A particular reaction maintains a steady and highly specific temperature coefficient exactly equal t — Chemical Kinetics Chemistry Question
Question
A particular reaction maintains a steady and highly specific temperature coefficient exactly equal to $2$. If the environmental temperature of the reaction vessel is steadily raised from a baseline of $25^\circ \text{C}$ all the way up to $85^\circ \text{C}$, the overall reaction rate will drastically compound to become exactly $X$ times its original baseline rate. Determine the precise integer value of $X$.
💡 Solution & Explanation
The temperature coefficient dictates that for every uniform $10^\circ \text{C}$ incremental rise in temperature, the reaction rate multiplies by a fixed factor of 2. The total total jump in temperature is $\Delta T = 85^\circ \text{C} - 25^\circ \text{C} = 60^\circ \text{C}$. This constitutes exactly $60 / 10 = 6$ distinct sequential increments. The overall rate multiplier $X$ is therefore $2^6$. Calculating this power yields precisely $64$.