Category: Intermediate Chemistry

Hess’s law is named after Germain Hess, a Russian chemist, who published it in 1840. It is based on the principle of conservation of energy, and states that:

The total enthalpy change in a chemical reaction is sum of enthalpy changes of all steps from the reactants to the products regardless of the route taken.

For example, there are two possible chemical routes (indicated by red arrows in the diagram below) for the combustion of methane to form carbon dioxide and water:

On closer scrutiny, ΔH₁^o is composed of the following standard enthalpy changes of formation:

Similarly, ΔH₂^o is composed of the following standard enthalpy changes of formation:

The choice of the indices R and P will be apparent shortly. Hence,

where v_R and v_P are the stoichiometric coefficients of the products of the respective standard enthalpy change of formation reactions.

In general, for a reaction:

where R denotes the reactants and P denotes the products. Hess’ law states that:

Eq 6 is a very useful formula for calculating standard enthalpy changes.

 

 

 

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The Born-Haber cycle is a method to analyse reaction enthalpies, particularly to calculate the standard enthalpy change of lattice energy, ΔH_latt^o, which cannot be measured precisely via experiments. It is based on Hess’ law and was developed by the German scientists Max Born and Fritz Haber in 1916.

Born-Haber cycles are best represented in the form of energy diagrams. For example, if we want to calculate the standard enthalpy change of lattice energy of calcium fluoride ΔH_latt^o[CaF₂(s)], we start by writing the equations for ΔH_latt^o[CaF₂(s)] and the standard enthalpy change of the formation of calcium fluoride ΔH_f^o[CaF₂(s)] :

Applying Hess’ law, we can combine the two equations into a cycle:

ΔH₁^o is composed of a few standard enthalpy changes. If we rewrite the cycle to include every standard enthalpy change (starting with the reactants of ΔH_f^o), we have the Born-Haber cycle for CaF₂(s):

The Born-Haber cycle (also known as the Born-Haber energy diagram) reveals that ΔH₁^o is composed of:

1. 1. the standard enthalpy change of atomisation of Ca (ΔH^o_at),
   2. the standard enthalpy change of the first ionisation of Ca (ΔH^o_{1st ion}),
   3. the standard enthalpy change of the second ionisation of Ca (ΔH^o_{2nd ion}),
   4. the standard enthalpy change of atomisation of F₂ (ΔH^o_at), and
   5. the standard enthalpy change of electron gain of F (ΔH^o_eg).

It is also evident that the sum of the magnitudes of each enthalpy on the left-hand side of the energy diagram is equal to that on the right-hand side, i.e.

The above computation shows that ΔH^o_latt for CaF₂ can be +2635 kJmol^-1 or -2635 kJmol^-1, depending on its definition. Since we have defined the standard enthalpy change of lattice energy as an endothermic process (see eq7, where ΔH^o_latt is the change in enthalpy to break the bonds in one mole of a solid ionic compound and separate its gaseous ions to an infinite distance under standard conditions),  ΔH_latt^o = +2635 kJmol^-1.

In summary, the steps involved in generating the Born-Haber cycle are:

1. 1. Write the equations for the standard enthalpy change of lattice energy and the standard enthalpy change of formation of the ionic compound.
   2. Combine the two equations into a cycle using Hess’ law.
   3. Expand the cycle in a stepwise manner to include every standard enthalpy change.
   4. Draw the Born-Haber cycle energy diagram starting with the reactants of the standard enthalpy change of formation of the compound and ending with the ionic compound. There is no strict rule regarding what must be on the left or right side of the cycle, provided that the steps are shown sequentially and the arrow directions correctly reflect the signs of the enthalpy changes.
   5. Sum the magnitude of enthalpies on each side of the cycle and equate them to find ΔH_latt^o.

 

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Cell notation is a shorthand representation of an electrochemical cell.

For example, the electrochemical cell depicted in the diagram above has a cell notation of

A vertical line represents a phase boundary, while a double vertical line signifies a phase boundary with negligible junction potential, such as a salt bridge. The anode half-cell is denoted on the left and the cathode half-cell on the right, with the electrodes (Pt and Cu) positioned at both ends of the notation.

A gas is always written adjacent to the electrode. Furthermore, spectator ions are usually omitted and state symbols and concentrations may be included for emphasis, e.g.

If the standard hydrogen electrode is undergoing reduction, its cell notation is:

 

 

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Other than the standard hydrogen electrode (SHE), two other standard or reference electrodes are widely used: the calomel electrode and the silver chloride electrode. Each of these electrodes, like the SHE, provides a constant potential that is insensitive to the electrolyte.

Silver chloride electrode

The silver chloride reference electrode consists of a AgCl coated silver wire dipped in a saturated KCl solution (also saturated with AgCl). The porous frit, which allows for the slow passage of ions, forms a liquid junction with the test solution. The electrode potential of 0.199 V versus SHE at rtp is given by the following half-cell reaction:

Just as the constant bubbling of H₂ in a H⁺ (1 M) electrolyte of the SHE half-cell provides the electrode with a constant potential,  the Ag wire and the equilibrium between AgCl coated on the wire and the saturated AgCl internal solution ensure that the AgCl electrode maintains a constant potential. Some literature quotes the potential vs SHE as 0.22 V at rtp. This value corresponds to a KCl concentration of 1.0 M, whereas 0.199 V is measured when KCl is saturated.

The calomel electrode

The calomel reference electrode consists of mercury in contact with a saturated solution of Hg₂Cl₂ (calomel), which is in turn in contact with saturated KCl. The electrode potential of 0.244 V versus SHE at rtp is given by the following half-cell reaction:

Both AgCl and calomel reference electrodes are used for a wide range of electrochemical measurements. However, the toxicity of mercury in the calomel electrode poses health and environmental issues.

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Standard electrode potentials are crucial measurements that indicate the tendency of a chemical species to gain or lose electrons, providing a fundamental basis for predicting the direction of redox reactions in electrochemistry.

The electrochemical series described in a basic level article is, in fact, a tabulation of the half-cell standard electrode potentials, E^o, of various chemical species. Just as the metal reactivity series compares the reactivity of metals, the electrochemical series lists the reactivity of metals and ions in an electrochemical cell. A summary of the electrochemical series is as follows:-

The more positive the potential of a half-cell is, the more spontaneous its reaction is from left to right. Hence, when we connect two half-cells,

the overall cell potential is:

For example, the combined redox reaction of Zn²⁺/Zn and Cu²⁺/Cu is

Adding the two cell reactions, we have the E_cell reaction equation, whose E_cell value is E_right – E_left:

The above diagram can be simplified by omitting the standard hydrogen electrodes to give:

 

 

 

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What is the effect of concentration on \(E^o\) ?

Consider the following standard electrochemical cell potential:

where [Cu²⁺] = [Ag⁺] = 1 M.

If [Ag⁺] > 1 M, the equilibrium will shift to the right according to Le Chatelier’s principle. This implies that the reaction has become more spontaneous from left to right, resulting in a more positive E^o. Conversely, if [Ag⁺] < 1 M, the equilibrium will shift to the left, giving a less positive E^o. In general, the effects of concentration of chemical species on the electrochemical cell potential is given by the Nernst equation:

where

• • E is the potential of the cell under non-standard conditions, e.g., when T is not 298 K, or concentrations of species are not at 1 M and 1 atm.
  • E^o is the overall standard electrode potential of the cell.
  • R is the gas constant
  • T is temperature
  • n is the number of moles of electrons transferred
  • F is the Faraday constant
  • Q is the reaction quotient, which for the above reaction is:

For example, if [Cu²⁺] = 1.8 M and [Ag⁺] = 0.02 M at rtp,

It is important to note that the Nernst equation applies to situations where no current flows, i.e., it allows the potential of a cell to be calculated under open circuit situations. This means that the calculated value, E, for the above example, is the predicted potential of the cell (containing[ Cu²⁺] = 1.8 M and [Ag⁺] = 0.02 M at rtp), which is connected to an external emf that exactly balances this calculated potential.

 

 

 

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Standard electrode potentials are used to analyse and predict reactions.

Under standard conditions, a reaction is thermodynamically feasible or spontaneous if the standard electrode potential of the electrochemical cell, E_cell, is positive. Let’s look at the following example:

The more positive the potential of a half-cell is, the more spontaneous its reaction from left to right. Hence, the first half-cell equation occurs at the cathode and the second one at the anode. Multiplying the second equation by a factor of three and combining it with the first,

Note that the \(E^o\) value of the second half-cell equation is unchanged when the equation is multiplied by a factor of three. This is because the unit of standard electrode potential is joules per coulomb. When we multiply the equation by three, we triple the number of moles of electrons (coulomb) as well as the amount of energy (joules) conveyed by the electrons. Thus, we say that the value of \(E^o\) is intensive (i.e. doesn’t depend on the amount of matter or the size of the system).

In general, a reaction with a positive E_cell value is thermodynamically feasible. There are, however, exceptions. One such example is

The combined reaction has a positive value of +0.10 V but it does not proceed. This is because the combined reaction, even though thermodynamically feasible, is not kinetically viable, which implies that the activation energy for the reaction is high.

 

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What is the relationship between the Nernst equation and the equilibrium constant?

When an electrochemical cell discharges, its electrolyte’s concentration changes. The concentrations of the reaction species stop changing when the overall reaction reaches equilibrium. When this happens, no electrons flow in the circuit and E = 0. The Nernst equation becomes,

 

where K is the equilibrium constant or the reaction quotient at equilibrium.

Therefore,

For example, the equilibrium constant for the reaction

is

 

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The lithium ion battery is a rechargeable battery that is used in many portable electronic devices. The anode is made of graphite while the cathode is a lithium metal oxide, e.g. lithium cobalt oxide or lithium manganese oxide. The electrolyte consists of lithium salt complexes (e.g. LiBF₄) in a mixture of organic carbonates (e.g. ethylene carbonate).

 

Discharging process

Lithium is oxidised at the anode as follows:

Electrons move to the copper collector and flow out to power an electronic device like a laptop, while lithium ions migrate across the electrolyte to the cathode. On their return, the electrons move from the aluminium collector to the cathode where they participate in the following reduction reaction:

When fully discharged, most of the lithium ions are stored at the cathode in the form of lithium cobalt oxide.

 

Charging process

During charging, an external alternating current power source connected to the circuit is converted to a direct current with a voltage that is higher than that produced by the lithium ion battery, i.e. an over-voltage. Electrons are therefore forced to flow to the anode where the reverse reaction takes place:

As lithium ions are reduced at the graphite electrode which is now the cathode, lithium cobalt oxide at the other electrode undergoes oxidation:

with the free electrons flowing via the aluminium collector out to the circuit and lithium ions migrating back across the electrolyte to the graphite electrode. When fully charged, most of the lithium ions are stored in the form of LiC₆.

The separator is a thin membrane that plays an important role of keeping the two electrodes apart. If it is damaged (punctured, torn or degraded), the electrodes can come into contact with each other, causing a short circuit, which can then lead to thermal runaway, fires or explosions.

 

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The electrolysis of water uses electricity to dissociate water into hydrogen gas and oxygen gas. In this article, we are concerned with the following cases:

1. 1. Electrolysis of pure water
   2. Electrolysis of water with a salt
   3. Electrolysis of acidified water
   4. Electrolysis of alkaline water

1) Electrolysis of pure water

Water is a poor conductor of electricity, as it has a very small auto-ionisation constant (K_w = 10^-14), i.e. water exists predominantly in its molecular form H₂O instead of H⁺ and OH^– ions. Therefore, the electrochemical reaction at the anode involves molecular H₂O rather than OH^–, and the reaction at the cathode involves H₂O instead of H⁺.

At the anode:       2H₂O (l) → O₂ (g) + 4H⁺ (aq) + 4e^–         E^o = -1.23 V

At the cathode:   2e^– + 2H₂O (l) → H₂ (g) + 2OH^– (aq)       E^o = -0.83 V

Overall reaction: 2H₂O (l) → O₂ (g) + 2H₂ (g)                       E^o = -2.06 V

In the bulk solution, H⁺ and OH^– from the autodissociation of water migrate to the cathode and anode respectively, neutralising the OH^– and H⁺ produced at the respective electrodes. However, due to the very small amounts of H⁺ and OH^– from the autodissociation of water, H⁺ (from the anodic reaction) and OH^– (from the cathodic reaction) accumulate at the anode and cathode respectively over time. This produces a counter potential that retards and eventually stops the electrolytic processes at both electrodes.

2) Electrolysis of water with a salt

As described above, the electrolysis of pure water cannot proceed after a while, rendering the process useless. This is why we add compounds to water to allow its electrolysis to proceed unhindered. If we add NaCl to water, the electrode half-cell equations remain the same. However, substantial amounts of Na⁺ and Cl^– are able to migrate to the cathode and anode respectively to compensate the negatively charged OH^– and positively charged H⁺, allowing the electrolysis to continue. The larger the amount of NaCl added, the longer the electrolysis of water proceeds. If NaCl becomes too concentrated, chlorine will be produced at the anode instead of O₂, as Cl^– will be oxidised preferentially.

3) Electrolysis of acidified water

If we add an acid, e.g. H₂SO₄, then instead of NaCl to water, we have

At the anode:       2H₂O (l) → O₂ (g) + 4H⁺ (aq) + 4e^–        E^o = -1.23 V

At the cathode:   2e^– + 2H⁺ (aq) → H₂ (g)                              E^o = 0.00 V

Overall reaction: 2H₂O (l) → O₂ (g) + 2H₂ (g)                      E^o = -1.23 V

4) Electrolysis of alkaline water

If we add a base, e.g. NaOH, to water, we have

At the anode:       4OH^– (aq) → O₂ (g) + 2H₂O (l) + 4e^–       E^o = -0.40 V

At the cathode:   2e^– + 2H₂O (l) → H₂ (g) + 2OH^– (aq)       E^o = -0.83 V

Overall reaction: 2H₂O (l) → O₂ (g) + 2H₂ (g)                        E^o = -1.23 V

Note that the overall standard electrode potential for the electrolysis of acidified water is the same as that for the electrolysis of alkaline water. Since most water electrolysis experiments involve either the addition of an acid or a base to water, the typical overall standard electrode potential quoted is E^o = -1.23 V instead of E^o = -2.06 V.

 

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