 # 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 NH3 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 kp and kc
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
Ea → 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
k1, k2 → equilibrium constant
Case 1 : If ΔH = 0
logK2 − logK1 = 0 : k1 = k2
Case 2 : If ΔH > 0 endo
k2 > k1

Prediction of extent of completion of reaction :
kc > 1 forward reaction is favourable
kc < 1 backward reaction is favourable
A + B \rightleftharpoons C + D
k_{c} = \frac{[C] [D]}{[A][B]} ∴ kC = 103 forward favours
kc = 10−3 backward favours
If kc = 1 equilibrium

Reaction quotient (QC):
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 QC = kC , reaction is in equilibrium
Case II : If QC < kC forward reaction
Case III : QC > kC back ward reaction

### 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, kf and kb are rate constants.

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, Kc 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 Kc and Kp
K_{p} = K_{c}\left[RT\right]^{\Delta n_{g}}
Where, Δng = 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}}