Batteries, Fuel Cells and Electrolytic Cells – Electrochemical Cells and Applications (Senior 6 Chemistry) | Ganzaa

Electrochemical Cells and Applications

Lessons

Senior 6 · Chemistry

Electrochemical Cells and Applications

5 lessons

Lesson 5 of 5

Batteries, Fuel Cells and Electrolytic Cells

25 min

The cells in your pocket

A torch, a mobile phone and a car each carry a different galvanic cell. The torch's alkaline cell is thrown away when it is flat; the phone's lithium-ion cell and the car's lead–acid battery are recharged hundreds of times. A fuel cell, used in some buses and in spacecraft, never goes flat at all as long as hydrogen is supplied.

This lesson applies the ideas of the unit to these practical cells, and then compares galvanic cells with the electrolytic cells you studied in Senior 3 and used for extracting metals in Unit 2.

Definition

Battery: one or more galvanic cells connected together to supply electrical energy. Example: a 12 V car battery contains six lead–acid cells in series.

Primary cell: a cell whose reaction cannot be reversed in practice, so it is discarded when used up. Example: the alkaline cell. Secondary (rechargeable) cell: a cell whose reaction is reversed by passing a current through it from an external supply. Example: the lead–acid and lithium-ion cells.

Fuel cell: a galvanic cell in which the reactants (a fuel and oxygen) are supplied continuously and the products removed. Example: the hydrogen–oxygen fuel cell.

Electrolytic cell: a cell in which an external power supply drives a non-spontaneous redox reaction. Example: the electrolysis of molten aluminium oxide.

A primary cell: the alkaline cell

Zinc powder is the anode and manganese(IV) oxide the cathode, in a paste of potassium hydroxide:

$\text{anode: } \mathrm{Zn(s) + 2OH^{-}(aq) \rightarrow ZnO(s) + H_2O(l) + 2e^{-}}$

$\text{cathode: } \mathrm{2MnO_2(s) + 2H_2O(l) + 2e^{-} \rightarrow 2MnO(OH)(s) + 2OH^{-}(aq)}$

Its nominal voltage is 1.5 V. The products do not easily turn back into the reactants, so the cell is not recharged.

A secondary cell: the lead–acid battery

Each cell has a lead anode and a lead(IV) oxide cathode in sulfuric acid. On discharge:

$\text{anode: } \mathrm{Pb(s) + HSO_4^{-}(aq) \rightarrow PbSO_4(s) + H^{+}(aq) + 2e^{-}}$

$\text{cathode: } \mathrm{PbO_2(s) + HSO_4^{-}(aq) + 3H^{+}(aq) + 2e^{-} \rightarrow PbSO_4(s) + 2H_2O(l)}$

$\text{overall: } \mathrm{Pb(s) + PbO_2(s) + 2H_2SO_4(aq) \rightarrow 2PbSO_4(s) + 2H_2O(l)} \qquad E^{\circ}_{\text{cell}} = 2.05\,\mathrm{V}$

Both electrodes turn into lead(II) sulfate, which stays stuck to them, and the acid becomes more dilute. Charging from the car's alternator drives the reactions backwards, so the cell is then working as an electrolytic cell. Six cells in series give the familiar "12 V" battery.

A secondary cell: the lithium-ion battery

On discharge, lithium atoms stored between the graphite layers of the anode give up electrons, and the $\mathrm{Li^{+}}$ ions move through the electrolyte into a metal oxide cathode such as cobalt oxide:

$\mathrm{LiC_6 \rightarrow C_6 + Li^{+} + e^{-}} \qquad \mathrm{CoO_2 + Li^{+} + e^{-} \rightarrow LiCoO_2}$

Lithium's very negative $E^{\circ}$ (−3.04 V) and low mass give a high voltage (about 3.6–3.7 V per cell) and a lot of energy per kilogram, which is why these cells power phones, laptops and electric vehicles. Charging pushes the $\mathrm{Li^{+}}$ ions back into the graphite.

The hydrogen–oxygen fuel cell

Figure 5.1: A hydrogen–oxygen fuel cell with an acidic membrane. The only product is water.

$\text{anode: } \mathrm{2H_2(g) \rightarrow 4H^{+}(aq) + 4e^{-}} \qquad \text{cathode: } \mathrm{O_2(g) + 4H^{+}(aq) + 4e^{-} \rightarrow 2H_2O(l)}$

$E^{\circ}_{\text{cell}} = 1.23 - 0.00 = 1.23\,\mathrm{V}$

Fuel cells convert chemical energy to electrical energy directly, without burning, and give out only water. But hydrogen is hard to store, it is mostly made today from fossil fuels, and the electrodes need costly platinum catalysts.

Galvanic and electrolytic cells compared

Feature	Galvanic cell	Electrolytic cell
energy change	chemical energy → electrical energy	electrical energy → chemical energy
cell reaction	spontaneous: $E_{\text{cell}} > 0$ , $\Delta G < 0$	non-spontaneous: needs an applied voltage greater than the cell's emf
anode	oxidation; negative electrode	oxidation; positive electrode
cathode	reduction; positive electrode	reduction; negative electrode
arrangement	usually two half-cells joined by a salt bridge	usually both electrodes in one electrolyte
examples	Daniell cell, alkaline cell, a battery while it is in use, fuel cell	electroplating, extraction of aluminium and sodium, refining copper, a battery while it is being charged

Worked example

Problem. The standard emf of the lead–acid cell is 2.05 V, and $E^{\circ}(\mathrm{PbSO_4/Pb}) = -0.36\,\mathrm{V}$ . Calculate $E^{\circ}$ for the positive electrode, $\mathrm{PbO_2/PbSO_4}$ , and explain why at least six cells are needed for a 12 V battery.

Solution. The lead electrode is the anode, so

$E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}} \quad\Rightarrow\quad E^{\circ}_{\text{cathode}} = 2.05 + (-0.36) = +1.69\,\mathrm{V}$

Cells in series add their voltages: $\frac{12}{2.05} = 5.9$ , so six cells are needed, giving about $6 \times 2.05 = 12.3\,\mathrm{V}$ .

Answer: $E^{\circ}(\mathrm{PbO_2/PbSO_4}) = +1.69\,\mathrm{V}$ ; six cells in series.

Worked example

Problem. (a) Calculate $\Delta G^{\circ}$ per mole of hydrogen for the hydrogen–oxygen fuel cell. (b) What is the maximum electrical energy, in kW h, that 1.00 kg of hydrogen could supply? ( $M(\mathrm{H_2}) = 2.016\,\mathrm{g\,mol^{-1}}$ ; 1 kW h = 3600 kJ)

Solution.

(a) Per mole of $\mathrm{H_2}$ , $\mathrm{H_2 + \tfrac{1}{2}O_2 \rightarrow H_2O}$ , 2 mol of electrons are transferred:

$\Delta G^{\circ} = -nFE^{\circ}_{\text{cell}} = -2 \times 96\,485 \times 1.229 = -2.37 \times 10^{5}\,\mathrm{J\,mol^{-1}} = -237\,\mathrm{kJ\,mol^{-1}}$

(b) $n(\mathrm{H_2}) = \frac{1000}{2.016} = 496\,\mathrm{mol}$ ; energy $= 496 \times 237 = 1.18 \times 10^{5}\,\mathrm{kJ}$ ; $\frac{1.18 \times 10^{5}}{3600} = 32.7\,\mathrm{kW\,h}$ .

Answer: (a) −237 kJ mol⁻¹; (b) at most about 33 kW h. Real fuel cells deliver less, because some energy is always lost as heat.

Warning

Common mistakes

Saying the anode is always negative. It is negative in a galvanic cell but positive in an electrolytic cell; in a rechargeable battery the same electrode swaps roles when you charge it.
Trying to recharge a primary cell. It can leak or burst.
Thinking a fuel cell stores energy like a battery. It converts the energy of a fuel that is supplied continuously.

Safety. Lead–acid batteries contain sulfuric acid and give off hydrogen while charging: keep sparks and flames away and wear eye protection. If battery acid splashes into the eyes or onto skin, rinse with plenty of clean running water for at least 15 minutes and get medical help. Damaged lithium-ion cells can overheat and catch fire; never puncture or crush them. Lead is toxic: used batteries should go for recycling, not into ordinary waste.

Tip

For any cell, ask two questions. Is it making electricity or using it? Making = galvanic (anode −); using = electrolytic (anode +). Can the reaction be pushed back? Yes = secondary (rechargeable); no = primary.

TED-Ed: How batteries work, by Adam Jacobson. Watch for how the separation of the two half-reactions forces electrons through the circuit, and why some batteries can be recharged.

✦

Practice

Distinguish between a primary cell, a secondary cell and a fuel cell, with one example of each.
Write the overall equation for the discharge of an alkaline cell, by combining the two half-equations in the lesson.
Explain why the density of the acid in a lead–acid battery falls as the battery discharges, and how this can be used to test its state of charge.
A phone battery is rated 4000 mA h at 3.7 V. Calculate the charge it can deliver, the energy stored in kJ, and the mass of lithium whose ions carry this charge ( $M(\mathrm{Li}) = 6.94\,\mathrm{g\,mol^{-1}}$ ).
Write the half-equations for a hydrogen–oxygen fuel cell with an alkaline electrolyte, given that the cathode reaction is $\mathrm{O_2 + 2H_2O + 4e^{-} \rightarrow 4OH^{-}}$ ( $E^{\circ} = +0.40\,\mathrm{V}$ ) and $E^{\circ}(\mathrm{2H_2O/H_2, 2OH^{-}}) = -0.83\,\mathrm{V}$ . Calculate $E^{\circ}_{\text{cell}}$ and compare it with the acid cell.
Copy and complete: in a galvanic cell the cathode is the ___ electrode; when a lead–acid battery is being charged, the electrode that was the cathode becomes the ___.
Evaluate the claim that hydrogen fuel-cell vehicles are "pollution-free".

Show answersHide answers

Primary: reaction not reversible, used once (alkaline cell). Secondary: reaction reversed by charging (lead–acid, lithium-ion). Fuel cell: reactants supplied continuously, does not run down or need charging while fuel lasts (hydrogen–oxygen cell).
$\mathrm{Zn + 2MnO_2 + H_2O \rightarrow ZnO + 2MnO(OH)}$ .
Sulfuric acid is used up and water is formed ( $\mathrm{Pb + PbO_2 + 2H_2SO_4 \rightarrow 2PbSO_4 + 2H_2O}$ ), so the acid becomes more dilute and less dense. A hydrometer reading of the acid's density shows how far the battery is charged.
$Q = 4.000\,\mathrm{A} \times 3600\,\mathrm{s} = 1.44 \times 10^{4}\,\mathrm{C}$ . Energy $= QV = 1.44 \times 10^{4} \times 3.7 = 5.3 \times 10^{4}\,\mathrm{J} = 53\,\mathrm{kJ}$ . $n(e^{-}) = \frac{1.44 \times 10^{4}}{96\,485} = 0.149\,\mathrm{mol}$ = $n(\mathrm{Li^{+}})$ ; mass $= 0.149 \times 6.94 = 1.04\,\mathrm{g}$ .
Anode: $\mathrm{H_2 + 2OH^{-} \rightarrow 2H_2O + 2e^{-}}$ ; cathode: $\mathrm{O_2 + 2H_2O + 4e^{-} \rightarrow 4OH^{-}}$ . $E^{\circ}_{\text{cell}} = 0.40 - (-0.83) = 1.23\,\mathrm{V}$ , the same as the acid cell, because the overall reaction, $\mathrm{2H_2 + O_2 \rightarrow 2H_2O}$ , is the same.
Positive; anode (it is now where oxidation happens, $\mathrm{PbSO_4 + 2H_2O \rightarrow PbO_2 + HSO_4^{-} + 3H^{+} + 2e^{-}}$ ).
Partly true. At the vehicle, the only product is water, so there are no exhaust gases such as $\mathrm{CO_2}$ , CO or nitrogen oxides. But most hydrogen is made today from natural gas, which releases $\mathrm{CO_2}$ , and making the platinum catalysts, tanks and vehicle has environmental costs. The claim is fair only if the hydrogen comes from renewable electricity.

1The cells in your pocket

2A primary cell: the alkaline cell

3A secondary cell: the lead–acid battery

4A secondary cell: the lithium-ion battery

5The hydrogen–oxygen fuel cell

6Galvanic and electrolytic cells compared