## Equilibrium

# Law of Chemical Equilibrium and Equilibrium Constants, Henry's Law

**Law of mass action : (by guldberg and waage)**

A + B → Products

rate ∝ [A] [B]

[A], [B] are the active masses of A and B.

Rate = k[A] [B] , where k = rate constant

**Active mass :**

Molar concentration = \frac{n}{V_{L}} for both gases and solution. For gases active mass can be expressed in partial pressures also.

8.5 gm of NH_{3} is present in 500ml vessel

Active mass of \left[NH_{3}\right] = \frac{wt}{m.wt}\times \frac{1000}{V_{ml}}

=\frac{8.5}{17}\times\frac{1000}{500} = 1

rate = k[A] [B] ⇒ k = \frac{rate}{[A][B]}

⇒ rate ∝ k

**Equilibrium constant in terms of partial pressure (Kp) :**

k_{p} = \frac{P_C^c \ P_D^d}{P_A^a \ P_B^b}

Relation between k_{p} and k_{c}

PV = nRT ⇒ p = \left(\frac{n}{v}\right)RT

P = CRT

k_{p} = \frac{\left(C_{C}RT\right)^{C}.\left(C_{D}RT\right)^{D}}{\left(C_{A}RT\right)^{A}.\left(C_{B}RT\right)^{B}}

k_{p} = k_{c}RT^{\Delta n}

**Arrhenius equation with equilibrium constant :**

According to Arrhenius k = A.e^{\frac{-E_{a}}{RT}}

A → frequency factor

R → Gas constant

T → Temperature

E_{a} → Activation energy

\log k = \log A - \frac{E_{a}}{2.303 \ RT}

\log\frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 \ R}\left[\frac{1}{T_{1}} - \frac{1}{T_{2}}\right]

\log\frac{k_{2}}{k_{1}} = \frac{\Delta H}{2.303 \ R}\left[\frac{1}{T_{1}} - \frac{1}{T_{2}}\right] Van't Hoff reaction

ΔH = enthalpy of reaction

k_{1}, k_{2} → equilibrium constant**Case 1** : If ΔH = 0

logK_{2} − logK_{1} = 0 : k_{1} = k_{2}**Case 2 :** If ΔH > 0 endo

k_{2} > k_{1}

**Prediction of extent of completion of reaction :**

k_{c} > 1 forward reaction is favourable

k_{c} < 1 backward reaction is favourable

A + B \rightleftharpoons C + D

k_{c} = \frac{[C] [D]}{[A][B]}

∴ k_{C} = 10^{3} forward favours

k_{c} = 10^{−3} backward favours

If k_{c} = 1 equilibrium

**Reaction quotient (Q _{C}):**

A + B \rightleftharpoons C + D

Q_{C} = \frac{[C] [D]}{[A][B]} and Q_{P} = \frac{P_{C}\times P_{D}}{P_{A}\times P_{B}}

case I : If Q

_{C}= k

_{C}, reaction is in equilibrium

Case II : If Q

_{C}< k

_{C}forward reaction

Case III : Q

_{C}> k

_{C}back ward reaction

### Part1: View the Topic in this Video from 0:11 to 11:26

### Part2: View the Topic in this Video from 3:55 to 14:00

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1. For a general reaction, \tt aA + bB \rightleftharpoons cC + dD

Rate of forward reaction \propto \left[A\right]^{a} \left[B\right]^{b} = k_{f}\left[A\right]^{a} \left[B\right]^{b}

Rate of backward reaction \propto \left[C\right]^{c} \left[D\right]^{d} = k_{b}\left[C\right]^{c} \left[D\right]^{d}

Where, *k _{f}* and

*k*are rate constants.

_{b}2. At equilibrium,

Rate of forward reaction = Rate of backward reaction

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

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

Where, K_{c} is called the **equilibrium constant**.

3. For a gaseous reaction, \tt aA + bB \rightleftharpoons cC + dD

K_{p} = \frac{P_C^c \times P_D^d}{P_A^a \times P_B^b}

4. **Relation between K _{c} and K_{p}**

K_{p} = K_{c}\left[RT\right]^{\Delta n_{g}}

Where, Δn

_{g}= moles of products − moles of reactants (gaseous only)

5. For a general reaction, \tt aA + bB \rightleftharpoons cC + dD

Which is not at equilibrium,

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