Category: Intermediate Chemistry

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.

 

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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, 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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The standard hydrogen electrode (SHE) has the following specifications:

1. • hydrogen gas at 1 bar or 100 kPa in equilibrium with a 1.00 mol dm^-3 solution (strictly speaking, the parameter is not [H⁺] = 1 M but , where is the activity of hydrogen. For simplicity, we have assumed ).
   • a platinum black (finely divided platinum) coated platinum electrode in contact with both gas and solution
   • electrode potential of SHE is defined as 0V.

We can measure and record the electrode potential of a half-cell of electrolyte activity of 1, or for simplicity, of electrolyte concentration of 1.00 mol dm^-3, by connecting it to the SHE. To maintain consistency in data reporting and avoid confusion, we adhere to the IUPAC convention as follows:

1. 1. Place the SHE on the left and the half-cell of interest on the right.
   2. Connect the positive lead of a high impedance voltmeter to the right-hand electrode and the ground lead to the left-hand electrode. Note that with the voltmeter connected in series to the circuit, we are measuring the potential difference of an open circuit with almost no current flowing. This is an accurate way to measure the potential difference, as it allows the concentration of the electrolytes to remain at 1.00 mol dm^-3. Alternatively, we can use a potentiometer.
   3. The potential difference of the electrochemical cell, E_cell, is defined as E_cell = E_right – E_left.
   4. E_cell, measured at 25^oC, is called the standard electrode potential, and is defined as a reduction potential, i.e. the potential for the reaction:

By following this convention, the value of E_cell , which is equal to E_right, measures the spontaneity of the half-cell reaction from left to right. For example, the diagram below shows that H₂ is oxidised to H⁺ in the left half-cell, with the electron migrating to the right cell where Cu²⁺ is reduced to Cu. 

The voltmeter records a value of +0.34V at 25^oC. Since,

the electrode potential of E_right is +0.34 V by convention, and represents the reduction half-cell reaction of

We call this electrode potential the standard electrode potential of Cu²⁺/Cu and denote it with the symbol, E^o.

The electrochemical cell can be regarded as a battery with its positive end connected to the positive lead of the voltmeter. The current flows from the positive end of the battery (Cu electrode) to the negative end of the battery (H electrode). Along the way, it flows through the voltmeter and gives it a positive reading,

An electrochemical reaction is spontaneous when its Gibbs reaction energy, Δ_rG^o = –nFE^o, is less than zero. Since the value of E_cell or E^o is positive, the Cu²⁺/Cu half-cell reaction is spontaneous from left to right and the overall electrochemical cell reaction is

Let’s replace the half-cell with a Zn electrode in aqueous ZnSO₄. The voltmeter now records a value of -0.76 V. Since,

the electrode potential of E_right = -0.76 V, by convention, represents the reduction half-cell reaction of

E^o is now negative, meaning that the Zn²⁺/Zn half-cell reaction is not spontaneous from left to right. However, the fact that a current flows in the electrochemical cell is evidence that reactions are occurring in both half-cells. Furthermore, the current flow is reversed, which implies that the Zn²⁺/Zn half-cell reaction is spontaneous in the opposite direction, with Zn oxidising to Zn²⁺ because Zn is more electropositive than H.

Therefore, in the SHE, H₂ must be reduced to H⁺ and the overall electrochemical cell reaction is:

By replacing the right hand half-cell with different systems, we can measure their standard electrode potentials and tabulate the data to give the electrochemical series.

 

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As mentioned in a basic level article, an electrode potential arises due to the formation of an electric double layer.

To quantify the electrode potential of a metal/metal-ion system, such as Zn²⁺/Zn, we need to connect one lead of a voltmeter to the electrode and place the other lead in the electrolyte. However, this measurement is not accurate because we are measuring the potential difference between the electrode and the solid-solution interface created by the second lead. In fact, there is no accurate way to quantify the absolute electrode potential of the electrochemical system. Instead, we can measure the electrode potential of a system relative to another system—i.e., another half-cell—accurately.

As there are many different half-cells (e.g. Fe³⁺/Fe²⁺, Cu²⁺/Cu, Ag⁺/Ag etc.) we can use to measure the relative potential of a particular half-cell, it is wise to select a reference half-cell for all measurements. The choice of this reference electrode falls on the standard hydrogen electrode (SHE).

 

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Buffer solutions are very useful in a wide range of industrial processes. They are also vital to many biochemical systems.

Manufacture of shampoos

In the manufacture of shampoos, a citric acid/citrate buffer is added to the solution to maintain the pH of the shampoo at a slightly acidic level (about pH = 5.5).

The outer most region of a fibre of hair is called the cuticle, which acts as a barrier to the entry of harmful chemicals into the inner regions of the hair. The cuticle consists of superimposed layers of cells linked by cysteine molecules. When the disulphide bonds of these cysteine linkages are disrupted by hydroxyl molecules (see diagram below), the structure of the cuticle changes, opening up the cuticle and allowing entry of undesirable chemicals into the hair. Since the pH of an unbuffered shampoo increases when we soap our hair with water (due to the hydrolysis of soap), a buffer is added during the manufacturing process to maintain an acidic pH.

Fermentation of alcoholic beverages

During fermentation of alcoholic beverages, yeast enzymes convert sugars to alcohols:

These enzymes function optimally within a certain pH range, usually 4 < pH < 7. If the solution is either too acidic or too alkaline, the enzymes are inhibited and/or yeast may not survive.

Carbon dioxide formed during fermentation acidifies the solution via the following equilibria:

Therefore, the change in pH during fermentation can be resisted by the addition of bicarbonate salts or using a phosphoric acid/phosphate buffer.

 

Biological buffers

Finally, human biological fluids require constant pH levels for biochemical processes to function properly.

The pH of blood (pH = 7.4) is maintained by a carbonic acid/bicarbonate buffer, while the pH of intracellular fluid is stabilised by the carbonic acid/bicarbonate buffer, protein buffers and the dihydrogen phosphate/hydrogen phosphate buffer.

 

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The effects of dilution on the pH of a strong acid (unbuffered solution) and a weak acidic buffer are shown in the diagram below.

It is evident from the diagram that the pH of the buffer solution is resistant to dilution. The pH of the systems are expressed by the following formulae:

System	Approximate pH formula	More accurate pH formula
HCl	—————            (link)        ————–
CH3COOH/CH3COO– buffer	(link)	(link)

With reference to the above formulae, [H⁺] of a strong acid like HCl, decreases upon dilution and hence pH increases. According to the Henderson-Hasselbalch equation, the ratio of the concentration of the salt to the concentration of the acid is unchanged upon dilution and we would expect the buffer pH curve in the above diagram to be a horizontal line. However, the curve shows that the pH of a buffer solution appears relatively constant up to a thousand-fold dilution and subsequently increases at lower buffer concentrations. This is because the data points of the buffer curve in the diagram is calculated using the more accurate pH formula (i.e. the complete pH titration curve formula) instead of the Henderson-Hasselbalch equation, which only provides an approximation of the buffer’s pH. The Henderson-Hasselbalch equation is relatively accurate at high buffer concentrations or when K_a < 10^-3, but unreliable at low buffer concentrations or when K_a > 10^-3, where the assumptions used to derive it are no longer valid.

 

 

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How do we prepare a buffer solution?

In the previous article, we explained the factors affecting the buffer capacity of a solution. To prepare an effective buffer (e.g. an acidic buffer), we need to:

• • 1. Select a weak acid with a pK_a  value at a specific temperature that closely matches the desired pH for the buffer at that temperature.
    2. Choose a corresponding conjugate base, i.e. salt of the weak acid.
    3. Use the Henderson-Hasselbalch equation to calculate the ratio of the conjugate base concentration to the weak acid concentration, which should be as close to unity as possible to achieve maximum buffer capacity.
    4. Calculate the volumes and concentrations of the weak acid and its conjugate base for mixing.

 

 

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What are the factors affecting the capacity of a buffer solution?

The effectiveness (or capacity) of a buffer is dependent on a few factors, namely,

1. 1. Absolute concentrations of the conjugate acid and conjugate base.
   2. Relative concentrations of the conjugate acid and conjugate base.
   3. pK_a (for an acidic buffer) of the weak acid in relation to the pH that the buffer is intended to maintain.
   4. Absolute value of pK_a.
   5. Temperature.

To rationalise the first factor affecting buffer capacity, we refer to the acidic buffer equilibrium:

As mentioned in the previous article, a base OH^– added to the buffer reacts with H₃O⁺ to form water. According to Le Chatelier’s principle, the system counteracts this change by shifting the above equilibrium to the right, with some HA further dissociating to replace the H₃O⁺ that has been removed. The higher the concentration of the conjugate acid HA, the greater the amount of HA that can replace the removed H₃O⁺. Similarly, the larger the amount of the conjugate base A^–, the greater the buffer’s ability to react with any acid that is added. Hence, buffer capacity is proportional to the combined concentrations of the conjugate acid and conjugate base. Mathematically, the buffer capacity of a weak conjugate acid/conjugate base pair is given by the following equation (see this article for derivation):

where [HA]_T = [HA] + [A^–], i.e. the analytical concentration of HA.

The equation clearly shows that the buffer capacity of an acidic buffer is proportional to the combined concentrations of the conjugate acid and conjugate base.

The second factor states that the relative concentrations of the conjugate acid and conjugate base affects buffer capacity. In fact, the maximum buffer capacity of a solution occurs when the concentration of the conjugate acid equals to the concentration of the conjugate base (see this article for details). Substituting into the Henderson-Hasselbalch equation, we have pH = pK_a. In other words, for an acidic buffer to achieve maximum buffer capacity, the pK_a of the chosen weak acid must be as close as possible to the pH that the buffer is intended to maintain. This is how the third factor affects buffer capacity.

It is also important to select an acid with pK_a that is neither too high nor too low (fourth factor). An acid with a pK_a < 3 (K_a > 10^-3) is a relatively strong acid with a high degree of dissociation. Likewise, an acid with a pK_a > 11 (K_a < 10^-11) is a relatively strong base. As explained in this article, a strong acid (or a strong base) has very low or negligible buffer capacity.

Finally, the buffer capacity of a solution is affected by changes in temperature (fifth factor) since the equilibrium constant is temperature-dependent:

which implies that pK_a is also temperature-dependent.

In short, these five factors are important in preparing a buffer solution, which we will discuss in the next article.

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A buffer solution is one that resists changes in pH upon dilution or the addition of acids and bases. The pH of a buffer solution does change when diluted or when acids and bases are added but the change is much less than that compared to an unbuffered solution.

A buffer solution is usually composed of a weak conjugate acid-base pair, e.g. the ethanoic acid/ethanoate pair (acidic buffer) or the ammonium chloride/ammonia pair (basic buffer). It is most effective (or has a maximum buffer capacity) when it contains equal equilibrium concentrations of the weak acid and its conjugate base.

For an acidic buffer, we have the following equilibrium:

If a small amount of acid H₃O⁺ is added to the solution, it reacts with the conjugate base A^– to form the weak conjugate acid HA, thereby removing the added acid and resisting the change in pH. Similarly, when a small amount of base OH^– is added, it combines with H₃O⁺ to form water; again, resisting the change in pH. The degree to which a buffer solution resists the change in pH is dependent on a few factors, which shall be discussed in the next article.

 

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The improved Henderson-Hasselbalch equation, a modified version of the original formula, provides a better approximation of the shape of a titration curve than the original equation.

In deriving the Henderson-Hasselbalch equation, we made the following three assumptions:

• • [H⁺] from water is negligible, i.e. H⁺ in the flask containing the weak acid is solely due to that of the acid, [H⁺]_a as the dissociation of water is again suppressed at this stage.
  • For a weak acid, [HA] is approximately equal to the concentration of the undissociated acid, [HA]_ud, i.e. the dissociation of the weak acid HA is negligible and the remaining concentration of HA after the addition of base is [HA]_r = [HA]_ud – [A^–]_s.
  • [A^–] is approximately equal to the concentration of the salt, [A^–]_s, in the solution, i.e. A^– is completely attributed to the salt formed, with no contribution from the further dissociation of HA.

However, the Henderson-Hasselbalch equation is unreliable when K_a ≥ 10^-3. If we disregard the 2^nd and 3^rd assumptions, the equilibrium expression is:

Rearranging the above equation and solving the quadratic equation in [H⁺]_a,

where C_a and C_b are the analytical concentrations of the acid and base respectively (i.e. the concentrations of the acid and base before any dissociation occurs). Eq6 is the improved version of the Henderson-Hasselbalch equation.

The diagram below shows the superimposition of eq6 (green curve) over the complete pH titration curve (red curve) that disregard all three assumptions, for the titration of 10 cm³ of 0.200 M of CH₃COOH (K_a = 1.75 x 10^-5) with 0.100 M of NaOH.

The fit is much better than the Henderson-Hasselbalch curve even though the two curves (i.e. eq6 and the complete pH titration curve) do not actually coalesce and are still two separate curves when the axes of the plot are scaled to a very high resolution. Furthermore, eq6 doesn’t become invalid when K_a ≥ 10^-3, for example, the diagram below is the superimposition of eq6 on the complete pH titration curve for the titration of 10 cm³ of 0.200 M of an acid (K_a = 1.75 x 10^-2) with 0.100 M of NaOH:

If we further superimpose the Henderson-Hasselbalch curve (purple curve) onto the above diagram for the same titration, we have,

Clearly, the Henderson-Hasselbalch equation breaks down when K_a ≥ 10^-3.

 

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