Source: https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/implementation/

instrument implementation / implementation-contract

# Arrhenius Plot (ln k vs 1/T) Tool implementation

A source-bound implementation contract for Arrhenius Plot (ln k vs 1/T) Tool; deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-with-binding-errata

**Evidence ID**: t6-123

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

````
[
  {
    "vector": 2,
    "field": "slope/intercept/Ea/A/R2",
    "wrong": "-2000 / 12 / 16628.93 / 162754.79 / 1.0",
    "correct": "-653.333 / 9.42667 / 5432.12 / 12415.07 / 0.914667 (index-wise OLS on the GIVEN k list)",
    "cause": "working admits the supplied k list does not fit the intended line, then invents a 'corrected known-good input' and ships outputs for the invented data instead of the stated inputs"
  },
  {
    "vector": 3,
    "field": "slope/intercept/Ea/A/R2",
    "wrong": "-678.571 / 9.08333 / 5641.96 / 8807.27 / 0.954074",
    "correct": "-857.143 / 9.5 / 7126.68 / 13359.73 / 0.979592",
    "cause": "Sxy slip: y-deviation for ln(k)=6 vs mean 7.5 written as -1 instead of -1.5 (and Syy 2.25 vs true 3.5)"
  }
]
````

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/qualification/>)

## 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`

- `tranche errata record`