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

instrument / verified-with-binding-errata

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

The current ledger marks this instrument verified with errata that must be applied at binding time.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/arrhenius-plot-ln-k-vs-1-t-tool/qualification/>)

## Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

**Area**: Chemistry & Materials

**Tranche**: tranche-6

**Evidence ID**: t6-123

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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).

### Formula and scope findings

No additional record

### Unit assumptions

- 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.

## Boundary hardening

**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.

## Errata and corrections

### Tranche errata

**slope/intercept/Ea/A/R2** · vector 2

-2000 / 12 / 16628.93 / 162754.79 / 1.0

-653.333 / 9.42667 / 5432.12 / 12415.07 / 0.914667 (index-wise OLS on the GIVEN k list)

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

**slope/intercept/Ea/A/R2** · vector 3

-678.571 / 9.08333 / 5641.96 / 8807.27 / 0.954074

-857.143 / 9.5 / 7126.68 / 13359.73 / 0.979592

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 example

4 review vectors are recorded. One source-bound sample is shown below.

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

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`