Activation Energy — Revision Notes

⚡ 30-Second Revision

Definition: — Minimum energy for reactants to form products.
Symbol: — $E_a$
Arrhenius Equation: — $k = A e^{-E_a / RT}$
Logarithmic Form: — $\ln k = \ln A - \frac{E_a}{RT}$
Two-point Form: — $\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$
Catalyst Effect: — Lowers $E_a$ (for both forward & reverse), increases rate, no change in $\Delta H$.
Temperature Effect: — Increases fraction of molecules with $E \ge E_a$, increases rate, no change in $E_a$.
Energy Profile: — $E_a$ is energy difference between transition state and reactants.
Units: — $E_a$ in J/mol or kJ/mol; $T$ in Kelvin; $R = 8.314\,\text{J K}^{-1}\text{ mol}^{-1}$.

2-Minute Revision

Activation energy ($E_a$) is the critical energy barrier that reactant molecules must overcome to transform into products. It's the minimum energy required to reach the 'transition state' – a high-energy, unstable intermediate. The Arrhenius equation, $k = A e^{-E_a / RT}$, quantifies this, showing an inverse exponential relationship between $E_a$ and the rate constant ($k$). A lower $E_a$ means a faster reaction, as more molecules possess the necessary energy at a given temperature.

Catalysts are vital for speeding up reactions; they achieve this by providing an alternative reaction pathway with a lower $E_a$. Importantly, catalysts do not change the overall enthalpy change ($\Delta H$) of the reaction.

Temperature, on the other hand, increases reaction rates by increasing the fraction of molecules that have energy $\ge E_a$, but it does not alter the value of $E_a$ itself. Energy profile diagrams visually represent these concepts, showing the relative energies of reactants, products, transition state, $E_a$, and $\Delta H$.

Remember the relationship $\Delta H = E_{a, \text{forward}} - E_{a, \text{reverse}}$.

5-Minute Revision

Activation energy ($E_a$) is the fundamental concept explaining why chemical reactions have varying rates. It's the minimum energy that colliding reactant molecules must possess to overcome the energy barrier and form an unstable 'transition state' (or activated complex), which then proceeds to form products. Only 'effective collisions' – those with energy $\ge E_a$ and proper orientation – lead to a reaction.

The Arrhenius equation, $k = A e^{-E_a / RT}$, is the mathematical backbone. Here, $k$ is the rate constant, $A$ is the pre-exponential factor (related to collision frequency and orientation), $R$ is the gas constant, and $T$ is the absolute temperature. This equation highlights that a higher $E_a$ leads to a smaller $k$ (slower reaction), and higher $T$ leads to a larger $k$ (faster reaction) because more molecules can overcome the barrier.

Key applications and effects:

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Catalysis: — Catalysts accelerate reactions by providing a new reaction mechanism with a lower $E_a$. They lower $E_a$ for both forward and reverse reactions equally, thus speeding up both and helping achieve equilibrium faster, without changing $\Delta H$ or the equilibrium constant. Example: Enzymes in biological systems.
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Temperature: — Increasing temperature increases the average kinetic energy of molecules, leading to a larger fraction of molecules having energy $\ge E_a$. This increases the frequency of effective collisions and thus the reaction rate. However, temperature does not change the intrinsic value of $E_a$ itself.
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Energy Profile Diagrams: — These diagrams are crucial for visualizing $E_a$. They plot potential energy against reaction progress. $E_a$ is the difference in energy between the reactants and the transition state (peak). The overall enthalpy change ($\Delta H$) is the difference between products and reactants. For an exothermic reaction, $\Delta H < 0$, and for an endothermic reaction, $\Delta H > 0$. The relationship $\Delta H = E_{a, \text{forward}} - E_{a, \text{reverse}}$ is vital.

Worked Example: If a reaction has $E_a = 75\,\text{kJ/mol}$ and a catalyst lowers it by $25\,\text{kJ/mol}$, calculate the factor by which the rate constant increases at $300\,\text{K}$.

Uncatalyzed $E_{a1} = 75000\,\text{J/mol}$. Catalyzed $E_{a2} = 50000\,\text{J/mol}$. Factor increase $= \frac{k_{\text{catalyzed}}}{k_{\text{uncatalyzed}}} = e^{(E_{a1} - E_{a2}) / RT}$ Factor $= e^{(75000 - 50000) / (8.314 \times 300)} = e^{25000 / 2494.2} = e^{10.02} \approx 22460$. This shows the dramatic effect of lowering $E_a$ on reaction rate.

Prelims Revision Notes

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Definition: — Activation energy ($E_a$) is the minimum kinetic energy that colliding reactant molecules must possess to overcome the energy barrier and form products. It's the energy difference between reactants and the transition state.
2
Transition State (Activated Complex): — A high-energy, unstable intermediate formed at the peak of the energy profile, where old bonds are breaking and new bonds are forming.
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Arrhenius Equation: — $k = A e^{-E_a / RT}$.

* $k$: rate constant * $A$: pre-exponential factor (frequency factor), related to collision frequency and orientation. * $E_a$: activation energy (J/mol or kJ/mol) * $R$: gas constant ($8.314\,\text{J K}^{-1}\text{ mol}^{-1}$) * $T$: absolute temperature (Kelvin)

1
Logarithmic Forms:

* $\ln k = \ln A - \frac{E_a}{RT}$ (Plot $\ln k$ vs $1/T$ gives a straight line with slope $-E_a/R$) * $\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$ (For calculating $E_a$ from two rate constants at two temperatures).

1
Effect of Catalyst:

* **Lowers $E_a$** by providing an alternative reaction pathway. * Increases reaction rate significantly. * **Does NOT change $\Delta H$** (enthalpy change) of the reaction. * Does NOT change equilibrium constant; only helps attain equilibrium faster. * Lowers $E_a$ for both forward and reverse reactions by the same amount.

1
Effect of Temperature:

* Increases reaction rate (typically doubles for every $10^\circ\text{C}$ rise). * **Does NOT change $E_a$** itself. $E_a$ is an intrinsic property of the reaction. * Increases the fraction of molecules possessing energy $\ge E_a$.

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Energy Profile Diagrams:

* Reactants $\rightarrow$ Transition State $\rightarrow$ Products. * $E_{a, \text{forward}} = E_{\text{transition state}} - E_{\text{reactants}}$. * $E_{a, \text{reverse}} = E_{\text{transition state}} - E_{\text{products}}$.

* $\Delta H = E_{\text{products}} - E_{\text{reactants}}$. * Relationship: $\Delta H = E_{a, \text{forward}} - E_{a, \text{reverse}}$. * Exothermic reaction: $\Delta H < 0$, $E_{\text{products}} < E_{\text{reactants}}$.

* Endothermic reaction: $\Delta H > 0$, $E_{\text{products}} > E_{\text{reactants}}$.

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Important Note: — $E_a$ is always positive. If $E_a = 0$, the reaction is extremely fast, limited only by collision frequency ($k=A$).

Vyyuha Quick Recall

All Chemists Think Energy Required:

Arrhenius Equation
Catalyst (lowers $E_a$)
Temperature (increases rate, not $E_a$)
Energy Profile Diagram
Rate (inversely proportional to $E_a$)