Law of mass action and Kc, Kp — Hinglish notes

2.6.2 · Chemistry › Equilibrium

LAW OF MASS ACTION kya hai?

For an elementary reaction $a A + b B \to c C + d D$ : $rate_{f or w a r d} = k_{f} [A]^{a} [B]^{b}$

Powers kyun? Kyunki ek reaction event mein $a$ molecules of A aur $b$ of B ko simultaneously milna hota hai. Us meeting ki chance $[A]^{a} [B]^{b}$ ki tarah scale karti hai — independent events ki probabilities multiply karne jaisa hi logic hai.

$K_{c}$ derive kaise karte hain (kinetic route)

Reversible reaction consider karo: $a A + b B ⇌ c C + d D$

Step 1 — Forward rate (kyun: A,B collide karke products banate hain): $r_{f} = k_{f} [A]^{a} [B]^{b}$

Step 2 — Backward rate (kyun: C,D collide karke reactants reform karte hain): $r_{b} = k_{b} [C]^{c} [D]^{d}$

Step 3 — Equilibrium par rates equal hoti hain (kyun: koi net change nahi matlab forward = backward): $k_{f} [A]^{a} [B]^{b} = k_{b} [C]^{c} [D]^{d}$

Step 4 — Rearrange karo (kyun: dono rate constants ikattha karo, dono fixed $T$ par constant hain): $\frac{k _{f}}{k _{b}} = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}} = K_{c}$

$K_{p}$ kaise milta hai (gases ke liye)

Gases ke liye partial pressures measure karna aasaan hota hai. Partial pressures se define karo: $K_{p} = \frac{p _{C}^{c} p _{D}^{d}}{p _{A}^{a} p _{B}^{b}}$

$K_{p}$ ko $K_{c}$ se relate karo ideal gas law $p V = n R T$ use karke:

Step 1 — Har gas ke liye, partial pressure (kyun: ideal gas ke liye pressure ∝ concentration): $p_{i} = \frac{n _{i}}{V} R T = [i] R T where [i] = \frac{n _{i}}{V}$

Step 2 — $p_{i} = [i] R T$ ko $K_{p}$ mein substitute karo: $K_{p} = \frac{([ C ] R T ) ^{c} ([ D ] R T ) ^{d}}{([ A ] R T ) ^{a} ([ B ] R T ) ^{b}}$

Step 3 — $R T$ powers ko alag karo (kyun: $R T$ ke exponents collect karo): $K_{p} = K_{c} \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}} \cdot (R T)^{(c + d) - (a + b)}$

Step 4 — $Δ n_{g} = (c + d) - (a + b)$ = gaseous products ke moles − gaseous reactants ke moles let karo:

Important rules (YEH kyun hold karte hain)

Equilibria ko manipulate karna:

Reaction reverse karo → $K^{'} = 1/ K$ (numerator aur denominator swap ho jaate hain).
Coefficients ko $n$ se multiply karo → $K^{'} = K^{n}$ (har term $n$ ki power tak raise ho jaati hai).
Do reactions add karo → $K = K_{1} \times K_{2}$ (rates chain multiply hoti hain).

Worked examples

Common mistakes

Flashcards

Law of mass action states rate ∝ ?

product of active masses of reactants, each raised to its stoichiometric coefficient

K_{c}

for

a A + b B ⇌ c C + d D

K_{c} = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}

Kinetic origin of

K_{c}

at equilibrium

k_{f} [A]^{a} [B]^{b} = k_{b} [C]^{c} [D]^{d}

, so

K_{c} = k_{f} / k_{b}

Relation between

K_{p}

and

K_{c}

K_{p} = K_{c} (R T)^{Δ n_{g}}

Definition of

Δ n_{g}

gaseous moles of products − gaseous moles of reactants

When does

K_{p} = K_{c}

when

Δ n_{g} = 0

Why omit pure solids/liquids from K

their activity (concentration) is constant, absorbed into K

Effect of catalyst on K

none — speeds both directions equally

Only factor that changes K

temperature

Reverse a reaction, new K = ?

1/ K

Multiply all coefficients by n, new K = ?

K^{n}

K_{p}

for

C a C O_{3} (s) ⇌ C a O (s) + C O_{2} (g)

K_{p} = p_{C O_{2}}

Recall Feynman: 12-saal ke bachche ko explain karo

Ek busy playground swap imagine karo: bachche marbles ke badle stickers trade karte hain aur wapas bhi. Kuch time baad marbles-to-stickers trade karne ki rate stickers-to-marbles ki rate ke barabar ho jaati hai. Kuch change nahi lagta, lekin trades hoti rehti hain. Agar tum "kitne stickers per marble" crowd mein count karo, toh jab tak mausam (temperature) same rehta hai, tum hamesha same number paate ho. Wahi fixed number $K$ hai. Zameen par baithe thande marbles (solids) count nahi hote — sirf woh jo actively hawaon mein udd rahe hain (gases/dissolved) matter karte hain.

Connections

Chemical Equilibrium – Dynamic Nature
Le Chatelier's Principle
Reaction Quotient Q vs K
Gibbs Free Energy and K ( $Δ G^{\circ} = - R T ln K$ )
Rate Constants and Arrhenius Equation
Ionic Equilibrium – Ka, Kb, Kw