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Adsorption isotherm — mass balance and model choice

Analyse equilibrium adsorption using measured initial and equilibrium concentrations plus sorbent mass. Compare model assumptions and residuals; a good fit alone does not prove a microscopic adsorption mechanism.

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{
  "nodes": [
    { "id": "c0", "type": "rounded", "label": "Initial concentration and volume", "x": 40, "y": 40, "width": 150, "height": 104, "fill": "#ede9fe", "stroke": "#6d28d9" },
    { "id": "mass", "type": "rounded", "label": "Sorbent mass", "x": 40, "y": 360, "width": 150, "height": 104, "fill": "#ede9fe", "stroke": "#6d28d9" },
    { "id": "eq", "type": "rounded", "label": "Equilibrated samples", "x": 215, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
    { "id": "ce", "type": "card", "label": "Measured equilibrium concentration", "x": 390, "y": 200, "width": 150, "height": 104, "fill": "#ccfbf1", "stroke": "#0f766e" },
    { "id": "blank", "type": "octagon", "label": "Container / solution blanks", "x": 390, "y": 520, "width": 150, "height": 104, "fill": "#e0f2fe", "stroke": "#0369a1" },
    { "id": "bal", "type": "rounded", "label": "Mass-balance uptake", "x": 565, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
    { "id": "lang", "type": "rounded", "label": "Langmuir candidate model", "x": 740, "y": 40, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
    { "id": "freund", "type": "rounded", "label": "Freundlich candidate model", "x": 740, "y": 360, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
    { "id": "diag", "type": "rounded", "label": "Residuals and parameter uncertainty", "x": 915, "y": 200, "width": 150, "height": 104, "fill": "#fce7f3", "stroke": "#be185d" }
  ],
  "edges": [
    { "id": "e0", "source": "c0", "target": "eq", "label": "prepare series" },
    { "id": "e1", "source": "mass", "target": "eq", "label": "normalise uptake" },
    { "id": "e2", "source": "eq", "target": "ce", "label": "measure" },
    { "id": "e3", "source": "ce", "target": "bal", "label": "remaining solute" },
    { "id": "e4", "source": "c0", "target": "bal", "label": "starting solute" },
    { "id": "e5", "source": "mass", "target": "bal", "label": "mass basis" },
    { "id": "e6", "source": "blank", "target": "bal", "label": "non-sorbent losses", "style": "dashed" },
    { "id": "e7", "source": "bal", "target": "lang", "label": "candidate fit" },
    { "id": "e8", "source": "bal", "target": "freund", "label": "candidate fit" },
    { "id": "e9", "source": "lang", "target": "diag", "label": "compare" },
    { "id": "e10", "source": "freund", "target": "diag", "label": "compare" }
  ]
}