2.6.1Equilibrium

Reversible reactions and dynamic equilibrium

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WHAT is a reversible reaction?

An irreversible reaction (like burning wood) goes essentially to completion — the reverse rate is negligible. A reversible reaction settles at a mixture of reactants and products.

"Dynamic" = molecules are still reacting (motion never stops). "Equilibrium" = the net change is zero (concentrations frozen).


WHY do concentrations become constant? (Derivation from scratch)

Let's build it, not memorise it. Take a simple reversible reaction: ABA \rightleftharpoons B

Step 1 — Write the two rates. For an elementary step, rate ∝ concentration.

  • Forward rate: rf=kf[A]r_f = k_f[A]Why? Only A can go forward, so it depends on how much A there is.
  • Backward rate: rb=kb[B]r_b = k_b[B]Why? Only B can go back.

Step 2 — Track what happens over time. At the start we pour in pure A:

  • [A][A] is large → rfr_f is large.
  • [B]=0[B]=0rb=0r_b = 0.

So initially A → B dominates. As the reaction runs:

  • [A][A] fallsrfr_f falls.
  • [B][B] risesrbr_b rises.

Why this step? We're watching the two rates move toward each other like a closing scissor.

Step 3 — The meeting point. At some moment rf=rbr_f = r_b. From then on: rate of A consumed=rate of A produced\text{rate of A consumed} = \text{rate of A produced} so [A][A] can't change any more, and neither can [B][B]. That is equilibrium.

Step 4 — Get the equilibrium relationship. Set the rates equal: kf[A]eq=kb[B]eqk_f[A]_{eq} = k_b[B]_{eq}

Why this matters: it proves equilibrium concentrations are fixed by kinetics, and it explains why KcK_c is a constant at a given temperature (because kf,kbk_f, k_b are constants at that temperature).

Figure — Reversible reactions and dynamic equilibrium

HOW to recognise dynamic equilibrium (the 4 conditions)


Worked Examples


Common Mistakes (Steel-manned)


Recall Feynman: explain to a 12-year-old

Imagine a busy pond between two ponds joined by a stream. Fish swim from the left pond to the right pond, and other fish swim back from right to left. If the same number cross each way every minute, the number of fish in each pond stops changing — even though fish are always swimming! That's dynamic equilibrium: everything is still happening, but the totals stop moving. It only works if no fish can jump out of the ponds (a closed system).


Flashcards

What defines a reversible reaction?
One where products can react back to re-form reactants under the same conditions; written with \rightleftharpoons.
What is dynamic equilibrium?
A state in a closed system where forward and backward reaction rates are equal, so concentrations stay constant while both reactions continue.
Why is equilibrium called "dynamic"?
Because molecules are still reacting in both directions; only the net change is zero.
What are the four signs of dynamic equilibrium?
Closed system; constant macroscopic properties; equal nonzero forward/backward rates; reachable from either direction.
Derive the equilibrium ratio for ABA\rightleftharpoons B.
Set kf[A]=kb[B]k_f[A]=k_b[B][B]/[A]=kf/kb=Kc[B]/[A]=k_f/k_b=K_c.
Are reactant and product concentrations equal at equilibrium?
No — the rates are equal, not the concentrations.
What does an isotope-labelling experiment prove about equilibrium?
That reactions continue (label appears on the other side), so equilibrium is dynamic not static.
Effect of a catalyst on the equilibrium position?
None — it speeds up both directions equally, reaching equilibrium faster at the same concentrations; KcK_c unchanged.
Why must the system be closed to reach equilibrium?
If products escape, the backward rate can never rise to match the forward rate, so rates never balance.
On what does KcK_c depend?
Only on temperature (since kfk_f and kbk_b depend on temperature).

Connections

  • Equilibrium constant Kc and Kp — the constant this note derives, quantified.
  • Le Chatelier's principle — how equilibrium shifts when disturbed.
  • Rate of reaction and rate constants — the kf,kbk_f, k_b underpinning the derivation.
  • Collision theory — why rate ∝ concentration.
  • Effect of temperature on equilibrium — why KcK_c is temperature-dependent.
  • Catalysis — why catalysts don't move the equilibrium.

Concept Map

has

has

reaches in closed system

as A falls

as B rises

converge

converge

net change zero

concentrations

set rates equal

fixed at given temperature

Reversible reaction

Forward reaction rf equals kf A

Backward reaction rb equals kb B

Dynamic equilibrium

rf decreases

rb increases

rf equals rb

Concentrations constant

Kc equals kf over kb

Constant at fixed T

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, reversible reaction ka matlab hai ki reaction dono direction mein chal sakti hai — reactants product banate hain (forward), aur products wapas reactants ban jaate hain (backward). Isko hum \rightleftharpoons (double arrow) se likhte hain. Dynamic equilibrium tab aata hai jab forward reaction ki speed aur backward reaction ki speed barabar ho jaati hai. Us moment ke baad concentrations change hona band ho jaati hain — par reaction rukti nahi hai, dono taraf chalti rehti hai. Isiliye "dynamic" bolte hain: kaam chal raha hai, bas net change zero hai.

Sabse bada confusion yeh hota hai ki students sochte hain reaction "ruk gayi". Nahi bhai — molecules abhi bhi aage-peeche convert ho rahe hain. Iska proof isotope experiment se milta hai: agar equilibrium par radioactive I2I_2 daalo, thodi der mein radioactivity HI mein bhi dikhne lagti hai, matlab reaction abhi bhi ho rahi hai. Dusra confusion: log sochte hain equilibrium par reactant aur product ki quantity barabar hoti hai. Galat — barabar hoti hai rates, quantities nahi.

Derivation simple hai: forward rate =kf[A]= k_f[A], backward rate =kb[B]= k_b[B]. Equilibrium par yeh barabar karo, to [B]/[A]=kf/kb=Kc[B]/[A] = k_f/k_b = K_c. Yeh KcK_c sirf temperature par depend karta hai. Ek important baat — equilibrium ke liye system closed hona chahiye, warna agar gas nikal gayi to backward reaction kabhi match nahi karegi. Aur catalyst equilibrium ko shift nahi karta, sirf jaldi pahunchata hai — dono directions ko equally fast karta hai. Bas yeh core samajh lo, poora chapter aasan ho jayega.

Go deeper — visual, from zero

Test yourself — Equilibrium

Connections