{
  "id": "gibbs-free-energy",
  "version": "5d67ecc3d51e",
  "status": "published",
  "name": "Gibbs Free Energy Calculator",
  "question": "What is the Gibbs free energy change?",
  "summary": "Solves ΔG = ΔH − TΔS for the Gibbs free energy change, the enthalpy change, the entropy change or the temperature, says whether the process is spontaneous, and gives the temperature where ΔG = 0 and the equilibrium constant.",
  "category": "chemistry",
  "subcategory": "stoichiometry",
  "url": "https://www.acalculator.org/chemistry/gibbs-free-energy-calculator",
  "markdown": "https://www.acalculator.org/chemistry/gibbs-free-energy-calculator.md",
  "kind": "function",
  "method": "ΔG = ΔH − T × ΔS ÷ 1000 (ΔH and ΔG in kJ/mol, ΔS in J/(mol·K), T in K); the temperature where ΔG = 0 is T = 1000 × ΔH ÷ ΔS; K = e^(−1000 × ΔG ÷ (R × T)) with R = 8.31446261815324 J/(mol·K).",
  "assumptions": [
    "ΔH and ΔS are taken as constant over the temperature range.",
    "Spontaneous means ΔG < 0 at constant temperature and pressure; it says nothing about how fast the process is.",
    "K is shown only when ΔG is the standard change ΔG°; the page cannot tell which you typed."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which of ΔG, ΔH, ΔS and T to work out from the other three.",
        "type": "string",
        "enum": [
          "g",
          "h",
          "s",
          "t"
        ]
      },
      "dh": {
        "title": "ΔH, kJ/mol",
        "description": "The enthalpy change in kJ/mol; negative for an exothermic process.",
        "type": "number",
        "minimum": -1000000,
        "maximum": 1000000
      },
      "ds": {
        "title": "ΔS, J/(mol·K)",
        "description": "The entropy change in J/(mol·K); note joules, not kilojoules.",
        "type": "number",
        "minimum": -1000000,
        "maximum": 1000000
      },
      "t": {
        "title": "Temperature",
        "description": "The absolute temperature; above absolute zero.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0.000001,
        "maximum": 100000
      },
      "dg": {
        "title": "ΔG, kJ/mol",
        "description": "The Gibbs free energy change in kJ/mol; 0 at equilibrium.",
        "type": "number",
        "minimum": -1000000,
        "maximum": 1000000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value worked out, to 6 significant figures.",
      "format": "text"
    },
    "spontaneity": {
      "label": "Spontaneous?",
      "description": "Spontaneous when ΔG is below 0, not spontaneous above 0, at equilibrium at 0.",
      "format": "text"
    },
    "dG": {
      "label": "ΔG (kJ/mol)",
      "description": "The Gibbs free energy change.",
      "format": "number"
    },
    "dH": {
      "label": "ΔH (kJ/mol)",
      "description": "The enthalpy change.",
      "format": "number"
    },
    "dS": {
      "label": "ΔS (J/(mol·K))",
      "description": "The entropy change.",
      "format": "number"
    },
    "tK": {
      "label": "T (K)",
      "description": "The temperature in kelvins.",
      "format": "number"
    },
    "tds": {
      "label": "TΔS (kJ/mol)",
      "description": "The temperature times the entropy change, in kJ/mol.",
      "format": "number"
    },
    "trend": {
      "label": "Spontaneous when",
      "description": "From the signs of ΔH and ΔS: at all temperatures, none, or above or below the temperature where ΔG = 0.",
      "format": "text"
    },
    "crossover": {
      "label": "T where ΔG = 0 (K)",
      "description": "ΔH ÷ ΔS, when ΔH and ΔS have the same sign.",
      "format": "number"
    },
    "lnK": {
      "label": "ln K",
      "description": "−ΔG ÷ RT, if ΔG is the standard free energy change ΔG°.",
      "format": "number"
    },
    "k": {
      "label": "K",
      "description": "The equilibrium constant e^(−ΔG° ÷ RT), if ΔG is the standard free energy change.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "g",
      "dh": 44.01,
      "ds": 118.8,
      "t": "298 K",
      "dg": 0
    },
    "outputs": {
      "result": "ΔG = 8.6076 kJ/mol",
      "spontaneity": "not spontaneous (ΔG > 0)",
      "dG": 8.6076,
      "dH": 44.01,
      "dS": 118.8,
      "tK": 298,
      "tds": 35.4024,
      "trend": "Above 370.455 K (ΔH > 0 and ΔS > 0)",
      "crossover": 370.45454545454544,
      "lnK": -3.4740145076032505,
      "k": 0.03099236151493241
    },
    "text": "ΔG = 8.6076 kJ/mol: not spontaneous (ΔG > 0)."
  },
  "examples": [
    {
      "given": {
        "find": "g",
        "dh": 44.01,
        "ds": 118.8,
        "t": 298
      },
      "expect": {
        "dG": 8.6076,
        "tds": 35.4024,
        "spontaneity": "not spontaneous (ΔG > 0)"
      },
      "source": "OpenStax, Chemistry 2e, §16.4 Free Energy (ΔG = ΔH − TΔS; ΔG° = −RT ln K), https://openstax.org/books/chemistry-2e/pages/16-4-free-energy, Example 16.7 Evaluation of ΔG° Change from ΔH° and ΔS°: TΔS° = 35.4 kJ, ΔG° = 8.6 kJ; Python 3"
    },
    {
      "given": {
        "find": "g",
        "dh": 90.46,
        "ds": 107.4,
        "t": 298
      },
      "expect": {
        "dG": 58.4548
      },
      "source": "OpenStax, Chemistry 2e, §16.4 Free Energy (ΔG = ΔH − TΔS; ΔG° = −RT ln K), https://openstax.org/books/chemistry-2e/pages/16-4-free-energy, Example 16.8 (b): ΔG° = 90.46 − 298 × 0.1074 = 58.45 kJ/mol; Python 3"
    },
    {
      "given": {
        "find": "t",
        "dh": 44.01,
        "ds": 118.8,
        "dg": 0
      },
      "expect": {
        "tK": 370.45454545454544,
        "result": "T = 370.455 K (97.3045 °C)"
      },
      "source": "OpenStax, Chemistry 2e, §16.4 Free Energy (ΔG = ΔH − TΔS; ΔG° = −RT ln K), https://openstax.org/books/chemistry-2e/pages/16-4-free-energy, Example 16.11 Equilibrium Temperature for a Phase Change: 370.5 K (97.3 °C); Python 3",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "g",
        "dh": 0,
        "ds": 0,
        "t": 298.15
      },
      "expect": {
        "dG": 0,
        "k": 1,
        "spontaneity": "at equilibrium (ΔG = 0)"
      },
      "source": "OpenStax, Chemistry 2e, §16.4 Free Energy (ΔG = ΔH − TΔS; ΔG° = −RT ln K), https://openstax.org/books/chemistry-2e/pages/16-4-free-energy, Table 16.4: K = 1 when ΔG° = 0; hand calculation in content.mdx"
    },
    {
      "given": {
        "find": "h",
        "dg": 55.7,
        "ds": 0,
        "t": 298.15
      },
      "expect": {
        "dH": 55.7,
        "k": 1.7449467881940037e-10
      },
      "source": "OpenStax, Chemistry 2e, §16.4 Free Energy (ΔG = ΔH − TΔS; ΔG° = −RT ln K), https://openstax.org/books/chemistry-2e/pages/16-4-free-energy, Example 16.13: Ksp = e^(−55,700 ÷ (8.314 × 298.15)) = 1.74 × 10⁻¹⁰ (the page uses R = 8.31446261815324); Python 3",
      "tolerance": 1e-9
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, §16.4 Free Energy: ΔG = ΔH − TΔS, ΔG° = −RT ln K, the four sign cases of ΔH and ΔS, T = ΔH ÷ ΔS where ΔG = 0, Example 16.7 (water boiling at 298 K: TΔS° = 35.4 kJ, ΔG° = 8.6 kJ), Example 16.8 (HgO: 58.45 kJ/mol), Example 16.11 (boiling point 370.5 K) and Example 16.13 (AgCl, Ksp = 1.74 × 10⁻¹⁰), Table 16.4 (K = 1 when ΔG° = 0). https://openstax.org/books/chemistry-2e/pages/16-4-free-energy (retrieved 2026-10-19)",
    "OpenStax, Chemistry 2e, §16.1 Spontaneity: spontaneity is not correlated to the speed of a process (diamond to graphite). https://openstax.org/books/chemistry-2e/pages/16-1-spontaneity (retrieved 2026-10-19)",
    "NIST, CODATA 2022 value: molar gas constant R = 8.314 462 618… J/(mol·K), exact (N_A × k). https://physics.nist.gov/cgi-bin/cuu/Value?r (retrieved 2026-10-19)"
  ],
  "related": [
    "enthalpy",
    "equilibrium-constant",
    "ksp",
    "ideal-gas-law"
  ],
  "changelog": []
}