Temperature Coefficient ($$\mu$$) of a Reaction

$$\mu = \frac{k_{T+10}}{k_T} \approx 2 \text{ to } 3$$

• General Formula for Temperature Jump ($$\Delta T$$):

$$\frac{k_{T_2}}{k_{T_1}} = \mu^{\frac{T_2 - T_1}{10}} = \mu^{\frac{\Delta T}{10}}$$

• Rate Ratio Formula:

$$\frac{\text{Rate}_2}{\text{Rate}_1} = \mu^{\frac{\Delta T}{10}}$$

Concept: The temperature coefficient ($$\mu$$) of a chemical reaction measures the factor by which the rate constant ($$k$$) increases for every $$10^\circ\text{C}$$ ($$10\text{ K}$$) rise in temperature. For the majority of chemical reactions, the rate of reaction approximately doubles or triples for every $$10^\circ\text{C}$$ rise in temperature.

Notation

• $$k_T$$ = Rate constant at initial temperature T
• $$k_{T+10}$$ = Rate constant at elevated temperature $$T + 10^\circ\text{C}$$
• $$\mu$$ = Temperature coefficient (dimensionless, usually between 2 and 3)
• $$\Delta T$$ = Temperature difference ($$T_2 - T_1$$)