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JEE MAIN 2023
08-04-2023 S1
Question
The number of given statement/s which is/are correct is____.
Select the correct option:
A
The stronger the temperature dependence of the rate constant, the higher is the activation energy.
B
If a reaction has zero activation energy, its rate is independent of temperature.
C
The stronger the temperature dependence of the rate constant, the smaller is the activation energy.
D
If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. $k=A \cdot e^{-E a / R T}$ $$ \log _y k=\log _c A-\underbrace{\frac{E a}{2.303 R}}_m \cdot \frac{1}{T} $$ Higher is Ea, stronger is the temperature dependence of k (i.e. steeper the slope) $$ \begin{aligned} (B) & \Rightarrow \frac{1}{k} \frac{d k}{d T}=\frac{E a}{R} \frac{1}{T^2} \\ & \Rightarrow \frac{d k}{d T}=A \times e^{-\frac{E a}{R}} \cdot \frac{E a}{R T^2} \end{aligned} $$
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