Rate of reaction — average vs instantaneous: Question bank

2.8.1 · D5 · Chemistry › Chemical Kinetics › Rate of reaction — average vs instantaneous

Yeh ek question bank hai jo tumhari misconceptions ko exam se pehle hi tod dega. Har line ek prompt hai; ::: ke baad wala part reasoning hai. Answer ko cover karo, socho, phir reveal karo. Yeh conceptual traps hain — koi heavy arithmetic nahi (woh calculation decks mein hai). Parent: Rate of Reaction — Average vs Instantaneous.

True or false — justify karo

Average rate hamesha interval ke midpoint par instantaneous rate ke barabar hoti hai.

False. Yeh tabhi hota hai jab concentration–time curve interval ke upar ek seedhi line ho; real reactant curves bend karti hain (woh slow down hoti hain), isliye midpoint tangent interval average nahi hoti.

Ek reactant ke liye,

- \frac{Δ [ A ]}{Δ t}

aur

- \frac{d [ A ]}{d t}

ke units same hote hain.

True. Dono (mol/L)/s = M/s hain;

Δ

aur

d

ek hi quantity mein change describe karte hain time ke over, isliye units identical hain — sirf time gap ki size alag hoti hai.

Instantaneous rate sirf bahut chhote time interval ke upar ek average rate hai.

Soch mein True. Yeh average rate ki limit hai jab

Δ t \to 0

; interval ko vanishingly small karo aur uske upar average woh exact rate ban jaata hai us instant par.

Ek reaction rate legitimately ek negative number ke roop mein report ki ja sakti hai.

False. Rate definition ke hisaab se positive hoti hai;

- d [A] / d t

mein minus sign isliye hota hai taaki ek disappearing reactant ki negative slope ko positive rate mein flip kar sake.

2 A \to B

ke liye, A ke disappearance ki rate B ke appearance ki rate ke barabar hoti hai.

False. Ek B banne par do A khatam hote hain, isliye A, B se do guna fast disappear hota hai; sirf coefficients se divide karne ke baad normalized rates match karti hain.

Ek lambe interval ke upar average rate generally initial instantaneous rate se chhoti hoti hai.

Typical reactions ke liye True. Jaise-jaise reactant use hota hai rate girti hai, isliye early fast period baad ke slow periods se dilute ho jaati hai, aur average starting rate se neeche aa jaati hai.

Time interval ki length double karna hamesha average rate ko half kar deta hai.

False. Average rate

Δ [A] /Δ t

hai, aur lambe interval par

Δ [A]

fixed nahi hota — numerator bhi badalta hai, usually proportionally se kam kyunki reaction slow hoti hai.

Reaction rate

r

ek hi number hoti hai chahe tum A, B, C ya D track karo.

True — stoichiometric coefficients se divide karne ka yahi poora point hai. Har species ki apni

d [] / d t

hoti hai, lekin

\frac{1}{ν} d [] / d t

unhe ek shared value par collapse kar deta hai.

Error dhundo

"Rate

= Δ [A] /Δ t = (0.20 - 0.50) /10 = - 0.030

M/s, isliye rate

- 0.030

M/s hai."

Definition ka negative sign drop kar diya gaya. Correct rate

= - Δ [A] /Δ t = + 0.030

M/s hai; ek reactant ki rate positive aani chahiye.

2 N_{2} O_{5} \to 4 NO_{2} + O_{2}

ke liye, kyunki NO₂,

3.0 \times 1 0^{- 4}

M/s par banta hai, reaction rate

3.0 \times 1 0^{- 4}

M/s hai."

NO₂ ka coefficient 4 hai, isliye

r = \frac{1}{4} d [NO_{2}] / d t = 7.5 \times 1 0^{- 5}

M/s. 4 se divide karna bhoolne par reaction rate char guna inflate ho jaati hai.

"Maine

t = 50

s par tangent slope

- 0.030

M/s nikali, isliye instantaneous rate

- 0.030

M/s hai."

Wahi sign trap:

r_{inst} = - d [A] / d t = + 0.030

M/s. Tangent slope negative hai; rate uski positive counterpart hai.

"[A] 0–100 s mein 0.5 se 0.2 M tak gira, isliye

t = 50

s par rate

3.0 \times 1 0^{- 3}

M/s hai."

Woh value poore 0–100 s window par average hai, 50 s par instantaneous rate nahi; baad waali ke liye exactly 50 s par tangent slope chahiye.

"Kyunki

2 H_{2} O_{2} \to 2 H_{2} O + O_{2}

mein O₂ ka coefficient 1 hai, O₂ formation rate reaction rate ke barabar hai."

Yahan True sirf isliye kyunki coefficient 1 hai:

r = \frac{1}{1} d [O_{2}] / d t

. Statement sahi hai lekin galat stated reason ke liye agar tumne socha coefficients kabhi matter nahi karte — karte hain, yeh sirf 1 hota hai.

"Rate ki units mol hain, kyunki hum track karte hain kitne moles react karte hain."

Galat — rate concentration per time track karti hai, isliye units M/s = mol·L⁻¹·s⁻¹ hain. Akele moles dono volume (concentration) aur time bhool jaate hain.

Why questions

Hume sirf ek ki jagah dono average aur instantaneous definition ki zaroorat kyun hai?

Kyunki reaction speed continuously change hoti hai; average ek interval ka overall throughput capture karta hai, jabki instantaneous ek moment par exact speed capture karta hai (woh "speedometer reading").

Minus sign sirf reactant terms ke aage kyun aata hai, product terms ke nahi?

Reactant concentration decrease hoti hai, negative slope deti hai; minus use positive kar deta hai. Product concentration increase hoti hai, already positive slope deti hai, isliye koi sign ki zaroorat nahi.

Hum har species ki rate ko uske stoichiometric coefficient se kyun divide karte hain?

Ek single "reaction rate" paane ke liye jo is baat par independent ho ki tum kaun sa molecule dekh rahe ho; coefficients batate hain har reaction event mein kitne consume/bante hain, isliye divide karna "per event" par normalize karta hai.

Instantaneous rate ke liye ek tangent line ki zaroorat kyun hai na ki ek chord (do points ke beech seedhi line)?

Chord do alag points ke beech average slope deta hai (ek average rate); tangent curve ko ek instant par touch karta hai, exact slope deta hai — wahan derivative.

Initial instantaneous rate aksar sabse badi rate kyun hoti hai jo reaction kabhi bhi have karti hai?

t = 0

par reactant concentration sabse zyada hoti hai, isliye reactant molecules ke beech collisions sabse zyada frequent hote hain (dekho Collision theory); jaise-jaise reactant use hota hai rate girti hai.

Kyun do students jo same flask mein N₂O₅ aur O₂ track kar rahe hain woh alag raw

d [] / d t

values report kar sakte hain phir bhi reaction rate par agree kar sakte hain?

Unki species alag molecular speeds par khatam/banti hain (coefficients 2 aur 1 se set), lekin

\frac{1}{ν} \frac{d [ ]}{d t}

unhe differences divide kar deta hai, ek shared

r

chhod kar.

0–1000 s par average rate ek decaying reaction ke liye

t = 900

s par rate ka achha estimate kyun nahi hai?

Average fast early period se dominated hota hai;

t = 900

s tak reactant almost khatam ho jaata hai aur true instantaneous rate poore-interval average se bahut chhoti hoti hai.

Edge cases

Exactly us moment par instantaneous rate kya hoti hai jab ek reactant khatam ho jaata hai (concentration zero hit karti hai)?

Ek irreversible reaction ke liye yeh zero ki taraf approach karta hai — koi reactant nahi bacha toh flat curve ka tangent horizontal hota hai, isliye

d [A] / d t = 0

Agar ek concentration–time graph perfectly seedhi line hai, toh average vs instantaneous rate ke baare mein kya true hai?

Woh har jagah barabar hoti hain — ek seedhi line ka constant slope hota hai, isliye har tangent har chord se match karta hai; yeh rare zero-order-like case hai.

Equilibrium par ek reaction ke liye, concentration mein change ki net rate kya hoti hai, aur kya iska matlab hai kuch nahi ho raha?

Net

d [] / d t = 0

isliye concentrations constant hain, lekin forward aur reverse reactions equal speed par chalti rehti hain — dynamic balance, dead stop nahi.

Kya instantaneous rate kabhi us instant ko contain karne wali har average rate se zyada ho sakti hai?

Haan. Agar reaction momentarily speed up hoti hai (jaise ek autocatalytic burst), toh us point par tangent kisi bhi surrounding chord se steep ho sakti hai, isliye uski rate enclosing averages se zyada hoti hai.

Kya hota hai average rate ka jab tum interval

Δ t

ko ek fixed time

t

ke around zero ki taraf shrink karte ho?

Yeh

t

par instantaneous rate ki taraf converge karta hai — yeh limit derivative ki definition hai aur isliye instantaneous rate ki bhi.

Kya "rate of reaction" define hoti hai jab balanced equation unknown ya unbalanced ho?

Koi single

r

assign nahi ki ja sakti — tumhe divide karne ke liye stoichiometric coefficients chahiye; bina balanced equation ke tum sirf species-specific

d [] / d t

values report kar sakte ho.

Ek zero-order reaction ke liye, alag-alag times par instantaneous rate kaise compare hoti hai?

Yeh concentration ki parwah kiye bina constant rehti hai (rate [A] se independent hoti hai), isliye instantaneous rate poore time average rate ke barabar hoti hai — ek link aur explore kiya gaya hai Rate law and order of reaction aur Integrated rate laws mein.

Recall Ek-line self-test

Woh two-word rule bolo jo sign fix karta hai aur woh two-word rule jo coefficient fix karta hai. Sign :::: "add minus (reactants ke liye)"; Coefficient :::: "divide by (stoichiometric number)".