Temperature sensitivity rule of thumb If the rate of a chemical reaction doubles for every 10 °C rise, by what factor does the rate increase when temperature is raised from 30 °C to 70 °C?

Introduction / Context:A common engineering rule of thumb states that many reaction rates approximately double for each 10 °C temperature increase. This is a practical approximation derived from Arrhenius behavior for moderate temperature ranges.

Given Data / Assumptions:

• Rate doubles for every ΔT = 10 °C.
• Temperature change: 30 °C to 70 °C (ΔT = 40 °C).

Concept / Approach:Apply the doubling rule in discrete steps equal to 10 °C increments. Each 10 °C step multiplies the rate by 2. For 40 °C total increase, there are 4 such steps.

Step-by-Step Solution:Number of 10 °C steps = (70 − 30)/10 = 4.Overall multiplicative factor = 2^4 = 16.Therefore, rate at 70 °C ≈ 16 times the rate at 30 °C.

Verification / Alternative check:Arrhenius equation k = A exp(−Ea/RT) shows exponential sensitivity to 1/T; the doubling rule is an empirical simplification consistent with moderate Ea values over modest ranges.

Why Other Options Are Wrong:

• 8 corresponds to three doublings (30 to 60 °C).
• 12 is not a power-of-two doubling outcome.
• 32 would require five doublings (30 to 80 °C).

Common Pitfalls:

• Counting the number of temperature intervals incorrectly or including the starting temperature as a “step.”

Final Answer:16