Question

The temperature coefficient for a reaction is two. By how many times does the rate of reaction increase if the temperature of the reaction is increased from 340 k to 380 k?

Answer 1

Step 1 Understanding the concept:

• The rate constant ratio for two temperatures that differ by $10°\mathrm{C}$, often between $25°\mathrm{C}$ and $35°\mathrm{C}$, is known as the temperature coefficient of the reaction.

Step 2 Determine the rate of reaction increases in a given range of temperature:

• Temperature coefficient =$2$
• Temperature Range = 340 K($67°\mathrm{C}$ )to 380 K($107°\mathrm{C}$)
• Temperature difference = $107°\mathrm{C}-67°\mathrm{C}=40°\mathrm{C}$
• Thus,$$\begin{gathered} \mathrm{n}=\frac{40}{10} \\ =4 \end{gathered}$$
• The number of times the rate increase is given, by,$2^{\mathrm{n}}$.
• Thus the rate of reaction increase when the temperature of a reaction is increased by $340\mathrm{K}\mathrm{to}380\mathrm{K}$ is $2^4=16$.