Equilibrium Constant is a quantity that is used to measure the relative concentrations of reactants and products in a chemical reaction at equilibrium.

The equilibrium constant of a chemical reaction (usually denoted by the symbol K) provides insight into the relationship between the products and reactants when a chemical reaction reaches equilibrium. For example, the equilibrium constant of concentration (denoted by Kc) of a chemical reaction at equilibrium can be defined as the ratio of the concentration of products to the concentration of the reactants, each raised to their respective stoichiometric coefficients. It is important to note that there are several different types of equilibrium constants that provide relationships between the products and the reactants of equilibrium reactions in terms of different units.

The equilibrium constant for a chemical reaction can be defined as the ratio of the amount of reactant to the amount of product, which is used to determine the chemical behaviour.

At equilibrium, the rate of the forward reaction is equal to the rate of the backward reaction.

i.e.

rf = rb

Or,

kf × α × [A]a[B]b =  kb × α × [C]c[D]d

The rate constants of a reaction remain constant at a particular temperature. The ratio of the rate constant of the forward reaction to the rate constant of the backward reaction is known as the equilibrium constant (K_equ), and should remain constant.

Table of Contents

Equilibrium Constant Formula

Units of Equilibrium Constant

△G, Qc, and Kc

KC vs KP

Characteristics of Equilibrium Constant

Applications of Equilibrium Constant

Calculating the Equilibrium Concentration

Factors Affecting Equilibrium Constant

Equilibrium Constant Formula: K = [products]/[reactants]

Kequ = (kf/kb) = [(C)c (D)d]/[(A)a (B)b] = Kc

Where K_c indicates the equilibrium constant measured in moles per litre.

The Equilibrium Constant Formula in Terms of Partial Pressure for Reactions Involving Gases is:

K_eq = K_f/K_b = $\frac{[p_C]_c[p_D]_d}{[p_A]_a[p_B]_b}$ = K_p

Where K_p indicates the equilibrium constant formula in terms of partial pressures.

Larger Kc/Kp values indicate more product formation and a higher percentage conversion.— title: “Equilibrium Constant” link: “/equilibrium-constant” draft: false

Equilibrium Constant is a value that is used to describe the relationship between the products and reactants of a chemical reaction at equilibrium.

The equilibrium constant of a chemical reaction (usually denoted by the symbol K) provides insight into the relationship between the products and reactants when a chemical reaction reaches equilibrium. For example, the equilibrium constant of concentration (denoted by Kc) of a chemical reaction at equilibrium can be defined as the ratio of the concentration of products to the concentration of the reactants, each raised to their respective stoichiometric coefficients. It is important to note that there are several different types of equilibrium constants that provide relationships between the products and the reactants of equilibrium reactions in terms of different units.

The equilibrium constant for a chemical reaction can be defined as the ratio of the amount of reactant to the amount of product, which is used to determine the chemical behaviour.

At equilibrium, the rate of the forward reaction is equal to the rate of the backward reaction.

i.e.

rf = rb

Or,

kf × α × [A]a[B]b =  kb × α × [C]c[D]d

The rate constants of a reaction at a particular temperature are constant. The ratio of the rate constant of the forward reaction to the rate constant of the backward reaction is called the equilibrium constant (K$_{\text{eq}}$) and is constant.

Table of Contents

Equilibrium Constant Formula

Units of Equilibrium Constant

△G, Qc and Kc

KC vs KP

Characteristics of Equilibrium Constant

Applications of Equilibrium Constant

Calculating the Equilibrium Concentration

Factors Affecting Equilibrium Constant

Equilibrium Constant Formula

Kequ = kf/kb = [C]c[D]d/[A]a[B]b = Kc

Where K_c indicates the equilibrium constant measured in moles per litre.

The Equilibrium Constant Formula in Terms of Partial Pressure for Reactions Involving Gases is:

K_eq = K_f/K_b = [ [p_C]_c [p_D]_d ] / [ [p_A]_a [p_B]_b ] = K_p

Where Kp indicates the equilibrium constant formula in terms of partial pressures.

Larger Kc/Kp values indicate a greater amount of product formation and a higher percentage of conversion.

Lower Kc/Kp values indicate a lower rate of product formation and a lower percentage conversion.

Medium Kc/Kp values indicate that the product formation is optimal.

Units of Equilibrium Constant

The equilibrium constant is the ratio of the concentrations raised to the stoichiometric coefficients. Therefore, the unit of the equilibrium constant is [Mole L^-1]△n.

∆n = $\sum$ Stoichiometric Coefficients of Products $-$ $\sum$ Stoichiometric Coefficients of Reactants

⇒ Also Read:

Chemical Equilibrium

Ionic Equilibrium

Le Chatelier’s Principle

Equilibrium Constant, Reaction Quotient, and Gibbs Free Energy

The relationship between △G (Gibbs Free Energy), K (Equilibrium Constant), and Q (Reaction Quotient) is that K is the ratio of the relative amount of products to reactants at equilibrium, while Q is the ratio at any point of time of the reaction. Comparing the Q value to K can help determine the direction of the reaction to take place, and the spontaneity of the process is related to the free energy change.

1. △G < 0 and (Qc ˂ Kc or Qp ˂ Kp) at the start of the reaction: The reaction will proceed to form products.

2. △G = 0, Qc = Kc or Kp, and the concentrations of the mixture remain constant at equilibrium.

3. △G > 0 and (Qc > Kc or Kp > Qc) after equilibrium: The reaction will proceed in the direction to form reactants.

Equilibrium Constant vs Reaction Quotient

Kc = Equilibrium constant measured in moles per liter.

Kp = Equilibrium Constant calculated from the Partial Pressures

The Relationship Between KC and KP

cC + dD ⇄ aA + bB

The equilibrium constant for the reaction expressed in terms of the concentration (mole/litre):

(\begin{array}{l} \Rightarrow K_{c}=\frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}} \end{array})

The equilibrium constant in terms of partial pressures, when the equilibrium involves gaseous species, is given by:

(\begin{array}{l}K_{c} = \frac{[pC]^{c} \cdot [pD]^{d}}{[pA]^{a} \cdot [pB]^{b}}\end{array})

If gases are assumed to be ideal, then according to the ideal gas equation, where pA, pB, pC and pD represent the partial pressures of substances A, B, C and D respectively.

p = nRT/V
pV = nRT he said, ‘is the library?’

“Where,” he asked, “is the library?”

P is the pressure in Pa.

The number of moles of gas, n,

V is the volume in m³

T is the temperature in Kelvin.

n/V = molar concentration = [C]

⇒ Check: Ideal Gas Equation

p = CRT, where C = mol dm$^3$, p = bar, and R = 0.0831 bar dm$^3$ mol$^{-1}$ K$^{-1}$

Substituting concentration for pressure:

pA = [A] RT;
pB = [B] RT;
pC = [C] RT;
pD = [D] RT;

Substituting the following values in the expression for Kp:

(\begin{array}{l} \Rightarrow K_p = \frac{[(C)RT^{c}] \times [(D)RT^{d}]}{[(A)RT^{a}] \times [(B)RT^{b}]} \end{array})

(\begin{array}{l} K_p = \frac{[C]^c (RT)^c [D]^d (RT)^d}{[A]^a (RT)^a [B]^b (RT)^b} \end{array})

(\begin{array}{l}\Rightarrow K_p=\frac{[(C)]^c [(D)]^d (RT)^c (RT)^d}{[(A)]^a [(B)]^b (RT)^a (RT)^b}\end{array})

(\begin{array}{l} \Rightarrow K_P = \frac{[(C)]^c [(D)]^d (RT)^{c+d}}{[(A)]^a [(B)]^b (RT)^{a+b}} \end{array})

(\begin{array}{l}\Rightarrow K_p=\frac{[A]^a[B]^b[C]^c[D]^d(RT)^{c+d-a-b}}{[A]^a[B]^b}\end{array})

$$K_p=K_c(RT)^{(c+d)-(a+b)}$$

Where, △n = (c+d) – (a+b) i.e. number of moles of gaseous products minus number of moles of gaseous reactants in the balanced chemical reaction.

Characteristics of Equilibrium Constant

1. The equilibrium constant is independent of the concentrations of the reactants and products.

2. The equilibrium constant is independent of the volume of the container in which the reaction takes place.

3. The equilibrium constant is independent of the temperature at which the reaction takes place.

4. The equilibrium constant is independent of the pressure of the system.

5. The equilibrium constant is a constant for a particular reaction at a given temperature.

6. The reaction rate is specific to the reaction and remains constant at a set temperature.

2. A catalyst does not affect the value of the equilibrium constant, but it does change the rate of both the forward and backward reactions equally.

3. Changes in concentration, pressure, temperature, inert gases can influence the equilibrium, shifting it in either the forward or backward direction, but not affecting the equilibrium constant.

△G⁰ = -RT ln K_equ

5. The equilibrium constant (K_eq) for a reversible reaction varies with temperature.

K_rev = 1/K_equ

If the stoichiometry of an equilibrium reaction is altered, the magnitude of the equilibrium constant will also be altered proportionally.

For the equilibrium reaction 3A = 3B ⇒ 3C + 3D, the equilibrium constant is K³.

K = K1 × K2 × K3, where K is the net equilibrium constant, K1, K2 and K3 are the equilibrium constants of the stepwise equilibria leading to the final products.

The product concentrations will be reduced due to the higher concentration of the common product, even though the equilibrium constant of the simultaneous equilibrium reactions does not change.

Applications of Equilibrium Constant

Calculating the Equilibrium Constant for Reaction Extent Prediction

The equilibrium constant (Kc) can be used to predict the extent of a reaction, i.e. the degree of the disappearance of the reactants. The magnitude of the equilibrium constant gives an idea of the relative amount of the reactants and the products.

Case 1: The equilibrium constant being greater than 103 indicates that the forward reaction is favored, meaning that the concentration of products is much higher than that of the reactants at equilibrium.

For Example:

For Example:

2HBr(g) ⇌ H2(g) + Br2(g) ⇒ Kc = 5.4×1018

2HCl(g) ⇌ H2(g) + Cl2(g) ⇒ Kc = 4×10^31

2H2(g) + 12O2(g) ⇌ 10H2O(g) ⇒ Kc = 2.4×1047

It is evident that the equilibrium concentration of the products is very high, indicating that the reaction goes almost to completion.

Case 2: The equilibrium constant in the intermediate range (10^-3 to 10³) indicates that the concentrations of the reactants and products are comparable.

For Example:

[Fe(SCN)]2 (aq) ⇄ Fe3 (aq) + SCN (aq) ⇒ Kc = 138 at 298 K

2H₂(g) + I₂(g) ⇌ 2HI(g) ⇒ K_c = 57 at 700 K.

Case 3: A low equilibrium constant (<10^-3) indicates that the backward reaction is favored, meaning the concentration of reactants is much greater than that of products, thus resulting in the reaction proceeding to a very small extent in the forward direction.

For Example:

For example

2N_2(g) + O_2(g) <=> 2NO(g) ⇒ K_c = 4.8 × 10^-31 at 298K

H2O (g) <=> H2 (g) + (1/2) O2 (g) ⇒ Kc = 4.1 x 10^-48

Calculating the Equilibrium Constant for Predicting the Direction of a Reaction

The equilibrium constant (K) can be used to predict the direction of the reaction. We need another term, the reaction quotient (Qc expressed in terms of concentrations or Qp in terms of partial pressures), which is similar to K but is used when the conditions are not at equilibrium.

For a balanced reaction, aA + bB $\rightleftharpoons$ cC + dD

The reaction quotient (Qc or Qp) is:

Qc = $\frac{[C]c[D]d}{[A]a[B]b}$

Qp = (pcC * pdD) / (paA * pbB)

Comparing Kc and the Direction of the Reaction:

If Q = Kc, the reaction is in equilibrium [where Kc is the equilibrium constant]

If Q > Kc, Q will tend to decrease until it is equal to K, causing the reaction to proceed in the reverse direction.

If Q is less than Kc, Q will tend to increase until it is equal to K. As a result, the reaction will proceed in the forward direction.

Calculating the Equilibrium Concentration

1. From Equilibrium Constant:

The degree of dissociation of an equilibrium involving a gas can be calculated by using the equilibrium constant and the concentration of the gaseous reactant/product.

The number of moles of carbon dioxide produced in the decomposition of carbonate can be calculated from the equilibrium constant by assuming an ideal gas behavior.

CaCO₃ ↔ CaO + CO₂ K_p = [p_CO2]

The Decomposition of Ammonia Gas: NH₃ → N₂ + 3H₂

| Decomposition of Ammonia Reaction: 2NH₃ ⇄ N₂ + 3H₂ |

| For initial moles | 1 | 0 | 0 |

| Moles at equilibrium | 1 - 2α | α | 3α |

| For C moles at equilibrium | C${1-2\alpha}$ | C$\alpha$ | 3C$_\alpha$ |

Number of moles at equilibrium = $C\left(1 - 2\alpha \right) + C\alpha + 3C\alpha = C\left(1 + 2\alpha \right)$

Partial pressure of ammonia = $\frac{C(1 - 2 \alpha)}{C(1 + 2 \alpha)} = \left[\frac{1 - 2 \alpha}{1 + 2 \alpha}\right]P_t$ (where $P_t$ is the total pressure)

Partial pressure of nitrogen = $\frac{C\alpha}{C(1 + 2\alpha)} = \frac{\alpha}{1 + 2\alpha}P_t$

Partial pressure of hydrogen = $$\frac{3\alpha}{C(1+2\alpha)} = \left[\frac{3\alpha}{1+2\alpha}\right]P_t$$

K_p = \frac{[pN_2][pH_2]^3}{[pNH_3]^2}

$\frac{[pN_2][pH_2]^3}{[pNH_3]^2}$

\frac{[\frac{\alpha}{1+2\alpha} \cdot \frac{3\alpha}{1+2\alpha}^3]}{[\frac{1-2\alpha}{1+2\alpha} \cdot \frac{Pt}{2}]}

=27α^4 \frac{Pt^2}{[1+2α]^2[1-2α]^2}

27α^4 Pt^2 / (1 - 4α^2)

Knowing K_p and the total pressure, the degree of dissociation of ammonia can be calculated.

2. From Vapour Density Measurements:

Number of Moles and Vapour Density:

For ideal gases, pV = nRT = [ω/M] × RT

M = $\frac{\omega RT}{VP}$ = $\rho \frac{RT}{P}$ = $\rho \frac{RTV}{RTn}$ = $\rho \frac{V}{n}$ = $2 \times Vapour Density$

Vapour density = ρ × V/2n = α × n^-1

At equilibrium, V and $\rho$ are constant, and Vapour Density is $\alpha \times \frac{1}{n}$

Vapour Density and Equilibrium:

M/m = D/d = Moles at equilibrium/Moles at start

M = initial molecular weight and M_eq = molecular weight at equilibrium

Example:

This is an example

This is an example

| Reaction: PCl₃ + Cl₂ ⇌ PCl₅ |

| For initial moles | C | 0 | 0 |

| Moles at Equilibrium | C_{1 - α} | C_α | C_α |

Number of moles at equilibrium = C*(1 + α)

C(1 + α)C = D/d: 1 + α

\alpha = \frac{D}{d} - 1

Knowing D and d, or M and m, α can be calculated.

Factors Affecting Equilibrium Constant

Some factors that affect equilibrium constant are:

1. Temperature

2. Pressure

3. Concentration of reactants and products

4. Catalyst

5. Variation in concentration of any product or reactant.

2. Change in the pressure of the system.

3. Change in temperature of the system.

4. Adding Inert Gas.

5. Adding Catalyst