Reactions at equilibrium are characterized by equal rates of forward and reverse reactions. This state of equilibrium does not mean that the reactions have stopped, but rather that they are occurring at identical rates. As a result, the concentrations of reactants and products remain constant over time.
The equilibrium constant, denoted as 'K', is a key factor in understanding this state of equilibrium. 'K' is the ratio of the rate constant of the forward reaction to the rate constant of the reverse reaction. This provides a quantitative measure of the relative speed of the forward and reverse reactions.
Beyond this, 'K' can also be calculated using the concentrations of the components of the reaction. It's determined by the ratio of the concentration of products to the concentration of reactants, with each concentration raised to a power that matches its stoichiometric coefficient in the balanced chemical equation.
Additionally, for any point in the reaction (not necessarily at equilibrium), the reaction quotient Q represents the ratio of product to reactant concentrations in the same stoichiometric manner. At equilibrium, Q equals K.
The relationship between Gibbs free energy and the reaction composition is given by the equation:
ΔrG = ΔrG° + RT ln Q
where ΔrG refers to the Gibbs energy change under the current conditions of the system, ΔrG° is the standard Gibbs energy change only under standard conditions (1 M concentration, 1 atm pressure), R is the gas constant, and T is the temperature in Kelvin. At equilibrium, where Q = K, this equation simplifies to:
0 = ΔrG° + RT ln K
This equation links thermodynamic favorability with equilibrium composition.
The values of 'K' and ΔrG° can provide insights into the feasibility and direction of a reaction. If 'K' is greater than one and ΔrG° is negative, the reaction is thermodynamically favorable and will proceed towards the formation of products. Conversely, if 'K' is less than one and ΔrG° is positive, the reaction is not feasible, and the equilibrium mixture will predominantly consist of reactants. If 'K' equals one, this indicates that the equilibrium mixture has substantial quantities of both reactants and products.
The equilibrium constant ‘K’ is defined as the ratio of the concentration of products to the concentration of reactants, each raised to the power of their coefficients in the chemical reaction.
The reaction quotient Q has the same form as K but applies to the system at any point—not necessarily at equilibrium. It helps assess the system’s current state.
ΔrG is the Gibbs free energy change of a reaction under current conditions. The standard Gibbs free energy change, ΔrG°, refers to standard conditions: 1 molar concentration and 1 atmospheric pressure.
They are related by the equation:
ΔrG = ΔrG° + RT ln Q
At equilibrium, ΔrG is zero and Q = K, giving:
ΔrG° = –RT ln K
If ‘K’ is much greater than one and ΔrG° is negative, the reaction favors the products.
On the other hand, if ‘K’ is much less than one and ΔrG° is positive, it favors reactants.
When ‘K’ equals one, both reactants and products are present in significant amounts.
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