{
 "about": "pK at 4, 25 and 37 °C for buffers from Goldberg et al. 2002, by their equation 12 (the Clarke and Glew form with the ΔrCp° term) in NumPy; the recommended pK, ΔrH° and ΔrCp° transcribed here a second time from the paper. pK at 25 °C equals the published pK at 298.15 K by construction. The engine is compared within 0.01.",
 "oracle": {
  "name": "Goldberg 2002 equation 12 in NumPy",
  "version": "NumPy 2.4.6; Python 3.11.15",
  "script": "pipeline/lab-calculators/reference.py",
  "command": "python pipeline/lab-calculators/reference.py buffers"
 },
 "constants": {
  "R": 8.31451,
  "referenceTemperatureK": 298.15
 },
 "recordedOn": "2026-10-06",
 "count": 15,
 "cases": [
  {
   "id": "tris",
   "name": "Tris",
   "input": {
    "pK": 8.072,
    "dH": 47.45,
    "dCp": -59,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 8.7103,
     "25": 8.072,
     "37": 7.7527
    },
    "vanTHoffOnlyAt": {
     "4": 8.7019,
     "25": 8.072,
     "37": 7.7504
    },
    "linearSlopePerK": -0.02788
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "hepes",
   "name": "HEPES",
   "input": {
    "pK": 7.564,
    "dH": 20.4,
    "dCp": 47,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 7.8281,
     "25": 7.564,
     "37": 7.4238
    },
    "vanTHoffOnlyAt": {
     "4": 7.8348,
     "25": 7.564,
     "37": 7.4257
    },
    "linearSlopePerK": -0.01199
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "mops",
   "name": "MOPS",
   "input": {
    "pK": 7.184,
    "dH": 21.1,
    "dCp": 25,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 7.4605,
     "25": 7.184,
     "37": 7.04
    },
    "vanTHoffOnlyAt": {
     "4": 7.4641,
     "25": 7.184,
     "37": 7.041
    },
    "linearSlopePerK": -0.0124
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "mes",
   "name": "MES",
   "input": {
    "pK": 6.27,
    "dH": 14.8,
    "dCp": 5,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 6.4657,
     "25": 6.27,
     "37": 6.1695
    },
    "vanTHoffOnlyAt": {
     "4": 6.4665,
     "25": 6.27,
     "37": 6.1697
    },
    "linearSlopePerK": -0.0087
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "pipes",
   "name": "PIPES",
   "input": {
    "pK": 7.141,
    "dH": 11.2,
    "dCp": 22,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 7.2865,
     "25": 7.141,
     "37": 7.0642
    },
    "vanTHoffOnlyAt": {
     "4": 7.2897,
     "25": 7.141,
     "37": 7.0651
    },
    "linearSlopePerK": -0.00658
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "phosphate-2",
   "name": "Phosphate (pK2)",
   "input": {
    "pK": 7.198,
    "dH": 3.6,
    "dCp": -230,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 7.2786,
     "25": 7.198,
     "37": 7.1828
    },
    "vanTHoffOnlyAt": {
     "4": 7.2458,
     "25": 7.198,
     "37": 7.1736
    },
    "linearSlopePerK": -0.00212
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "tes",
   "name": "TES",
   "input": {
    "pK": 7.55,
    "dH": 32.13,
    "dCp": 0,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 7.9765,
     "25": 7.55,
     "37": 7.3322
    },
    "vanTHoffOnlyAt": {
     "4": 7.9765,
     "25": 7.55,
     "37": 7.3322
    },
    "linearSlopePerK": -0.01888
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "imidazole",
   "name": "Imidazole",
   "input": {
    "pK": 6.993,
    "dH": 36.64,
    "dCp": -9,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 7.4807,
     "25": 6.993,
     "37": 6.745
    },
    "vanTHoffOnlyAt": {
     "4": 7.4794,
     "25": 6.993,
     "37": 6.7446
    },
    "linearSlopePerK": -0.02153
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "ches",
   "name": "CHES",
   "input": {
    "pK": 9.394,
    "dH": 39.55,
    "dCp": 9,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 9.9177,
     "25": 9.394,
     "37": 9.1256
    },
    "vanTHoffOnlyAt": {
     "4": 9.919,
     "25": 9.394,
     "37": 9.1259
    },
    "linearSlopePerK": -0.02324
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "taps",
   "name": "TAPS",
   "input": {
    "pK": 8.44,
    "dH": 40.4,
    "dCp": 15,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 8.9741,
     "25": 8.44,
     "37": 8.1656
    },
    "vanTHoffOnlyAt": {
     "4": 8.9763,
     "25": 8.44,
     "37": 8.1662
    },
    "linearSlopePerK": -0.02374
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "glycine-2",
   "name": "Glycine (pK2)",
   "input": {
    "pK": 9.78,
    "dH": 44.2,
    "dCp": -57,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 10.3749,
     "25": 9.78,
     "37": 9.4827
    },
    "vanTHoffOnlyAt": {
     "4": 10.3667,
     "25": 9.78,
     "37": 9.4804
    },
    "linearSlopePerK": -0.02597
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "citrate-3",
   "name": "Citrate (pK3)",
   "input": {
    "pK": 6.396,
    "dH": -3.38,
    "dCp": -254,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 6.3874,
     "25": 6.396,
     "37": 6.4291
    },
    "vanTHoffOnlyAt": {
     "4": 6.3511,
     "25": 6.396,
     "37": 6.4189
    },
    "linearSlopePerK": 0.00199
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "acetate",
   "name": "Acetate",
   "input": {
    "pK": 4.756,
    "dH": -0.41,
    "dCp": -142,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 4.7708,
     "25": 4.756,
     "37": 4.7645
    },
    "vanTHoffOnlyAt": {
     "4": 4.7506,
     "25": 4.756,
     "37": 4.7588
    },
    "linearSlopePerK": 0.00024
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "bicine",
   "name": "Bicine",
   "input": {
    "pK": 8.334,
    "dH": 26.34,
    "dCp": 0,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 8.6836,
     "25": 8.334,
     "37": 8.1555
    },
    "vanTHoffOnlyAt": {
     "4": 8.6836,
     "25": 8.334,
     "37": 8.1555
    },
    "linearSlopePerK": -0.01548
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  },
  {
   "id": "tricine",
   "name": "Tricine",
   "input": {
    "pK": 8.135,
    "dH": 31.37,
    "dCp": -53,
    "temperaturesC": [
     4.0,
     25.0,
     37.0
    ]
   },
   "expected": {
    "pKAt": {
     "4": 8.559,
     "25": 8.135,
     "37": 7.9245
    },
    "vanTHoffOnlyAt": {
     "4": 8.5514,
     "25": 8.135,
     "37": 7.9224
    },
    "linearSlopePerK": -0.01843
   },
   "method": "pka-temperature-goldberg",
   "oracle": "Goldberg 2002 equation 12 in NumPy",
   "source": "Goldberg RN, Kishore N, Lennen RM. J Phys Chem Ref Data 2002;31:231-370, section 8, doi:10.1063/1.1416902 (text read 6 October 2026)"
  }
 ],
 "workedExample": {
  "buffer": "tris",
  "pHAt25": 8.0,
  "pHAt4": 8.64,
  "shift": 0.638
 }
}