# Arrhenius Kinetics API
> Arrhenius reaction-kinetics maths as an API, computed locally and deterministically. The rate-constant endpoint applies the Arrhenius equation k = A·exp(−Ea/RT), relating the rate constant, the pre-exponential (frequency) factor A, the activation energy Ea and the absolute temperature: give any three and it solves for the fourth, with the activation energy in joules or kilojoules per mole and the temperature in kelvin or Celsius. The activation-energy endpoint uses the two-point method — from two rate constants measured at two temperatures it returns the activation energy, Ea = R·ln(k2/k1)/(1/T1 − 1/T2), and the pre-exponential factor. The temperature-effect endpoint gives the factor by which the rate changes between two temperatures, k2/k1 = exp(−Ea/R·(1/T2 − 1/T1)), along with the Q₁₀ — the rate multiplier per 10 K rise — and the new rate constant if you supply the old one. The gas constant R is 8.314462618 J/(mol·K). Everything is computed locally and deterministically, so it is instant and private. Ideal for chemistry and chemical-engineering tools, reaction and process-design apps, shelf-life and stability modelling, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is reaction kinetics; for the ideal gas law use a gas-law API and for radioactive decay use a half-life API.

## Authentication
All requests require your oanor API key in the `x-oanor-key` header. Get one at https://www.oanor.com/developer/keys.

```bash
curl -H "x-oanor-key: oanor_live_…" "https://api.oanor.com/arrhenius-api/..."
```

## Pricing
- **Free** (Free) — 3,000 calls/Mo, 2 req/s
- **Starter** ($4/Mo) — 40,000 calls/Mo, 5 req/s
- **Pro** ($14/Mo) — 250,000 calls/Mo, 15 req/s
- **Mega** ($44/Mo) — 1,500,000 calls/Mo, 40 req/s

## Endpoints

### Kinetics

#### `GET /v1/activation-energy` — Activation energy (two-point)

**Parameters:**
- `k1` (query, required, string) — Rate constant at T1 Example: `1`
- `t1` (query, required, string) — Temperature 1 Example: `300`
- `k2` (query, required, string) — Rate constant at T2 Example: `1.9`
- `t2` (query, required, string) — Temperature 2 Example: `310`
- `temperature_unit` (query, optional, string) — k|c Example: `k`

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/arrhenius-api/v1/activation-energy?k1=1&t1=300&k2=1.9&t2=310&temperature_unit=k"
```

**Response:**
```json
{
    "data": {
        "k1": 1,
        "k2": 1.9,
        "note": "Two-point Arrhenius. A positive Ea means the rate rises with temperature.",
        "formula": "Ea = R·ln(k2/k1) / (1/T1 − 1/T2); A = k1·exp(Ea/RT1).",
        "pre_exponential": 437886570,
        "temperature_1_K": 300,
        "temperature_2_K": 310,
        "activation_energy": {
            "J_per_mol": 49631.0323,
            "kJ_per_mol": 49.631032
        }
    },
    "meta": {
        "timestamp": "2026-06-04T10:18:56.746Z",
        "request_id": "e0562476-aac6-4ef6-b683-fc6486016e79"
    },
    "status": "ok",
    "message": "Activation energy (two-point)",
    "success": true
}
```

#### `GET /v1/rate-constant` — k = A·exp(−Ea/RT) solver

**Parameters:**
- `rate_constant` (query, optional, string) — Rate constant k
- `pre_exponential` (query, optional, string) — Pre-exponential factor A Example: `1e13`
- `activation_energy` (query, optional, string) — Activation energy Ea Example: `75`
- `ea_unit` (query, optional, string) — j|kj per mol (default j) Example: `kj`
- `temperature` (query, optional, string) — Temperature Example: `298`
- `temperature_unit` (query, optional, string) — k|c (default k) Example: `k`

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/arrhenius-api/v1/rate-constant?pre_exponential=1e13&activation_energy=75&ea_unit=kj&temperature=298&temperature_unit=k"
```

**Response:**
```json
{
    "data": {
        "formula": "k = A·exp(−Ea/RT).",
        "solved_for": "rate_constant",
        "rate_constant": 0.71442175,
        "temperature_K": 298,
        "pre_exponential": 10000000000000,
        "activation_energy": {
            "J_per_mol": 75000,
            "kJ_per_mol": 75
        }
    },
    "meta": {
        "timestamp": "2026-06-04T10:18:56.843Z",
        "request_id": "bab002f1-5e17-4e90-8785-cef28ee20249"
    },
    "status": "ok",
    "message": "k = A·exp(-Ea/RT) solver",
    "success": true
}
```

#### `GET /v1/temperature-effect` — Rate ratio for a temperature change

**Parameters:**
- `activation_energy` (query, required, string) — Activation energy Ea Example: `50`
- `ea_unit` (query, optional, string) — j|kj Example: `kj`
- `t1` (query, required, string) — Temperature 1 Example: `300`
- `t2` (query, required, string) — Temperature 2 Example: `310`
- `temperature_unit` (query, optional, string) — k|c Example: `k`
- `k1` (query, optional, string) — Rate at T1 (to get rate at T2)

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/arrhenius-api/v1/temperature-effect?activation_energy=50&ea_unit=kj&t1=300&t2=310&temperature_unit=k"
```

**Response:**
```json
{
    "data": {
        "q10": 1.909088,
        "note": "Rate ratio when going from T1 to T2. Q10 is the factor per 10 K rise near T1.",
        "formula": "k2/k1 = exp(−Ea/R·(1/T2 − 1/T1)).",
        "temperature_1_K": 300,
        "temperature_2_K": 310,
        "activation_energy": {
            "J_per_mol": 50000,
            "kJ_per_mol": 50
        },
        "rate_ratio_k2_over_k1": 1.90908785
    },
    "meta": {
        "timestamp": "2026-06-04T10:18:56.947Z",
        "request_id": "74329fa2-528e-4b72-9f9c-604b9f2d15b3"
    },
    "status": "ok",
    "message": "Rate ratio for a temperature change",
    "success": true
}
```

### Meta

#### `GET /v1/meta` — Spec

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/arrhenius-api/v1/meta"
```

**Response:**
```json
{
    "data": {
        "api": "arrhenius",
        "note": "Arrhenius reaction-kinetics maths — computed locally and deterministically, no key, no third-party service. Ea in J/mol (or kJ via ea_unit), temperature in K (or °C).",
        "endpoints": [
            "/v1/rate-constant",
            "/v1/activation-energy",
            "/v1/temperature-effect",
            "/v1/meta"
        ],
        "gas_constant_R": 8.314462618
    },
    "meta": {
        "timestamp": "2026-06-04T10:18:57.053Z",
        "request_id": "c42e12c0-3c0a-4596-80f2-500e237380dd"
    },
    "status": "ok",
    "message": "Meta",
    "success": true
}
```


---
Marketplace page: https://www.oanor.com/api/arrhenius-api
OpenAPI spec: https://www.oanor.com/api/arrhenius-api/openapi.json