SCIENCE · INVESTIGATE AND EXPLAIN

Separate standard free energy from the current driving force

Composition enters reaction free energy through a dimensionless activity quotient.

Learning outcome: Compare Q below, at and above the calculated K using the continuous equation. Distinguish the local reaction driving force from a finite reversible work budget.

Starting recap

Refresh state-function boundaries, absolute temperature, dimensionless logarithms, written reaction/electron equivalents, conserved charge and formal orbital/identity bookkeeping.

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Try

At298.15 K and ΔrG°−2.50 kJ/mol, K=exp(2500/RT)≈2.7415. At Q10 the current ΔrG becomes positive despite the negative standard value.

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Predict

Must ΔrG° be zero when a reaction mixture reaches equilibrium?

Your prediction and reason

Experiment

Compare Q below, at and above the calculated K using the continuous equation. Distinguish the local reaction driving force from a finite reversible work budget.

Distinguish standard reaction tendency from the current quotient

Worked teaching model · synthetic values · Fictional reaction at298.15 K with consistent activity standards, ΔrG=ΔrG°+RT ln Q, K=exp(−ΔrG°/RT). Reaction free energy is an infinitesimal driving force per extent, not a constant work yield for arbitrary finite conversion; equilibrium has Q=K and ΔrG0, not generally ΔrG°0.

Standard reaction free energy: -2.5 kJ/mol reaction Log10 dimensionless activity quotient: 1 log10 Q

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Current reaction free energy: solid

Axes rescale. A multiplicity distribution, inverse-temperature relation and charge-budget graph have different meanings. Read each axis and do not treat a computed curve as additional measured evidence.

All calculated plot coordinates

Current reaction free energy
log10 dimensionless Q	reaction free energy (kJ/mol reaction)
-2	-13.91602
-1.933333	-13.53549
-1.866667	-13.15495
-1.8	-12.77442
-1.733333	-12.39388
-1.666667	-12.01335
-1.6	-11.63282
-1.533333	-11.25228
-1.466667	-10.87175
-1.4	-10.49121
-1.333333	-10.11068
-1.266667	-9.730145
-1.2	-9.349611
-1.133333	-8.969077
-1.066667	-8.588543
-1	-8.20801
-0.9333333	-7.827476
-0.8666667	-7.446942
-0.8	-7.066408
-0.7333333	-6.685874
-0.6666667	-6.30534
-0.6	-5.924806
-0.5333333	-5.544272
-0.4666667	-5.163738
-0.4	-4.783204
-0.3333333	-4.40267
-0.2666667	-4.022136
-0.2	-3.641602
-0.1333333	-3.261068
-0.06666667	-2.880534
0	-2.5
0.06666667	-2.119466
0.1333333	-1.738932
0.2	-1.358398
0.2666667	-0.9778641
0.3333333	-0.5973302
0.4	-0.2167962
0.4666667	0.1637378
0.5333333	0.5442717
0.6	0.9248057
0.6666667	1.30534
0.7333333	1.685874
0.8	2.066408
0.8666667	2.446942
0.9333333	2.827476
1	3.20801
1.066667	3.588543
1.133333	3.969077
1.2	4.349611
1.266667	4.730145
1.333333	5.110679
1.4	5.491213
1.466667	5.871747
1.533333	6.252281
1.6	6.632815
1.666667	7.013349
1.733333	7.393883
1.8	7.774417
1.866667	8.154951
1.933333	8.535485
2	8.916019

Calculated under the declared model
Quantity	Value	Unit
Dimensionless quotient	10	dimensionless
Equilibrium constant	2.741455	dimensionless
Current reaction free energy	3.20801	kJ/mol reaction
Standard reaction free energy	-2.5	kJ/mol reaction

Reverse infinitesimal reaction lowers Gibbs energy under fixed temperature/pressure.

ΔrG° is tied to standard states, while ΔrG includes the current activities. At equilibrium ΔrG=0 but ΔrG° may be nonzero. Maximum reversible non-expansion work delivered by a finite isothermal/isobaric process is−ΔGtotal, not a fixed current molar reaction value multiplied through an arbitrary composition change.

These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

Reverse infinitesimal reaction lowers Gibbs energy under fixed temperature/pressure.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Add the composition term

Reaction free energy is ΔrG=ΔrG°+RT ln Q, with a dimensionless activity quotient under compatible standard states. At fixed temperature and pressure, a negative value favors infinitesimal forward change; a positive value favors reverse change. This is a thermodynamic direction, not a kinetic rate law.

At298.15 K with ΔrG°−2.50 kJ/mol, K=exp(2500/RT), approximately2.7415. Q=1 gives the standard reaction value, but Q=10 adds about5.708 kJ/mol and makes the current driving force positive. Negative standard free energy therefore does not guarantee forward reaction for every composition.

Identify equilibrium and finite work separately

At Q=K, ΔrG is zero while ΔrG° generally is not. The minimum of a closed system’s total Gibbs energy must also satisfy its component inventories; the quotient relation alone does not specify all amounts.

For a reversible isothermal/isobaric finite process, maximum non-expansion work delivered is−ΔGtotal. As reaction changes composition, Q and the molar driving force change. Multiplying one initial ΔrG by a large arbitrary extent would ignore that variation and can invent available work.

Transfer and check

At the same temperature, suppose ΔrG°=0. Then K=1, but a mixture with Q=.10 has ΔrG=−RT ln10≈−5.708 kJ/mol. Explain why a zero standard value neither eliminates a current driving force nor implies an unchanging composition for every initial packet.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. All prose, cases, graphs and questions are original. These supplied thermodynamic, electrical, nuclear or orbital models are not actual measurements, apparatus instructions, synthesis protocols or practical certification. Retain conventions, independent constraints, changed-case reasoning and limits. No heating, wiring, electrolysis, source handling or chemical manipulation is requested.

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Why can one not multiply the current ΔrG by an arbitrary conversion while allowing Q to change?

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Previous: Construct a standard free-energy comparison with explicit states Next: Distinguish a van’t Hoff inference from an activation barrier

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