Gibbs Free Energy Simulator — Reaction Spontaneity and Equilibrium Constant
Use Delta G = Delta H - T Delta S to compute, in real time, the Gibbs free-energy change Delta G, T Delta S, spontaneity flag and equilibrium constant K = exp(-Delta G / RT) from enthalpy change Delta H, entropy change Delta S, temperature T and an entropy scaling factor. A Delta G-T line plot and van't Hoff line (1/T vs log K) visualise the temperature-dependent spontaneity crossover.
Parameters
Enthalpy change Delta H
kJ/mol
Entropy change Delta S
J/(mol K)
Temperature T
deg C
Delta S scale factor
x
Defaults: Delta H = -50 kJ/mol, Delta S = 100 J/(mol K), T = 25 deg C (298.15 K), scale = 1.0. The tool uses R = 8.314e-3 kJ/(mol K) and converts Delta S internally to kJ/(mol K). The effective entropy is Delta S_eff = Delta S x scale, so Delta G = Delta H - T x Delta S_eff. The physically correct value is scale = 1.0.
Results
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Delta G
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T Delta S
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Spontaneity
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Equilibrium constant K
Delta G-T line plot
X = temperature T (deg C) / Y = Delta G (kJ/mol) / blue = Delta G(T) = Delta H - T x Delta S_eff line / red dashed = Delta G = 0 boundary / yellow vertical = current T
van't Hoff line (1/T vs log10 K)
X = 1/T (1/K) / Y = log10 K / blue = van't Hoff line (slope -Delta H / (R ln10), intercept Delta S / (R ln10)) / yellow marker = current (1/T, log10 K)
Theory & Key Formulas
The Gibbs free-energy change determines spontaneity at constant temperature and pressure:
$$\Delta G = \Delta H - T\,\Delta S$$
$\Delta H$ is the enthalpy change (kJ/mol, heat of reaction), $\Delta S$ is the entropy change (J/(mol K), disorder) and $T$ is absolute temperature (K). $\Delta G < 0$ means spontaneous, $\Delta G > 0$ means non-spontaneous, and $\Delta G = 0$ means equilibrium. The standard-state equilibrium constant follows:
with $R = 8.314\times 10^{-3}$ kJ/(mol K). The van't Hoff form linearises the temperature dependence:
$$\ln K = -\frac{\Delta H^{\circ}}{R\,T} + \frac{\Delta S^{\circ}}{R}$$
A plot of $\ln K$ versus $1/T$ is a line of slope $-\Delta H / R$ and intercept $\Delta S / R$. This tool plots $\log_{10} K$ on the y-axis.
What is the Gibbs Free Energy Simulator
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In chemistry class I learned that a reaction is spontaneous when Delta G is negative, but why does the formula add the entropy term as well? I thought any exothermic reaction would just proceed on its own.
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Good question. The "exothermic so it proceeds" idea is only half right. Ice melting at room temperature is endothermic (Delta H > 0) yet it happens spontaneously because the entropy increase (Delta S > 0) times the temperature T makes T Delta S large enough to flip the sign of Delta G. The combination Delta G = Delta H - T Delta S can be negative even when Delta H is positive, provided T Delta S is larger. With the defaults (Delta H = -50, Delta S = 100, T = 25 deg C) the tool reports Delta G about -79.82 kJ/mol, T Delta S about 29.82 kJ/mol, Spontaneous and K about 9.62e+13.
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Can the sign of Delta G actually flip when you change temperature? That sounds counterintuitive.
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Yes — that is exactly what makes Delta G = Delta H - T Delta S so powerful. There are four regimes: (1) Delta H<0, Delta S>0 spontaneous at all T; (2) Delta H>0, Delta S<0 never spontaneous; (3) Delta H<0, Delta S<0 spontaneous only at low T; (4) Delta H>0, Delta S>0 spontaneous only at high T. Try Delta H = +100, Delta S = +150 and run the sweep — Delta G crosses zero around 400 deg C. CaCO3 decomposition (limestone calcining) is a real case of regime (4) — it only proceeds spontaneously above about 840 deg C.
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The equilibrium constant K is also shown — how is it tied to Delta G, and why is it an exponential?
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The key relation linking thermodynamics and statistical mechanics is Delta G deg = -RT ln K, or equivalently K = exp(-Delta G deg / RT). The exponential comes from the Boltzmann distribution: the probability of state i is proportional to exp(-E_i / kT). Changing Delta G by 10 kJ/mol changes K by roughly a factor of 50 at room temperature. With Delta G = -79.82 kJ/mol the tool gives K about 9.62e+13, essentially complete forward reaction. The van't Hoff form d(ln K)/d(1/T) = -Delta H / R linearises the temperature dependence, which is what the second plot shows.
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One last thing — what is the Delta S scale factor for? It feels suspicious to "scale" a thermodynamic quantity.
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Right call. The scale is an educational knob to feel how much the entropy term T Delta S contributes to Delta G. The physically correct value is 1.0, which is what you must use for any quantitative analysis. Sweeping the scale from 0.5 to 2.0 changes Delta G from -64.9 to -109.6 kJ/mol with the defaults, which shows how strongly entropy dominates at room temperature. Some practical contexts (gas-phase corrections, solvation entropy) use a similar effective Delta S, so the concept is not foreign — but as a pure thermodynamic value always use scale = 1.0.
FAQ
The Gibbs free energy G is a thermodynamic potential that represents the maximum useful work obtainable from a system at constant temperature and pressure. The reaction free-energy change Delta G = Delta H - T Delta S balances the enthalpy change Delta H against the entropy change Delta S. When Delta G is negative the reaction is spontaneous (exergonic); positive means non-spontaneous (endergonic); zero means equilibrium. With the defaults (Delta H = -50 kJ/mol, Delta S = 100 J/(mol K), T = 25 deg C) the tool reports Delta G about -79.82 kJ/mol, T Delta S about 29.82 kJ/mol, Spontaneous, and K about 9.62e+13.
In Delta G = Delta H - T Delta S the enthalpy term Delta H is roughly constant with temperature, while -T Delta S scales linearly with T. The signs of Delta H and Delta S split the parameter space into four regimes: (1) Delta H<0, Delta S>0 always spontaneous; (2) Delta H>0, Delta S<0 never spontaneous; (3) Delta H<0, Delta S<0 spontaneous only at low T; (4) Delta H>0, Delta S>0 spontaneous only at high T. Real examples include ice melting (4) and CaCO3 decomposition (4). Use the sweep button to scan T from -50 to 1500 deg C and watch the crossover.
At standard state K is tied to Delta G by Delta G deg = -RT ln K, i.e. K = exp(-Delta G deg / RT). The more negative Delta G is, the larger K grows exponentially and the more completely the reaction proceeds. With R = 8.314e-3 kJ/(mol K) and T in kelvin, the defaults Delta G about -79.82 kJ/mol at T = 298.15 K give K = exp(79.82 / (8.314e-3 * 298.15)) = exp(32.20) about 9.62e+13, essentially complete conversion. Conversely Delta G = +10 kJ/mol gives K about 0.018. The van't Hoff relation fixes how K varies with T.
The Delta S scaling factor is an educational knob to feel how strongly the entropy term T Delta S contributes to Delta G. Internally the tool computes an effective entropy Delta S_eff = Delta S x scale, with scale = 1.0 the physically correct value. Sweeping scale from 0.5 to 2.0 shows the entropy contribution change without moving the Delta S slider, which is convenient for comparing gas-evolving reactions with strongly positive Delta S against condensation reactions with negative Delta S. For quantitative analysis always keep scale = 1.0.
Real-world applications
Limestone calcining (CaCO3 to CaO + CO2): The backbone reaction of cement, steel and flue-gas desulphurisation industries. With Delta H about +178 kJ/mol (endothermic) and Delta S about +160 J/(mol K) (CO2 evolution gives a strong positive Delta S) this is a textbook regime (4) case: non-spontaneous at low T, with the crossover at T = Delta H / Delta S about 1113 K (about 840 deg C). Set Delta H = 178, Delta S = 160 in the tool and run the temperature sweep — Delta G crosses zero near 830 deg C. Real kilns run at 900 to 1100 deg C balancing fuel cost against reaction rate.
Hydrogen combustion (H2 + 1/2 O2 to H2O): The core reaction of fuel cells and hydrogen engines. Delta H about -286 kJ/mol (strongly exothermic), Delta S about -163 J/(mol K) (gas-to-liquid water cuts entropy) — regime (3): spontaneous at low T, less driving force at high T. Even at 25 deg C Delta G about -237 kJ/mol is so negative that K is around 10^41, so conversion is essentially complete. The ratio eta = Delta G / Delta H about 0.83 is the theoretical maximum fuel-cell efficiency at room temperature.
Ammonia synthesis (Haber-Bosch, N2 + 3H2 to 2NH3): One of the pillars of the chemical industry. Delta H about -92 kJ/mol (exothermic), Delta S about -198 J/(mol K) (4 to 2 gas molecules cuts entropy strongly) — regime (3). Thermodynamically favoured at low T but kinetically slow, so industrial plants operate at 400 to 500 deg C and 200 atm as the "Le Chatelier compromise". Plug Delta H = -92, Delta S = -198 into the tool and Delta G crosses into positive territory around 400 deg C, explaining why high pressure is also needed to push equilibrium back to the product side.
Protein folding and drug binding: In biochemistry and drug discovery, the Delta G = Delta H - T Delta S decomposition from isothermal titration calorimetry (ITC) is a "thermodynamic fingerprint" of binding. Enthalpy-driven binding (strong hydrogen bonds and electrostatics, Delta H very negative) is distinguished from entropy-driven binding (hydrophobic effect releasing water, Delta S very positive), which guides lead-compound optimisation. The tool lets you sweep Delta H and Delta S signs and magnitudes to visualise binding fingerprints.
Common misconceptions and pitfalls
The most common pitfall is the belief that "negative Delta G means the reaction is fast". Delta G only tells you the direction of spontaneity, not the rate. Rate is governed by the activation energy Ea via the Arrhenius law k = A exp(-Ea / RT). Diamond converting to graphite has Delta G about -3 kJ/mol and is thermodynamically spontaneous, yet does not happen on any practical timescale because Ea is huge. The Spontaneous flag in this tool reports direction, not speed.
A second confusion is mixing up Delta G deg with Delta G. Delta G deg refers to standard state (all species at 1 mol/L or 1 bar) and is what enters K = exp(-Delta G deg / RT). The true Delta G under arbitrary conditions is Delta G = Delta G deg + RT ln Q, where Q is the reaction quotient. As the reaction proceeds Q approaches K and Delta G approaches zero. This tool computes Delta G deg; for non-standard conditions you must evaluate Q separately.
Finally there is the assumption that Delta H and Delta S are temperature-independent. The tool uses the van't Hoff approximation that Delta H and Delta S do not depend on T. Strictly, Delta H(T) = Delta H(T_ref) + integral of Delta Cp dT and Delta S(T) = Delta S(T_ref) + integral of (Delta Cp / T) dT, so heat-capacity corrections matter for wide temperature spans (above 500 deg C) and precise crossover temperatures. For engineering work consult NIST-JANAF tables or HSC Chemistry. This tool is an educational approximation, not a precision database.