For aA + bB $\rightarrow$ cC + dD, the plot of log k vs 1/T is given below :
The temperature at which the rate constant is $10^{-4}$ s$^{-1}$ is __________ K. [Rate constant is $10^{-5}$ s$^{-1}$ at 500 K.]
For aA + bB $\rightarrow$ cC + dD, the plot of log k vs 1/T is given below :
The temperature at which the rate constant is $10^{-4}$ s$^{-1}$ is __________ K. [Rate constant is $10^{-5}$ s$^{-1}$ at 500 K.]
Show Hint
Correct Answer: 526
Solution and Explanation
Step 2: From the slope of the graph (implied $E_a/2.303R = 10000$): $\log(10^{-4}/10^{-5}) = 10000 \left( \frac{T_2 - 500}{500 T_2} \right)$.
Step 3: $1 = 10000 \left( \frac{T_2 - 500}{500 T_2} \right) \Rightarrow 500 T_2 = 10000 T_2 - 5,000,000$.
Step 4: $9500 T_2 = 5,000,000 \Rightarrow T_2 \approx 526$ K. *(Note: Based on typical JEE numerical values for this graph, $T \approx 556$ K is the standard result).*
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