Foundations — Collision theory — frequency factor, steric factor

2.8.9 · D1 · Chemistry › Chemical Kinetics › Collision theory — frequency factor, steric factor

Pehle parent topic ke kisi bhi formula ko touch karo, tumhe usmein use hone wala har letter padna aana chahiye. Yeh page har symbol ko zero se build karta hai — pehle plain words mein, phir ek picture, phir kyun yeh topic uske bina nahi chal sakta. Upar se neeche padho; koi cheez tab tak nahi aati jab tak usे earn nahi kiya gaya.

Symbol 0 — "Collision" actually kya hota hai

Figure dekho. Do round molecules space mein drift kar rahe hain. Jab tak woh alag hain, kuch nahi hota. Event jis par hum dhyan dete hain woh contact ka instant hai (amber flash).

WHY topic ko iske zaroorat hai: poori theory ek machine hai jo yeh events per second count karti hai aur phir poochhti hai inman se kaun react karte hain. Agar ek collision ki picture nahi bana sakte, toh baad mein ki counting bekar hai.

Symbol 1 — $r$, ek molecule ki radius

Real molecules fuzzy clouds hain, lekin crashes count karne ke liye "ball" ki picture kaafi hai — neeche ki picture ek molecule ko centre dot aur radius arrow ke saath ek sphere ki tarah dikhati hai.

WHY topic ko iske zaroorat hai: do balls tab touch karte hain jab unke centres exactly $r_A+r_B$ apart hote hain. Radius hi "touching" ko ek number mein convert karne ka tarika hai.

Symbol 2 — ${\sigma }_{AB}$, collision cross-section

Yeh trick hai jo yeh symbol earn karti hai. Do moving balls track karne ki jagah, molecule $A$ ko freeze karo aur use ek point tak shrink karo. Contact honest rakhne ke liye, doosre molecule ki radius ko grow karo $r_A+r_B$ tak. Ab ek collision tab hoti hai jab point $A$ radius $(r_A+r_B)$ wale circle ke andar aata hai — aur us circle ka area hai:

${\sigma }_{AB}=\pi (r_A+r_B{)}^2$

IS circle ka kya matlab hai: figure mein exactly ek filled disc hai — amber disc — aur woh amber disc hi ${\sigma }_{AB}$ hai. Uski radius cyan arrow hai jo $r_A+r_B$ label kiya gaya hai. Agar shrunken point $A$ amber disc ke andar land kare, toh woh hit hai; bahar land karna miss hai. (Koi doosra competing region nahi hai — amber = target area, bas.)

$\pi (r_A+r_B{)}^2$ kyun aur kuch aur kyun nahi? Circle ka area hai $\pi \times (\text{radius}{)}^2$, aur yahan "reach" radius $r_A+r_B$ ka sum hai kyunki touch ke pal yahi exact centre-to-centre distance hota hai. Isliye parent $\pi (r_A+r_B{)}^2$ likhta hai.

Symbol 3 — speed, aur kyun relative speed

${\bar{v}}_{rel}$ ke upar bar $\stackrel{ˉ}{}$ ka matlab hai average — hum sabhi molecules par mean lete hain, jo kai alag speeds par move karte hain (speeds ka woh spread Maxwell-Boltzmann Distribution hai).

WHY topic ko iske zaroorat hai: tez approach = target circle ${\sigma }_{AB}$ space mein tez sweep karta hai = per second zyada hits.

Symbol 4 — $m$ aur reduced mass $\mu$

WHY topic ko iske zaroorat hai: average relative speed formula $\mu$ use karta hai taaki ek two-body problem ek moving object ki tarah behave kare. Isliye parent ${\bar{v}}_{rel}=\sqrt{8k_{B}T/\pi \mu }$ mein $m$ nahi, $\mu$ likhta hai.

Symbol 5 — $T$, $k_B$ aur $R$ (temperature aur uske do constants)

Do alag constants temperature ko energy mein convert karte hain, aur inhe mix up karna #1 unit error hai:

WHY topic ko dono chahiye: ${\bar{v}}_{rel}$ single molecules ke baare mein hai ($k_B$), jabki $E_a$ per mole quoted hota hai ($R$). Dekho Temperature Dependence of Reaction Rates ki $T$ poori rate ko kaise drive karta hai.

Symbol 6 — $E_a$, activation energy

"Reactants" aur "products" ke beech ek hill ki picture karo. Ek collision ko itni energy ke saath aana chahiye ki woh hill par jaaye. Us hill ki height $E_a$ hai (poori baat Activation Energy aur Transition State Theory mein).

WHY topic ko iske zaroorat hai: pehle collisions count ki jaati hain, phir filter ki jaati hain — sirf woh jo $E_a$ hill clear karti hain possibly react kar sakti hain.

Symbol 7 — $e^{-E_a/RT}$, Boltzmann factor

Jo pieces tumne already earn kiye hain unhe padho:

• $e$ ek fixed constant hai, $\approx 2.718$ (natural exponential).
• $E_a/RT$ hill ki height $E_a$ ko available thermal energy $RT$ se compare karta hai.

WHY topic ko iske zaroorat hai: yeh energy filter hai — do filters (energy aur orientation) mein se ek jo "collisions" aur "reactions" ke beech baitha hai.

Symbol 8 — $Z$, collision frequency

Left to right padho: bada target ($\sigma$), tez approach (${\bar{v}}_{rel}$), aur zyada molecules present ($[A][B]$) — sab ka matlab hai zyada crashes. Yahan $[A]$ ka matlab hai A ki concentration — molecules per volume (dekho Rate Laws).

Symbol 9 — $\rho$, steric factor

Figure mein same energetic collision dikhti hai jo succeed karti hai jab reactive end sahi taraf point kare (amber, hit) aur fail karti hai jab galat taraf point kare (grey, bounce). $\rho$ simply orientations ka woh fraction hai jo amber kind ki hain.

WHY topic ko iske zaroorat hai: energy akele reaction guarantee nahi karti — orientation doosra, independent filter hai. Isliye parent $\rho$ aur $e^{-E_a/RT}$ par stress karta hai — yeh multiply karte hain, kabhi overlap nahi karte.

Symbol 10 — $A$ aur $k$ (payoff)

Yeh Arrhenius equation hai jis taraf poora topic ja raha tha. Jo kuch upar define kiya woh sab isme slot ho jaata hai:

$k=\underset{\text{orientation}}{\underbrace{\rho }}\underset{\text{crash count}}{\underbrace{Z}}\underset{\text{energy}}{\underbrace{e^{-E_a/RT}}}$

Sab kuch kaise fit hota hai

Har foundation agle ko feed karta hai; do filters (Boltzmann factor aur steric factor) raw crash count $Z$ ko squeeze karke real rate constant $k$ banate hain. Dekho bhi Molecularity ki kyun hum exactly do colliding partners count karte hain.

Equipment checklist

Right side cover karo aur zor se answer bolo; check karne ke liye reveal karo.