Chemistry · Lesson

Fuels, electrochemical storage and chemical energy conversion

Keep reversible-work, charge, energy-return and useful-heat comparisons on explicit reaction and service boundaries.

By the end, you can

Relate assigned reversible electrical work to a balanced reaction account.
Convert selected circulating charge to a formal water-reaction extent.
Distinguish returned charge from energy return and converter boundaries.
Compare available heat with heat actually matched to a service.

An energy comparison needs a stated boundary

Chemical reactions, electrical work and heat transfers can contribute to an energy account. Gibbs energy constrains reversible nonexpansion work under the relevant conditions; enthalpy and heating-value conventions describe different quantities.

A fuel comparison must state the amount or mass basis and whether product water is treated as liquid or vapour in the heating-value convention. Use compatible conditions before comparing numerical values.

A chemical account connects charge to a selected net

A reversible non-expansion-work bound at fixed temperature and pressure uses the Gibbs-energy change for the declared reaction. An enthalpy-based energy ratio uses another quantity and needs the same reaction extent and final-state convention. The original hydrogen values below are invented to keep those quantities distinct.

Charge amount uses the Faraday constant, obtained from the present exact elementary charge and Avogadro constant. The two-electron-per-H₂ cell relation connects circulating charge to a selected net extent. It does not add electrons to the neutral overall H/O atom balance.

A selected current fraction can allocate only part of supplied charge to that net. The rest needs its own chemical account before a full cell inventory can be asserted. The same-direction fractions in this teaching model should not replace the broader definition of current efficiency.

Charge, capacity and energy have different units

Current integrated over time gives electrical charge. An amount of electron equivalents is related to charge through the Faraday constant. A charge capacity alone does not specify energy; voltage and its change over the process also matter.

A constant-voltage model can multiply voltage by charge to obtain electrical energy. Real charging or discharge can need an integral and account for losses. Cell voltage is different from the charge-normalized capacity of a material.

The useful output depends on its boundary

Returned charge omits the voltage profile; electrical energy integrates voltage over transferred charge. Charge-weighted mean voltages make that integral explicit in the toy battery cycle. Discharge conversion then changes the delivered AC output. Including only one converter does not make the result a complete AC-to-AC system ratio.

Available heat also differs from delivered useful heat. A demand-limited account should keep unused heat separate. The original service case stipulates matching quality and timing for the used share, rather than demonstrating a practical heating system.

State whether an input basis uses LHV, HHV, total fuel, reacted fuel or another declared quantity. Energy conservation and an energy ratio alone do not establish resource sustainability, emissions, lifetime or exergy quality.

Charge return and declared energy return differ

Quantity	Mean discharge 44 V	Mean discharge 40 V
Returned charge / Ah	282	282
Charge-return fraction	0.940	0.940
Input DC energy / kWh	14.4	14.4
Output DC energy / kWh	12.408	11.28
Output AC energy / kWh	11.29128	10.2648
AC energy out / DC energy in	0.784116667	0.712833333

Original complete-cycle assigned battery example. Both columns exclude charging-converter and auxiliary losses. DC-input to AC-output ratios are not AC-to-AC system efficiencies.

An efficiency compares defined useful output with input

An efficiency ratio needs the specific useful output, input and common energy basis. A component efficiency, round-trip efficiency and overall system efficiency describe different boundaries. Sequential compatible efficiencies multiply for a serial energy path.

Losses can appear as heat or other outputs, and energy supplied to auxiliary systems may fall outside a narrow component calculation. A larger nominal capacity does not guarantee a greater useful delivered energy or a longer service life.

A chemical storage system needs several performance measures

Energy capacity, power capability, response time, cycling, stability and material requirements affect different functions. A source of energy and a carrier or storage mechanism have different roles.

The original energy balances below are assigned teaching models. They do not recommend a commercial system, provide current prices or specify construction or handling procedures for an energy device.

Worked examples

Reversible work and utilized fuel use different accounts

For formal H₂+½O₂→H₂O(l), assign Δ_rG=−212 and Δ_rH=−272 kJ per mol H₂ at one fixed unspecified temperature and pressure. These are invented values, not actual hydrogen thermodynamic data. Initially assign 1.30 mol H₂. Calculate a reversible electrical-work bound.

At full formal extent, H₂ consumption 1.30 mol, O₂ consumption 0.650 mol and water production 1.30 mol close H/O atoms and neutral charge. The neutral written extent has ten electrons on each side; circulating charge is a separate cell account.
Use the exact present-SI elementary charge e=1.602176634×10⁻¹⁹ C and Avogadro constant N_A=6.02214076×10²³ mol⁻¹. Faraday constant F=eN_A=96485.33212331 C mol⁻¹. Two mol electrons circulate per mol H₂ in the selected cell account.
Maximum reversible non-expansion work at the assigned constant temperature/pressure is −ξΔ_rG=275.6 kJ. The corresponding reversible voltage is 212000/(2F)=1.098612584 V.
The reversible enthalpy-basis ratio is 212/272=0.779411765. Actual fuel utilization, voltage losses and auxiliary inputs need separate accounts; the stated ratio is not a hardware performance guarantee or a general Carnot comparison.

Reversible work bound 275.6 kJ on the assigned reaction basis; enthalpy-basis ratio 0.779411765.

Selected charge does not describe every chemical channel

Supply 1.85 mol electron charge to an abstract cell and assign fraction 0.760 to the selected neutral water net 2H₂O(l)→2H₂(g)+O₂(g). Four mol electrons circulate per formal extent of that written net. Selected and other currents have the same direction in this toy model.

Total charge is 1.85F=178497.864428 C. Selected charge amount is 1.85×0.760=1.406 mol electrons; other-channel amount is 0.444 mol.
The selected net gives H₂=1.406/2=0.703 mol, O₂=1.406/4=0.3515 mol and consumed water 0.703 mol. H/O atom amounts close; electrons are circulating charge carriers, not net participants in the neutral overall water equation.
Only the selected products are specified. Unidentified competing charge cannot be turned into a complete chemical cell balance. No current, time, electrolyte or equipment is supplied.
The assigned fraction lies between zero and one for these same-direction channels. The IUPAC definition of current efficiency can exceed one when simultaneous partial currents flow in opposite directions, so that bound is not universal.

Selected H₂/O₂ amounts 0.703/0.3515 mol; other-channel charge remains separately counted.

Returned charge is different from returned energy

Assign one complete battery cycle returning to its initial stored-charge and stored-energy state: charge input 300 Ah, charge-weighted mean charging voltage 48.0 V, returned charge fraction 0.940, discharge mean voltage 44.0 V and discharge-inverter efficiency 0.910. What energy ratios follow?

Charge output is 282 Ah. E=∫VdQ is evaluated using the assigned charge-weighted means: input DC energy 300×48/1000=14.4 kWh; output DC energy 282×44/1000=12.408 kWh.
The DC-to-DC energy ratio is 12.408/14.4=0.861666667, different from returned-charge ratio 0.940. AC output after the discharge inverter is 12.408×0.910=11.29128 kWh; inverter loss is 1.11672 kWh.
For the declared DC-input to AC-output boundary, the ratio is 11.29128/14.4=0.784116667. Charging-converter and auxiliary/rest losses are excluded; this is not AC-to-AC system round-trip efficiency.
No actual battery chemistry, profile, lifetime or charging protocol is specified. A ratio must retain its cycle and energy boundary.

Charge return 0.940; DC-to-DC energy ratio 0.861666667; declared DC-input/AC-output ratio 0.784116667.

Available heat becomes useful only when matched to service

On one assigned lower-heating-value basis, a hypothetical 32.0 kg fuel input at 9.00 MJ kg⁻¹ yields 60.0 MJ electricity and 150 MJ available heat in the same interval. Matching heat demand is 97.0 MJ. Close the energy ledger and useful-service ratio.

Input energy is 288 MJ. Other energy is 288−60−150=78.0 MJ, so the generation ledger closes.
Used heat is min(150,97)=97.0 MJ; unused available heat is 53.0 MJ. Electricity plus available heat gives 210/288=0.729166667, but electricity plus used heat gives 157/288=0.545138889.
Heat quality, timing, location and transport are stipulated compatible for the used share. Adding heat and electricity in an energy account does not make their exergy or quality equal. Lower- and higher-heating-value denominators should not be mixed.

Useful energy 157 MJ and useful-service ratio 0.545138889 on the stated assigned LHV basis.

Try it yourself

In a hypothetical loss scenario, only 82% of the initial hydrogen reacts and the assigned mean cell voltage is 0.68 V. Find charge, electrical work, remaining fuel and work divided by the initial-feed enthalpy magnitude.
Show the answer and reasoning
Reacted/unreacted H₂=1.066/0.234 mol; O₂ consumed 0.533 and water formed 1.066 mol; Q=205706.728087 C; W=139.880575 kJ; initial-feed enthalpy-basis ratio 0.395589862.
Use Q=2F times reacted fuel and W=Q times the assigned mean voltage; retain all initial fuel in the specified efficiency denominator.
Change only the assigned selected current fraction to 0.88 with the same total supplied electron amount.
Show the answer and reasoning
Selected electrons 1.628 mol, other channel 0.222 mol; H₂/O₂/water-consumed 0.814/0.407/0.814 mol; total charge unchanged.
The selected charge fraction changes the selected net extent; do not invent products for the other channel.
Change only the charge-weighted mean discharge voltage to 40 V. Recompute output energies and the declared DC-input to AC-output efficiency.
Show the answer and reasoning
Charge remains 282 Ah; DC output 11.28 kWh, AC output 10.2648 kWh; declared DC-input/AC-output ratio 0.712833333.
A lower assigned discharge voltage reduces energy return while the charge-return fraction stays fixed.
Change only the matching heat demand to 30 MJ, retaining the same hypothetical generation ledger.
Show the answer and reasoning
Used heat 30.0 MJ, unused heat 120 MJ; useful-service ratio (60+30)/288=0.3125; generation ledger unchanged.
The changed demand alters useful delivery rather than assigned generation or input energy.

What to carry forward

Reversible work uses a stated reaction and thermodynamic boundary.
Circulating charge and a neutral overall atom balance have different roles.
Charge return does not determine energy return without voltage and loss accounts.
Available heat contributes to useful service only when appropriately matched.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.