How to Calculate the Equilibrium Constant in Homogeneous Systems
The reaction in which the phase of all the products and the reactants is the same. For example- all the products and reactants are gases or all the products and reactants are liquids. An equilibrium reaction is the one in which the reaction can be reversed and forwarded and the concentrations of the reactants and products remain the same.
Equilibrium is a state of chemical reaction where the rate of forwarding and backward reaction is the same. Moreover, an equilibrium can be of two types: homogeneous equilibrium and heterogeneous equilibrium. A homogeneous equilibrium is defined as a homogeneous mixture (reactants and products in a single solution) in one phase. Remember, the reactants are on the left side of the equation and the products are on the right side of the equation. Therefore, the reaction which takes place between the solutes belongs to a single homogeneous equilibrium. A heterogeneous equilibrium, on the other hand, can be defined as a reaction system where the products and the reactants are found in two or more phases.
Homogeneous Reaction- Equilibrium Constant
Suppose a homogeneous system is given by the reaction given below-
\[N_{2}(g) + 3H_{2}(g) \leftrightarrow 2NH_{3} (g)\]
It is observed that gaseous nitrogen when reacted with gaseous hydrogen gives gaseous ammonia.
This reaction can be written in terms of molar concentration in the following way-
\[K_{c} = \frac{[NH_{3}]^{2}}{[N_{2}][H_{2}]^{3}}\]
The equilibrium concentration, for the reactions involving gases, is expressed in terms of parietal pressure.
By using the ideal gas equation,
PV = nRT
P and V here are the pressure and volume of the system respectively
The number of moles of the component present is expressed as n
R is for the universal gas constant
T is for the temperature
\[C = \frac{n}{v}RT = cRT\]
C is denoted for the concentration of the system which can also be written as
\[C = \frac{P}{RT}\]
Therefore the equilibrium constant for a homogeneous equilibrium can be written as
\[K_{p} = K_{c} (RT)^{\Delta n}\]
where \[K_{p}\] is the equilibrium constant being calculated from the partial pressure of a reaction equation
and
\[{\Delta n}\]represents the number of moles of the gaseous products
Homogeneous Equilibrium- Example
A homogeneous equilibrium can further be divided into two categories. In the first category, the number of molecules of the product is the same as the number of molecules of the reactants of that particular equation.
For example:
\[N_{2} (g) + O_{2} (g) = 2NO (g)\]
We can observe from the example above that there are two molecules of reactants (one of each) and the product also has two molecules on the right side.
In the second category of a homogeneous equilibrium equation, opposite circumstances are observed. The number of molecules of the product is not the same or equal to the number of molecules of the reactant.
For example:
\[2SO_{2} (g) + O_{2} (g) \rightleftharpoons 2SO_{3} (g)\]
From this above example, we can notice that there are only three molecules of reactant and only two molecules of the product present in the reaction.
In a homogeneous equilibrium, the reactions in liquid solutions between solutes belong to one type of homogeneous equilibria and the chemical species which are involved can be either molecules or ions or a mixture of both.
For the following homogeneous reaction
\[C_{2}H_{2}(aq) + 2Br_{2}(aq) C_{2}H_{2}B_{4}(aq)\]
\[K= \frac{[C_{2}H_{2}B_{4}]}{[C_{2}H_{2}][Br_{2}]^{2}}\]
where K is the equilibrium constant
Homogeneous Chemical Equilibrium
It is important to note that the two different equilibriums are dealt with in a different way and so are the calculations related to them.
In order to understand this further, a chemical equation is provided below about the homogeneous equilibrium.
\[C_{2}H_{2} (aq) + 2Br_{2} (aq) \rightleftharpoons C_{2}H_{2}Br_{2} (aq)\]
Moreover, a heterogeneous equilibrium example is also provided in order to learn about the difference between homogeneous and heterogeneous equilibrium. The example is given below:
\[H_{2}O (s) \rightleftharpoons H_{2}O (l)\]
Calculate Equilibrium Constant
You can solve or calculate the equilibrium constant for a given reaction. To explain this, let us take a hypothetical example of W, X, Y, and Z as reactants and products. Their coefficient, the number in front of the compound or molecule, is represented by w, x, y, and z. The equation with these molecules and their coefficient is given below:
\[wW + xX \rightleftharpoons yY +zZ\]
In order to find the equilibrium constant of this equation and similar equations, the products of the equation go in the numerator, with the coefficient as their exponent. The reactants, on the other hand, go in the denominator, with their coefficients as their exponents. The written expression will look similar to the one below:
\[K_{c}= \frac{Y^{Y}Z^{Z}}{W^{W}X^{X}}\]
Using this formula, one can calculate the equilibrium constant of any equation. Another example of a chemical equation that can be used to explain is given below:
Equation:
\[2SO_{2} (g) + O_{2} (g) \rightleftharpoons 2SO_{3} (g)\]
Equilibrium Constant:
\[K_{C} = \frac{ [SO_{3}]^{2} }{[SO_{2}]^{2}[O_{2}]}\]
Moreover, in terms of finding equilibrium constant for gases, partial pressure is taken into account. The first step involved here is to use the ideal gas equation. The formula for the ideal gas equation is given below:
PV = nRT; where
P- is the pressure,
V- is the volume
n- is the number of moles of components
R- is the universal gas constant
T- is the temperature
The above relationship can also be written as:
P = (n/v)RT; where
n/v = c (concentration of the system)
P = cRT
Therefore, the equilibrium constant can also be written using the concentration of the system in the formula. This relationship can be derived through the following steps:
\[K_{P} = K_{C}(RT)^{\Delta n}\]
\[{\Delta n}\]- is the number of moles of gaseous products,
\[K_{P}\]- is defined as the equilibrium constant that is calculated from the partial pressure of a reaction equation.
Difference between \[K_{C} and K_{P}\]
The main difference between the two equilibrium constants is that they are used for the different concentrations. \[K_{P}\] specifically represents the equilibrium constant at partial pressure during a reaction. In terms of calculation, these values can be found from the reactant and products, using the formulae and using the specific values of those formulae. A relationship between the two equilibrium constants has also been derived, which is given below:
\[K_{P} = K_{C}(RT)^{\Delta n}\]
FAQs on Homogeneous Equilibrium in Chemistry: Key Concepts & Examples
1. What exactly is a homogeneous equilibrium?
A homogeneous equilibrium is a state in a reversible chemical reaction where all the reactants and products are in the same physical phase. For instance, all substances might be gases, or all might be dissolved in a single liquid solution (aqueous phase).
2. Can you give some examples of homogeneous equilibrium reactions?
Certainly. Homogeneous equilibria are common in both gas and liquid phases. Here are a few examples:
- Gas Phase: The formation of ammonia in the Haber process: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Here, all components are gases.
- Aqueous Phase: The ionization of acetic acid in water: CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq). In this case, all species are dissolved in water.
3. How is homogeneous equilibrium different from heterogeneous equilibrium?
The main difference lies in the physical phases of the substances involved. In a homogeneous equilibrium, all reactants and products are in a single phase (e.g., all gas). In a heterogeneous equilibrium, the reactants and products exist in two or more different phases, such as a reaction involving a solid and a gas.
4. How do you write the equilibrium constant expression (Kc) for a homogeneous reaction?
For a homogeneous reaction, the expression for the equilibrium constant, Kc, is written as the ratio of the product of the molar concentrations of the products to that of the reactants. Each concentration term is raised to the power of its stoichiometric coefficient in the balanced chemical equation. For example, for the reaction aA + bB ⇌ cC + dD, the expression is: Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ.
5. Why is it important that all substances are in the same phase for a homogeneous equilibrium?
Having all substances in the same phase ensures that they can mix freely and interact with each other throughout the entire volume of the container. This creates a uniform system where concentration is meaningful everywhere. If phases were different (like a solid in a gas), the reaction would only occur at the surface of the solid, which is a characteristic of heterogeneous equilibrium.
6. How does changing pressure affect a homogeneous equilibrium involving gases?
According to Le Chatelier's principle, if you increase the pressure on a gaseous homogeneous equilibrium, the system will shift to favour the side with fewer moles of gas to counteract the pressure change. Conversely, decreasing the pressure will cause the equilibrium to shift towards the side with more moles of gas.
7. What is the relationship between Kp and Kc for a gaseous homogeneous equilibrium?
Kp and Kc are related by the equation: Kp = Kc(RT)Δn. In this formula, Kp is the equilibrium constant in terms of partial pressures, Kc is the constant in terms of molar concentrations, R is the ideal gas constant, T is the absolute temperature, and Δn is the change in the number of moles of gas (moles of gaseous products minus moles of gaseous reactants).
