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 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
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 :
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 = 10³ 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