Instrument 03
Arrhenius
k at two or more temperatures in; the activation energy, A and k at a new temperature out.
This is the instrument’s sample run (demo numbers). Change anything and press Run, or start from an empty form.
The first line, “T (°C), k (1/s)”, was read as column titles and skipped.
Result
Ea = 50.0 kJ mol−1
- Pre-exponential factor A
- 5.76 × 105 s⁻¹
- Slope of ln k vs 1/T
- −6,014 K
- R2
- 1.0000
- k at 70 °C
- 0.0141 s⁻¹
- Rate rise, 25 → 35 °C
- ×1.92
The working
Intermediate values are carried to six significant figures; results are rounded to three at the end.
- Temperatures in kelvin (°C + 273.15), then 1/T and ln k:
T °C T (K) k 1/T (K−1) ln k 25 298.15 0.001 3.35402 × 10−3 −6.90776 35 308.15 0.001924 3.24517 × 10−3 −6.25335 45 318.15 0.003554 3.14317 × 10−3 −5.63968 55 328.15 0.006322 3.04739 × 10−3 −5.06372 - Least-squares line through the 4 points: slope −6,014.12 K, intercept 13.2636.
- Ea = −slope × R = −(−6,014.12) × 8.31446 J mol−1 K−1 = 50,004.2 J mol−1 = 50.0 kJ mol−1.
- A = eintercept = e13.2636 = 5.76 × 105 s⁻¹.
- k at 343.15 K = A e−Ea/RT: first −Ea/RT = −50,004.2 / (8.31446 × 343.15) = −17.5262, then k = 5.7587 × 105 × e−17.5262 = 0.0141 s⁻¹.
- Rate rise from 25 °C to 35 °C: k(308.15 K)/k(298.15 K) = exp[(Ea/R)(1/298.15 − 1/308.15)] = exp(6,014.12 × 1.08844 × 10−4) = e0.654598 = 1.92.
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