Engineering
Arrhenius and Q10 temperature-rate ratios in a spreadsheet
Compare idealized temperature-rate models with explicit units and assumed coefficients. A rate ratio alone does not establish a product shelf life.
Use Kelvin temperatures and consistent energy units
For an Arrhenius model with constant activation energy and pre-exponential factor over the interval, k2/k1 = EXP((Ea/R)*(1/T1-1/T2)). Convert Celsius to Kelvin by adding 273.15, and convert kJ/mol to J/mol when R is in J/(mol*K). Changes in mechanism, phase or environment can invalidate extrapolation.
Ea=83.14 kJ/mol is an illustrative input, not a standard pharmaceutical value. It gives about 4.99 for 25 to 40 degrees Celsius. Multiplying a hypothetical six-unit time interval by the unrounded ratio gives 29.91 only under an additional inverse-rate, same-endpoint assumption. Six months of accelerated observations alone do not establish a 29.91-month medicine or food shelf life; product stability evidence and applicable requirements are separate.
| Illustrative kinetic model (assumed Ea = 83.14 kJ/mol) | Formula | Result |
|---|---|---|
| Kelvin Temperatures (25 °C -> 40 °C) | 25 + 273.15 & 40 + 273.15 | 298.15 K & 313.15 K |
| Arrhenius Acceleration Factor (k2 / k1) | EXP((83140 / 8.314) * (1/298.15 - 1/313.15)) | 4.99x faster |
| Hypothetical equivalent time, assuming inverse rate | 6 time units * unrounded ratio | 29.91 time units; not validated shelf life |
| Q10 Approximation (Q10 = 2, 25 °C -> 45 °C) | 2 ^ ((45 - 25) / 10) | 4.00x |
Arrhenius rate acceleration factor (k2 / k1)
A2=Ea_kJ_mol (83.14), B2=T1_C (25), C2=T2_C (40), D2=GasConstant_J_molK (8.314).
=IF(OR(COUNT(A2:D2)<>4,A2<0,B2<=-273.15,C2<=-273.15,D2<=0),"Invalid inputs",ROUND(EXP((A2 * 1000 / D2) * (1 / (B2 + 273.15) - 1 / (C2 + 273.15))), 2))Q10 temperature coefficient rule-of-thumb comparison
A constant Q10 is a separate empirical assumption, not generally identical to an Arrhenius model across all temperatures. E2 must be positive. This comparison does not certify food safety, medical expiry or product reliability.
=IF(OR(COUNT(B2:C2)<>2,NOT(ISNUMBER(E2)),E2<=0,B2<=-273.15,C2<=-273.15),"Invalid inputs",ROUND(E2 ^ ((C2 - B2) / 10), 2))Try the example
Use the original values or change them to test your understanding.