Temperature and Reaction Rates 🚀

When you heat a reaction, molecules zip around faster. In the decomposition of N₂O₅, half of it disappears in just 12 min at 50 °C, 5 h at 25 °C, and a whopping 10 days at 0 °C. A mix of purple KMnO₄ and oxalic acid also decolourises much faster in warm conditions. 🌡️➡️⚡ :contentReference[oaicite:0]{index=0}

Chemists love a rule of thumb: raise the temperature by 10 °C and the rate constant k almost doubles. It’s not magic—it’s math! 😄 :contentReference[oaicite:1]{index=1}

Arrhenius Equation 📈

The temperature effect shows up beautifully in the Arrhenius equation:

\[ k = A e^{-E_a / RT} \]

• A – frequency (pre-exponential) factor.
• E_a – activation energy (J mol^–1).
• R – gas constant (8.314 J mol^–1 K^–1).

:contentReference[oaicite:2]{index=2}

Activation Energy & the Energy Barrier 🏔️

Picture reactants climbing an energy hill to form a short-lived “activated complex.” They need the boost E_a to reach the top, then roll down to products. Lower hills mean quicker trips! ⛷️ :contentReference[oaicite:3]{index=3}

Hotter Means More Molecules Above the Barrier 🔥

The Maxwell–Boltzmann curve shows most molecules with moderate energy. Heating slides and broadens the curve to the right, so many more molecules clear the E_a hurdle. More qualified molecules → faster reaction! 📊 :contentReference[oaicite:4]{index=4}

Turning Data into E_a and A 🔍

Take natural logs and the Arrhenius equation turns linear:

\[ \ln k \;=\; -\frac{E_a}{R}\left(\frac{1}{T}\right) + \ln A \]

Plot \(\ln k\) (y-axis) vs \(1/T\) (x-axis). The slope gives \(-E_a/R\) and the intercept gives \(\ln A\). 😎 :contentReference[oaicite:5]{index=5}

No graph? Compare two temperatures directly:

\[ \ln\!\bigl(\tfrac{k_2}{k_1}\bigr) \;=\; \frac{E_a}{R}\!\left(\frac{1}{T_1} – \frac{1}{T_2}\right) \] :contentReference[oaicite:6]{index=6}

Catalysts: Friendly Shortcuts ✨

A catalyst like MnO₂ in the breakdown of KClO₃ hands reactants an easier path with lower E_a. It speeds both forward and backward steps, reaches equilibrium faster, but never changes ΔG or the equilibrium constant. Small amount, big effect! 🛣️⏩ :contentReference[oaicite:7]{index=7}

Collision Theory in One Minute ⚽➕🎯

Reactions happen when molecules collide with enough energy and the right orientation. For a simple bimolecular step:

\[ \text{Rate} \;=\; Z_{AB} P \, e^{-E_a / RT} \]

• Z_AB – collision frequency.
• P – steric factor (orientation probability).

Lower E_a or raise T and the exponential term skyrockets. 💥 :contentReference[oaicite:8]{index=8}

High-Yield NEET Nuggets 🎯

1. Arrhenius equation and the \(\ln k\) vs \(1/T\) straight-line trick for finding E_a and A. :contentReference[oaicite:9]{index=9}
2. Rule of thumb: a 10 °C rise roughly doubles k. :contentReference[oaicite:10]{index=10}
3. Activation energy concept and the activated complex picture. :contentReference[oaicite:11]{index=11}
4. Effect of catalysts—lower E_a without shifting equilibrium. :contentReference[oaicite:12]{index=12}
5. Collision theory: effective collisions need enough energy and proper orientation (steric factor). :contentReference[oaicite:13]{index=13}