Equilibrium Constant for the Reaction

The equilibrium constant (K) for a chemical reaction is a mathematical expression that relates the concentrations (or partial pressures) of the reactants and products at equilibrium. It is a measure of the extent to which a reaction proceeds in the forward or reverse direction.

The given reaction is: a = 2b

Here, 'a' represents the reactant and 'b' represents the product. The degree of dissociation of 'a' is represented by the symbol alpha, and the total pressure of the system is denoted by 'p'.

Deriving the Equilibrium Constant Expression

To derive the equilibrium constant expression, we can consider the following steps:

1. Write the balanced chemical equation:
a = 2b

2. Write the expression for the equilibrium constant:
K = ([b]^2) / [a]

Here, [b]^2 represents the square of the concentration of 'b', and [a] represents the concentration of 'a'.

3. Since the degree of dissociation of 'a' is alpha, we can express the concentrations in terms of alpha:
[a] = (1 - alpha) * [a]₀
[b] = 2 * alpha * [a]₀

Here, [a]₀ represents the initial concentration of 'a'.

4. Substituting the expressions for [a] and [b] into the equilibrium constant expression, we get:
K = (2 * alpha * [a]₀)^2 / ((1 - alpha) * [a]₀)

Simplifying the expression further, we have:
K = 4 * alpha^2 * [a]₀ / (1 - alpha)

Explanation and Interpretation of the Equilibrium Constant

The equilibrium constant (K) is a dimensionless quantity that indicates the ratio of the concentrations (or partial pressures) of the products to the reactants at equilibrium. It represents the balance between the forward and reverse reactions.

1. Effect of Degree of Dissociation (alpha):
The equilibrium constant expression contains the square of the degree of dissociation (alpha). As alpha increases, the value of K increases, indicating that the reaction proceeds more towards the product side. Conversely, as alpha decreases, the value of K decreases, indicating a shift towards the reactant side.

2. Interpretation of K:
- If K > 1, the concentration of products is greater than the concentration of reactants at equilibrium, indicating a favorable forward reaction.
- If K < 1,="" the="" concentration="" of="" reactants="" is="" greater="" than="" the="" concentration="" of="" products="" at="" equilibrium,="" indicating="" a="" favorable="" reverse="" />
- If K = 1, the concentrations of reactants and products are equal at equilibrium, indicating an equilibrium position in the middle.

3. Significance of K:
- The magnitude of K provides information about the relative amounts of reactants and products present at equilibrium.
- K is temperature-dependent and remains constant at a given temperature.
- K can be used to calculate the concentrations (or partial pressures) of reactants and products at equilibrium when the initial conditions are known.

Conclusion

In summary, the equilibrium constant (K) for the given reaction can be derived by writing the expression for the equilibrium

4a^2alpha2/1-a(alpha)