Appeared in: 2024 (3 sets)
Assertion (A) : Rate constant increases with increase in temperature.
Reason (R) : Increasing the temperature of the substance increases the fraction of molecules, which collide with energies greater than activation energy.
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Official Evaluation Steps & EL10 Insight
Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
According to the Arrhenius Equation, the rate constant $k$ of a reaction is given by:
$$k = A e^{-\frac{E_a}{RT}}$$Where:
- $k$ = Rate constant
- $A$ = Arrhenius pre-exponential factor (frequency factor)
- $E_a$ = Activation energy ($\text{J mol}^{-1}$)
- $R$ = Universal gas constant ($8.314 \text{ J K}^{-1} \text{mol}^{-1}$)
- $T$ = Absolute temperature ($\text{K}$)
- $e^{-\frac{E_a}{RT}}$ = Fraction of molecules having kinetic energy equal to or greater than activation energy ($E \ge E_a$)
Step 2 (Step-by-Step Analysis): [0.25 Mark]
- Evaluation of Assertion (A): As temperature $T$ increases, the exponent term $-\frac{E_a}{RT}$ becomes less negative. Consequently, the value of $e^{-\frac{E_a}{RT}}$ increases, which directly increases the rate constant $k$. Thus, Assertion (A) is TRUE.
- Evaluation of Reason (R): According to the Maxwell-Boltzmann distribution curve of kinetic energies, an increase in temperature flattens the curve and shifts it to the right. This significantly expands the area under the curve corresponding to energies $