Arrhenius Plot (ln k vs 1/T) Tool mechanism

Model scope

The Arrhenius equation, slope relation, and intercept relation are standard and correct. Verdict is NEEDS_REVIEW because T units, R value and units, positivity constraints, regression convention, weighting policy, numerical tolerances, and output units are unspecified. Vector 2's working explicitly corrects the initially listed first k value: for T=250 K and the intended line y=12-2000/T, k must be exp(4)=54.59815003, not exp(7).

No additional formula finding is recorded.

Units and conventions

• T must be absolute temperature in kelvin for 1/T; Celsius values must be converted using T(K)=T(°C)+273.15.
• k must be strictly positive and expressed in one consistent unit across all points because ln(k) is taken.
• R must be explicitly specified; using R=8.314462618 J mol^-1 K^-1 produces Ea in J mol^-1, while R=0.008314462618 kJ mol^-1 K^-1 produces Ea in kJ mol^-1.
• A has the same units as k.
• The regression should be ordinary unweighted least squares of y=ln(k) against x=1/T, with R² defined as 1-SSE/SST or equivalently the squared correlation for an intercept-containing fit.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "R": "8.314462618 J mol^-1 K^-1",
    "T_K": [
      250,
      500,
      1000
    ],
    "k": [
      403.4287935,
      2980.957987,
      8103.083928
    ],
    "regression": "ordinary least squares of ln(k) versus 1/T"
  },
  "expected_outputs": {
    "Ea": "8314.462618 J mol^-1",
    "A": "22026.465795 (same units as k)",
    "R2": 1,
    "slope": "-1000 K",
    "intercept": "10",
    "sampled_plot_points": [
      {
        "x": "1/250=0.004 K^-1",
        "y": "ln(403.4287935)=6"
      },
      {
        "x": "1/500=0.002 K^-1",
        "y": "ln(2980.957987)=8"
      },
      {
        "x": "1/1000=0.001 K^-1",
        "y": "ln(8103.083928)=9"
      }
    ],
    "key_curve_features": {
      "line": "y=10-1000x",
      "x_intercept": "x=0.010 K^-1",
      "no_positive_temperature_asymptote": true
    }
  },
  "working": "Transform the points: (x,y)=(0.004,6),(0.002,8),(0.001,9). Means: x̄=(0.004+0.002+0.001)/3=0.002333333333 K^-1 and ȳ=(6+8+9)/3=7.666666667. Slope m=Σ[(x-x̄)(y-ȳ)]/Σ[(x-x̄)^2]=-1000 K. Intercept b=ȳ-mx̄=7.666666667-(-1000)(0.002333333333)=10. Thus Ea=-mR=-(-1000)(8.314462618)=8314.462618 J mol^-1. A=e^b=e^10=22026.465795. Every point lies exactly on the fitted line, so SSE=0 and R²=1. The plotted line is y=10-1000x; setting y=0 gives x=10/1000=0.010 K^-1."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specified input domain contains several hazardous cases that must be rejected or specially handled: k=0 makes ln(k) undefined, T=0 makes 1/T undefined, and a constant-ln(k) dataset makes the conventional R² expression undefined. Temperature-unit ambiguity can also change Ea and A by orders of magnitude.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json