E.g. Zn²⁺(aq) + 2e == Zn(s)

E.g. Fe3+(aq) + e == Fe2+(aq)

E.g. Cl2(g) + 2e == 2Cl-(aq)

When two half-cells are connected to form a full electrochemical cell, the cell is written as follows:

- the more positive electrode is always placed on the right - the two half-cells are placed on either side of two vertical broken lines (which represent the salt bridge - the electrodes are placed on the far left and far right, and the other species are placed adjacent to the vertical broken lines in the centre - on the left (oxidation), the lower oxidation state species is written first, and the higher oxidation state species is written second. - on the right (reduction) the higher oxidation state species is written first, and the lower oxidation state species is written second.

E.g. Cell reaction = Zn(s) + 2H+(aq) à Zn2+(aq) + H2(g)

E.g. Cell Reaction = Cu2+(aq) + H2(g) à Cu(s) + 2H+(aq)

E.g. Cell reaction = Ag+(aq) + Fe2+(aq) à Ag(s) + Fe3+(aq)

This method of representing electrochemical cells is known as the conventional representation of a cell, and it is widely used.

One advantage of this notation is that it is easy to see the reduction and oxidation processes taking place.

On the LHS (oxidation): electrode à reduced species à oxidised species On the RHS (reduction): oxidised species à reduced species à electrode

THE ELECTROCHEMICAL SERIES [ edit | edit source ]

If all of the standard electrode potentials are arranged in order, usually starting with the most negative, a series is set up which clearly shows the relative tendency of all the half-reactions to undergo oxidation and reduction. This series is known as the electrochemical series, and a reduced form of this series is shown as follows:

HALF-EQUATION Eo/V

Li+(aq) + e == Li(s) -3.03

K+(aq) + e == K(s) -2.92

Ca2+(aq) + 2e == Ca(s) -2.87

Na+(aq) + e == Na(s) -2.71

Mg2+(aq) + 2e == Mg(s) -2.37

Be2+(aq) + 2e == Be(s) -1.85

Al3+(aq) + 3e == Al(s) -1.66

Mn2+(aq) + 2e == Mn(s) -1.19

V2+(aq) + 2e == V(s) -1.18

Zn2+(aq) + 2e == Zn(s) -0.76

Cr3+(aq) + 3e == Cr(s) -0.74

Fe2+(aq) + 2e == Fe(s) -0.44

2H2O(l) + 2e == H2(g) + 2OH-(aq) -0.42

PbSO4(s) + 2e == Pb(s) + SO42-(aq) -0.36

Co2+(aq) + 2e == Co(s) -0.28

V3+(aq) + e == V2+(aq) -0.26

Ni2+(aq) + 2e == Ni(s) -0.25

Sn2+(aq) + 2e == Sn(s) -0.14

CrO42-(aq) + 4H2O(l) + 3e == Cr(OH)3(s) + 5OH-(aq) -0.13

Pb2+(aq) + 2e == Pb(s) -0.13

CO2(g) + 2H+(aq) + 2e == CO(g) + H2O(l) -0.10

2H+(aq) + 2e == H2(g) 0.00

S4O62-(aq) + 2e == 2S2O32-(aq) +0.09

Cu2+(aq) + e == Cu+(aq) +0.15

4H+(aq) + SO42-(aq) + 2e == H2SO3(aq) + 2H2O(l) +0.17

Cu2+(aq) + 2e == Cu(s) +0.34

VO2+(aq) + 2H+(aq) + e == V3+(aq) + H2O(l) +0.34

Cu+(aq) + e == Cu(s) +0.52

I2(aq) + 2e == 2I-(aq) +0.54

2H+(aq) + O2(g) + 2e == H2O2(aq) +0.68

Fe3+(aq) + e == Fe2+(aq) +0.77

Ag+(aq) + e == Ag(s) +0.80

2H+(aq) + NO3-(aq) + e == NO2(g) + H2O(l) +0.81

VO2+(aq) + 2H+(aq) + e == VO2+(aq) + H2O(l) +1.02

Br2(aq) + 2e == 2Br-(aq) +1.09

2IO3-(aq) + 12H+(aq) + 10e == I2(aq) + 6H2O(l) +1.19

O2(g) + 4H+(aq) + 4e == 2H2O(l) +1.23

MnO2(s) + 4H+(aq) + 2e == Mn2+(aq) + 2H2O(l) +1.23

Cr2O72-(aq) + 14H+(aq) + 6e == 2Cr3+(aq) + 7H2O(l) +1.33

Cl2(g) + 2e == 2Cl-(aq) +1.36

PbO2(s) + 4H+(aq) + 2e == Pb2+(aq) + 2H2O(l) +1.46

MnO4-(aq) + 8H+(aq) + 5e == Mn2+(aq) + 4H2O(l) +1.51

PbO2(s) + 4H+(aq) + SO42-(aq) == PbSO4(s) + 2H2O(l) +1.69

MnO4-(aq) + 4H+(aq) + 3e == MnO2(s) + 2H2O(l) +1.70

H2O2(aq) + 2H+(aq) + 2e == 2H2O(l) +1.77

Ag2+(aq) + e == Ag+(aq) +1.98

F2(g) + 2e == 2F-(aq) +2.87

• Note that all half-equations are written as reduction processes. This is in accordance with the IUPAC convention for writing half-equations for electrode reactions.

The electrochemical series has a number of useful features:

• All the species on the left-hand side of the series are can accept electrons and be reduced to a lower oxidation state. They are therefore all oxidising agents. All the species on the right-hand side of the series can give up electrons and be oxidised to a higher oxidation state, and are thus reducing agents.

• The higher a half-equation is located in the electrochemical series, the more negative the standard electrode potential and the greater the tendency to undergo oxidation. The reducing agents at the top of the series are thus very strong, and the oxidising agents very weak. The lower down a half-equation is located in the electrochemical series, the more positive the standard electrode potential and the greater the tendency to undergo reduction. The oxidising agents at the bottom of the series are thus very strong, and the reducing agents very weak.

It can therefore be deduced that: i) oxidising agents increase in strength on descending the electrochemical series ii) reducing agents decrease in strength on descending the electrochemical series

• If two half-cells are connected, the half-cell higher up the electrochemical series (i.e. more negative) will undergo oxidation and the half-cell lower down the electrochemical series (i.e. more positive) will undergo reduction.

• Many of these electrode potentials cannot be measured experimentally, since one of the species involved reacts with water. In such cases the standard electrode potentials are calculated, often using a complex Born-Haber cycle.

SPONTANEOUS REACTIONS [ edit | edit source ]

If two half-cells are connected electrically and a current allowed to flow, the more positive electrode will undergo reduction and the more negative electrode will undergo oxidation. The oxidising agent at the more positive electrode is reduced, and thus oxidises the reducing agent at the more negative electrode.

E.g. If the zinc electrode and the copper electrode are connected, the following reaction takes place: Zn(s) + Cu2+(aq) à Zn2+(aq) + Cu(s)

It can be assumed that if a reaction occurs electrochemically, it will also occur chemically. Thus if zinc metal is added to a solution of copper (II) sulphate, the above reaction will occur. If copper metal is added to a solution of zinc (II) sulphate, however, no reaction will occur. If any reaction did occur, it would have to be Cu(s) + Zn2+(aq) à Cu2+(aq) + Zn(s)

This reaction is not the one which takes place if the two half-cells are connected, and therefore cannot be expected to take place in other circumstances.

Oxidising agents and reducing agents [ edit | edit source ]

Since the more positive electrodes are at the bottom of the electrochemical series, the oxidising agents in these systems will oxidise any reducing agent which lies above it in the electrochemical series.

E.g. H+(aq) will oxidise Pb(s) to Pb2+(aq), and any other metal above it, but will not oxidise Cu(s) to Cu2+(aq) or any metal below it. Pb(s) + 2H+(aq) à Pb2+(aq) + H2(g)

Acids such as nitric acid, however, which contains the more powerful oxidising agent NO3-(aq), will oxidise any reducing agent with a standard electrode potential more negative than +0.81V, e.g. Cu(s) Cu(s) + 4H+(aq) + 2NO3-(aq) à Cu2+(aq) + 2NO2(g) + 2H2O(l)

Reducing agents will reduce any oxidising agent which lies below it in the electrochemical series.

E.g. Fe2+(aq) will reduce VO2+(aq) to VO2+(aq), but not VO2+(aq) to V3+(aq) or V3+(aq) to V2+(aq) VO2+(aq) + 2H+(aq) + Fe2+(aq) à VO2+(aq) + H2O(l) + Fe3+(aq)

Cell potential [ edit | edit source ]

A more systematic method of predicting whether or not a reaction will occur is to construct two half-equations, one reduction and one oxidation, for the reaction trying to take place. Since reduction occurs at the more positive electrode, consider the reduction process to be the right-hand electrode and the oxidation process to be the left-hand electrode. The cell potential for the reaction is given by ERHS - ELHS, or EReduction - EOxidation. If the cell potential is positive, the reaction will occur. If the cell potential is negative, the reaction will not occur. This method can be used to predict whether or not any given redox reaction will take place.

Displacement reactions [ edit | edit source ]

E.g. Predict whether or not zinc metal will displace iron from a solution of FeSO4(aq). The reaction under consideration is Zn(s) + Fe2+(aq) == Zn2+(aq) + Fe(s) Reduction: Fe2+(aq) + 2e == Fe(s) (Eo = -0.44V) Oxidation: Zn(s) == Zn2+(aq) + 2e (Eo = -0.76V) ECELL = -0.44 -(-0.76) = +0.32V So the reaction will occur.

E.g. Predict whether or not zinc metal will desplace manganese from a solution of MnSO4(aq) The reaction under consideration is Zn(s) + Mn2+(aq) à Zn2+(aq) + Mn(s) Reduction: Mn2+(aq) + 2e == Mn(s) (Eo = -1.19V) Oxidation: Zn(s) == Zn2+(aq) + 2e (Eo = -0.76V) ECELL = -1.19 -(0.76) = -0.43V So the reaction will not occur.

E.g. Predict whether or not bromine will displace iodine from a solution of KI(aq) The reaction under consideration is Br2(aq) + 2I-(aq) == 2Br-(aq) + I2(aq) Reduction: Br2(aq) + 2e == 2Br-(aq) (Eo = +1.09V) Oxidation: 2I-(aq) == I2(aq) + 2e (Eo = +0.54V) ECELL = 1.09 - 0.54 = +0.55V So the reaction will occur.

E.g. Predict whether or not bromine will displace chlorine from a solution of NaCl(aq) The reaction under consideration is Br2(aq) + 2Cl-(aq) == 2Br-(aq) + Cl2(aq) Reduction: Br2(aq) + 2e == 2Br-(aq) (Eo = +1.09V) Oxidation: 2Cl-(aq) == Cl2(aq) + 2e (Eo = +1.36V) ECELL = 1.09 - 1.36 = -0.27V So the reaction will not occur.

Disproportionation [ edit | edit source ]

Standard electrode potentials can be used to predict whether or not a species will disproportionate.

E.g. Predict whether or not Ag+ ions will disproportionate in aqueous solution. Ag+ might be expected to disproportionate according to the following half-reactions: Ag+(aq) + e == Ag(s) reduction, Eo = + 0.80V Ag+(aq) == Ag2+(aq) + e oxidation, Eo = + 1.98V ECELL = 0.80 - 1.98 = -1.18V Therefore Ag+ will not disproportionate

E.g. Predict whether or not H2O2 will disproportionate in aqueous solution. H2O2 might be expected to disproportionate according to the following half-reactions: H2O2(aq) + 2H+(aq) + 2e == 2H2O(l) reduction, Eo = +1.77V H2O2(aq) == 2H+(aq) + O2(g) + 2e oxidation, Eo = +0.68V ECELL = 1.77 - 0.68 = +1.09V Therefore H2O2(aq) will disproportionate: 2H2O2(aq) + 2H+(aq) à 2H+(aq) + O2(g) + 2H2O(l) 2H2O2(aq) à 2H2O(l) + O2(g)

Non-standard conditions [ edit | edit source ]

Though cell potential is often a correct prediction of whether or not a given reaction will take place, it does strictly apply only to standard conditions. If the solutions used are either very concentrated or very dilute, then the electrode potentials will not be the standard electrode potentials and the sign of the cell potential may be different from that predicted under standard conditions. Thus many reactions which are not expected to occur do in fact take place if the solutions are hot or concentrated, and many reactions which are expected to occur do not take place if the solutions are too dilute.

E.g. The reaction between manganese dioxide and hydrochloric acid. MnO2(s) + 4H+(aq) + 2Cl-(aq) à Mn2+(aq) + Cl2(g) + 2H2O(l) Reduction: MnO2(s) + 4H2+(aq) + 2e == Mn2+(aq) + 2H2O(l) Eo = +1.23V Oxidation: 2Cl-(aq) àCl2(g) + 2e Eo = +1.36V ECELL = Er - Eo = -0.13V

This reaction does not occur under standard conditions. However if hot concentrated HCl is used, the high Cl- concentration favours oxidation, the electrode potential becomes less positive and ECELL thus becomes positive and the reaction occurs.

E.g. The reaction between potassium dichromate (VI) and hydrochloric acid. Cr2O72-(aq) + 14H+(aq) + 6Cl-(aq) à 2Cr3+(aq) + 3Cl2(g) + 7H2O(l) Reduction: Cr2O72-(aq) + 14H+(aq) + 6e == 2Cr3+(aq) + 7H2O(l) Eo = +1.33V Oxidation: 2Cl-(aq) == Cl2(g) + 2e Eo = +1.36V ECELL = Er - Eo = -0.03V This reaction does not occur under standard conditions. However if solid potassium dichromate is dissolved in hydrochloric acid, the high Cr2O72- concentration favours reduction and makes the electrode potential more positive. Thus ECELL becomes positive and the reaction occurs.

Kinetic stability [ edit | edit source ]

Cell potentials can be used effectively to predict whether or not a given reaction will take place, but they give no indication as to how fast a reaction will proceed. In many cases ECELL is positive but no apparent reaction occurs. This is because the reactants are kinetically stable; the reaction has a high activation energy so is very slow at room temperature. There are many examples of this in inorganic chemistry:

E.g. Mg(s) + 2H2O(l) à Mg2+(aq) + 2OH-(aq) + H2O(g) E = -0.42V, E = -2.38V so ECELL = Er - Eo = +1.96V So a reaction is expected but no reaction takes place. This is because the activation energy is too high (magnesium will react with steam and slowly with hot water).

Thus if a reaction is expected to take place but is found not to, there are two possible reasons: - the solutions are too dilute (i.e. conditions are non-standard) - the reaction is very slow (i.e. reactants are kinetically stable)

If a reaction is not expected to take place but does take place, then it is because the conditions are non-standard (i.e. the solutions are concentrated).

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Electrochemical Cell Conventions

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Using chemical reactions to produce electricity is now a priority for many researchers. Being able to adequately use chemical reactions as a source of power would greatly help our environmental pollution problems. In this section of electrochemistry, we will be learning how to use chemical reactions to produce this clean electricity and even use electricity to generate chemical reactions. In order to induce a flow of electric charges, we place a strip of metal (the electrode) in a solution containing the same metal, which is in aqueous state. The combination of an electrode and its solution is called a half cell . Within the half cell, metals ions from the solution could gain electrons from the electrode and become metal atoms;or the metal atoms from the electrode could lose electrons and become metals ions in the solution.

Introduction

We use two different half cells to measure how readily electrons can flow from one electrode to another, and the device used for measurement is called a voltmeter. The voltmeter measures the cell potential, denoted by E cell , (in units of Volts, 1 V=1 J/C), which is the potential difference between two half cells. The salt bridge allows the ions to flow from one half cell to another but prevents the flow of solutions.

As indicated in the diagram, the anode is the electrode where oxidation occurs; \(\ce{Cu}\) loses two electrons to form \(\ce{Cu^{+2}}\). The cathode is the electrode where reduction occurs; \(\ce{Ag^{+} (aq)}\) gains electron to become \(\ce{Ag(s)}\). As a convenient substitution for the drawing, we use a cell diagram to show the parts of an electrochemical cell. For example above, the cell notation is:

\[\underbrace{\ce{Cu(s) | Cu^{2+} (aq)}}_{\text{oxidation half-reaction}} \,||\, \underbrace{\ce{Ag^{+} (aq)| Ag(s)}}_{\text{reduction half-reaction}} \nonumber \]

Where we place the anode on the left and cathode on the right, "\(|\)" represents the boundary between the two phases, and "\(||\)" represents the salt bridge. There are two types of electrochemical cells:

A Galvanic Cell (aka Voltaic Cell) induces a spontaneous redox reaction to create a flow of electrical charges, or electricity. Non-rechargeable batteries are examples of Galvanic cells.

• A Reaction is spontaneous when the change in Gibb’s energy, \(∆G\) is negative.
• Electrons flow from the anode(negative since electrons are built up here) to the cathode (positive since it is gaining electrons).

An Electrolytic cell is one kind of battery that requires an outside electrical source to drive the non-spontaneous redox reaction. Rechargeable batteries act as Electrolytic cells when they are being recharged.

• A reaction is non-spontaneous when ∆G is > 0.
• Must supply electrons to the cathode to drive the reduction, so cathode is negative.
• Must remove electrons from the anode to drive the oxidation, so anode is positive.

Similarities between Galvanci and Electrolytic Cells

Both Galvanic and Electrolytic cells contain:

• Two electrodes: the anode where oxidation occurs and the cathode where reduction occurs (note that Cathode does not mean +, and Anode does not mean -)
• Volt meter: measures the electric current. In galvanic cells, this shows how much voltage is produced and in electrolytic cells, this shows how much voltage is applied to the system.
• conducting medium
• has contact with electrodes
• usually in aqueous solution of ionic compounds
• joins the two halves of the electrochemical cell
• filled with a salt solution or gel
• keeps the solution separate
• Completes the circuit

Basic Terminology

Electrochemical cells use a vast amount of terminology. Here is a brief definition of some of the more common terms:

• Voltage: The potential difference between two half cells, also the amount of energy that drives a reaction. Voltage is an intensive property (amount of voltage does matter).
• Current: The flow of electric charges (in units of electrons per second). It is an extensive property (amount of current does matter). NOTE: High voltage does not mean high current.
• Primary Battery: non-rechargeable batteries. AA, AAA, etc.
• Secondary Battery: Rechargeable batteries. Lithium, cell phone batteries, etc.
• Tertiary Battery also called Fuel cells. Although not always considered as batteries, these often require a constant flow of reactants.

Galvanic Cell (aka Voltaic Cells)

A galvanic cell produces an electrical charge from the flow of electrons. The electrons move due to the redox reaction. As we can see in Figure \(\PageIndex{1}\), \(\ce{Cu(s)}\) oxidizes to \(\ce{Cu^{2+}(aq)}\), while \(\ce{Ag^{+}(s)}\) reduces to \(\ce{Ag(s)}\). The cell notation for this cell is:

\[\underbrace{\ce{Cu (s) | Cu^{2+} (aq)}}_{\text{oxidation half-reaction}} \,||\, \underbrace{\ce{Ag^{+} (aq)| Ag(s)}}_{\text{reduction half-reaction}} \nonumber \]

To understand the cell, solve the redox equation.

First, split the reaction into two half reactions, with the same elements paired with one another.

\[\underbrace{\ce{Cu(s) -> Cu^{+2}(aq)}}_{\text{Oxidation reaction occurs at the Anode}} \nonumber \]

\[\underbrace{\ce{Ag^{+}(aq) -> Ag(s)}}_{\text{Reduction reaction occurs at the Cathode}} \nonumber \]

Next, we balance the two equations.

\[\text{Oxidation}: \ce{Cu(s) -> Cu^{2+}(aq) + 2e^{-} (Anode)} \nonumber \]

\[\text{Reduction}: \ce{e^{-} + Ag^{+}(aq) → Ag(s) (Cathode)} \nonumber \]

Finally, we recombine the two equations.

\[\ce{Cu(s) + 2Ag^{+}(aq) -> Cu^{2+}(aq) + 2Ag(s)} \nonumber \]

This is a spontaneous reaction that releases energy so this system does work on the surroundings.

Galvanic cells are quite common. A, AA, AAA, D, C, etc. batteries are all galvanic cells. Any non-rechargeable battery that does not depend on an outside electrical source is a Galvanic cell.

Electrolytic Cell

An electrolytic cell is a cell which requires an outside electrical source to initiate the redox reaction. The process of how electric energy drives the non-spontaneous reaction is called electrolysis . Whereas the galvanic cell used a redox reaction to make electrons flow, the electrolytic cell uses electron movement (in the source of electricity) to cause the redox reaction. In an electrolytic cell, electrons are forced to flow in the opposite direction. Since the direction is reversed of the voltaic cell, the E 0 cell for electrolytic cell is negative. Also, in order to force the electrons to flow in the opposite direction, the electromotive force that connects the two electrode-the battery must be larger than the magnitude of \(E^o_{cell}\). This additional requirement of voltage is called overpotential .

Reaction in Figure \(\PageIndex{1}\) can be switched by applying a voltage

\[\underbrace{\ce{Ag(s) -> Ag^{+}(aq) + e^{-}}}_{\text{Oxidation reaction occurs at the Anode}} \nonumber \]

\[\underbrace{\ce{Cu^{+2}(aq) + 2e^{-} -> Cu(s)}}_{\text{Reduction reaction occurs at the Cathode}} \nonumber \]

with the opposite total reaction

\[\ce{Cu^{2+}(aq) + 2Ag(s) ->[\text{applied voltage}] Cu(s) + 2Ag^{+}(aq)} \nonumber \]

• Galvanic: turns chemical energy into electrical energy
• Electrolytic Cell: turns electrical energy into chemical energy

The most common form of Electrolytic cell is the rechargeable battery (cell phones, mp3's, etc) or electroplating. While the battery is being used in the device it is a galvanic cell function (using the redox energy to produce electricity). While the battery is charging it is an electrolytic cell function (using outside electricity to reverse the completed redox reaction).

• Petrucci, Harwood, Herring, and Madura. General Chemistry: Principles and Modern Applications: Ninth Edition. New Jersey: Pearson, 2007.
• Professor Delmar Larsen. Lecture 2, 3, and 6. Spring 2010
• Rieger, Philip. Electrochemistry . 2, Illustrated. Springer Us, 1994. 112-113. Print.
• Hamann, Carl, Andrew Hamnett, and Wolf Vielstich. Electrochemistry . 2, Illustrated. Vch Verlagsgesellschaft Mbh, 2007. 82. Print.

Conventional Representation(Cancelled Nov 1959) ARP591

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Machine Drawing by N. D. Junnarkar

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Conventional Representation of Machine Components

This chapter contains symbolic representation of different commonly used mechanical components for assembly drawing work

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8.1 GENERAL DISCUSSION

A machine drawing is a graphical representation of assemblies and subassemblies of machine components. Here, either two or more than two components are involved in assembly. In many cases, common machine components like grears, ...

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Conventional cell

From online dictionary of crystallography.

Maille conventionnelle ( Fr ). Konventionelle Zelle ( Ge ). Cella convenzionale ( It ). 慣用単位胞 ( Ja ). Celda convencional ( Sp ).

For each lattice, the conventional cell is the cell obeying the following conditions:

• its basis vectors define a right-handed axial setting;
• its edges are along symmetry directions of the lattice;
• it is the smallest cell compatible with the above condition.

Crystals having the same type of conventional cell belong to the same crystal family .

• Primitive cell
• Chapter 1.3.2.4 of International Tables for Crystallography, Volume A , 6th edition
• Fundamental crystallography

Mechanical Engineering

Mother of all inovations, conventional representation of machine components.

 When the drawing of a component in its true projection involves a lot of time, its convention may be used to represent the actual component. Images shows typical examples of conventional representation of various machine components used in engineering drawing.

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Conventional Representation

To draw every part of a workpiece in full detail would be very time-consuming and would also be likely to make the drawing less readable. This particularly applies to parts that are often repeated, such as screw threads. Over the years, therefore, draughtsmen have developed many conventions or symbols to replace the detail representation of the feature these have gradually been standardised on a more or less international basis. I have already dealt with those referring to the sectioning of different materials on page 40. Figs 56 and 57 illustrate those referring to machine parts. In almost every case the convention is a stylised version of the appearance of the finished part.

In Fig. 56 are those for screw threads: (a), (b) and (c) show a semi-pictorial type for external, internal in section, and thread in hidden detail. Neither the pitch nor the core diameter are strictly to scale but should be in good proportion. Note that the extra penetration of the tapping drill is shown. This is a simple method, very clear even to a layman, and about the only way in which a male thread may be sectioned to show internal detail as at (d). It is very easy to draw, though can be ragged if hurried.

The type shown at (a), (f) and (g) was the British Standard preferred for many years. The thin lines represent the tops of the threads and the thick ones the root. Again, neither pitch nor core diameter need be accurately to scale. Draughtsmen would reverse their tee-squares on the board and use the tapered backs to get the slight angle to the lines. Note that (a) shows a right-hand thread and so does (b), although it appears to be reversed; this is because you are seeing the backot the thread in section. In more recent years the lines were drawn without slope, as at (h). There is no disadvantage, as the type of thread must be specified anyway.

The current British Standard convention is shown in (j), (k) and (I). Note the line showing the depth of full thread, and the slight taper beyond it to indicate the imperfect threads at the ends. It is clearly much quicker to draw than either of the other conventions.

All three methods are acceptable, and you can choose that which suits you best. However, for amateur use I would avoid the third type (j) to (I). It does not look like a

Fig.56 Conventional representation of screw threads.

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Readers' Questions

What is the drawing conventional reprsentation?

The drawing conventional representation is an illustration of an object or scene, usually in an artistic style. It is a visual representation of something that can be interpreted by the viewer.

What are conventional representation of materials?

Conventional representation of materials includes sketches and drawings, photographs, physical models, computer-generated models and animations, and augmented or virtual reality models.

What is the conventional representation of external screw thread?

A conventional representation of an external screw thread is a cross-section view of the thread that shows the profile, helix angle, and pitch. This representation is usually in the form of a line drawing.

Design Representations

• First Online: 26 October 2021

Cite this chapter

• Paolo Citti 4 ,
• Alessandro Giorgetti 4 ,
• Filippo Ceccanti 4 ,
• Fernando Rolli 4 ,
• Petra Foith-Förster 5 &
• Christopher A. Brown 6  

2261 Accesses

The results of design activities must be transmitted to people who need them for their tasks, e.g., manufacturing, construction, software development, etc. The objectives of this chapter are to understand how design information should be represented and conveyed using standards, geometric drawings, design matrices for the complete system, DP i /DP j matrices, and industry-specific functional diagrams. The goal of this chapter is to introduce how the design information is typically conveyed to its ultimate user.

Proper descriptions of design must address the needs of the users of the design results. For example, the manufacturing group may need the information on the geometry of each part, acceptable tolerances for each dimension, materials, the hardness of each piece, the complete assembly of the system, etc. On the other hand, those charged with the task of evaluating and implementing the design may need information on the entire assembly of parts, operating procedure, power requirements, etc. To facilitate these processes, different professional groups have established commonly used methods, conventions, and practices.

The “design information” is typically represented using representation methods that are used in a given profession, sometimes adapted by each company to deal with their specific needs. This chapter reviews some of the fundamental representation methods of design that have been developed by various professional groups, typically non-government entities. For instance, there are national professional organizations such as the American Society of Mechanical Engineers (ASME) that have established the standards for certain products such as pressure vessels and boilers to assure the safety of certain products. Globally, there is the International Organizations for Standardization (ISO), an international non-governmental organization that has established voluntary international standards, which facilitates world trade by providing common standards worldwide.

In this book that emphasizes Axiomatic Design (AD), the relationship between functional requirements (FRs) and design parameters (DPs) is the basis for product design. In AD, the design process begins with the identification of FRs first, followed by the development of DPs, which are specifically chosen to satisfy the FRs. Therefore, in AD, the relationship between FRs and DPs forms the core of design representation, in addition to the representation of geometric shapes in the case of the design that involves solid objects. A design matrix is a form of design representation that describes the relationship between the functions and physical entities. The design matrix between FRs and DPs is the most effective means of identifying the coupled designs that are to be avoided in AD.

To highlight the powerfulness of the design matrix representation and the wide applicability of AD, several families of representations, as stated above, have been considered. In particular, the chapter is structured in such a way to explain, in a first instance, what should be the connections between designing with AD and representing the results. The concept of module and tolerance will be introduced. Therefore, representation families will be presented: standard mechanical drawing, piping and instrumentation diagram (P&ID), and software. A case study is presented as well, to bring a real example of a complete application of AD. The choice to illustrate both mechanical drawing and software representation comes to the authors’ will to emphasize that the design process should follow a structured approach, in particular, the AD one, regardless the nature of what is designed.

Proper descriptions of a design must address the needs of a variety of users of the design information. Some may only be interested in knowing the functional and physical relationships in terms of FR and DP hierarchy. Some may need to exact geometric details of the designed parts in terms of DPs, their tolerances, the geometric shape, and their relationships. Some may need the information on the assembly of DPs, i.e., information on DP i /DP j relationships. The objectives of this chapter are to describe how design information is typically represented and conveyed using standards, geometric drawings, design matrices, DP i /DP j matrices, and industry-specific functional diagrams.

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Brown C (2011) Axiomatic design applied to a practical example of the integrity of shaft surfaces for rotating lip seals. Procedia Eng 19:53–59. https://doi.org/10.1016/j.proeng.2011.11.079

Brown C, Hansen H, Jiang X, Blateyron F, Berglund J, Senin N, Bartkowiak T, Dixon B, Le Goïc G, Quinsat Y, Stemp W, Thompson M, Ungar P, Zahouani H (2018) Multiscale analyses and characterizations of surface topographies. CIRP Ann. https://doi.org/10.1016/j.cirp.2018.06.001

Do SH, Suh NP (2000) Object-oriented software design with axiomatic design. In: Thomp-son MK (ed) First international conference on axiomatic design, Institute for Axiomatic Design, Axiomatic Design Solutions, Inc., Cambridge, MA, pp 278–284. https://axiomaticdesign.com/technology/icad/icad2000/icad2000_027.pdf

Foley JT, Símonarson AF, Símonarson HT, Ægisson LF, Goethe AT (2017) ADjustadesk—an adjustable height desk. In: Slǎtineanu L (ed) 11th international conference on axiomatic design (ICAD), MATEC Web of Conferences, Iasi, Romania, 01002, p 7

Girgenti A, Pacifici B, Ciappi A, Giorgetti A (2016) An axiomatic design approach for customer satisfaction through a lean start-up framework. In: Liu A (ed) 10th international conference on axiomatic design (ICAD), Procedia CIRP, Elsevier ScienceDirect, Xi’an, Shaanxi, China, vol 53, pp 151–157. https://doi.org/10.1016/j.procir.2016.06.101

Helgason H, Þórarinsson T, Ingvason S, Foley JT (2018) Design of a tablet holder with the help of axiomatic design. In: Puik E, Foley JT, Cochran D, Betasolo M (eds) 12th international conference on axiomatic design (ICAD), MATEC web of conferences, Reykjavík, Iceland, p. 7

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Citti, P., Giorgetti, A., Ceccanti, F., Rolli, F., Foith-Förster, P., Brown, C.A. (2021). Design Representations. In: Suh, N.P., Cavique, M., Foley, J.T. (eds) Design Engineering and Science. Springer, Cham. https://doi.org/10.1007/978-3-030-49232-8_4

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