What combines thermodynamics and kinetics into the equation ΔG° = - RT ln K

What is the common point between thermodynamics and kinetics?

Entropy is a common point in thermodynamics and kinetics which is instrumental in combining thermodynamics and kinetics.

In thermodynamics, entropy (S) is a measure of the randomness or disorder of a system. The second law of thermodynamics states that the total entropy of a system and its surroundings always increases for a spontaneous process. This means that an increase in entropy can drive a reaction towards spontaneity. Entropy change (?S) is a key factor in determining the overall change in Gibbs free energy (?G) of a reaction, along with enthalpy change (?H).

In kinetics, entropy also affects the reaction rate. An increase in entropy often leads to an increase in disorder in the system, which can facilitate the movement of particles and increase the likelihood of effective collisions between reactant molecules. This ultimately influences the rate at which the reaction proceeds.

Therefore, entropy change is a common point in thermodynamics and kinetics, as it influences the feasibility (thermodynamics) and speed (kinetics) of a reaction. By considering both entropy and its effects on the system, we can understand the driving forces behind a reaction and its dynamics.

What is ΔG° = - RT ln K?

Because ΔH° and ΔS° determine the magnitude of ΔG° and because K is a measure of the ratio of the concentrations of products to the concentrations of reactants, we should be able to express K in terms of ΔG° and vice versa.

Combining terms gives the following relationship between ΔG and the reaction quotient Q:

ΔG = ΔG° + RT ln Q

where ΔG° indicates that all reactants and products are in their standard states. For a system at equilibrium (K=Q), and ΔG = 0 for a system at equilibrium. Therefore, we can describe the relationship between ΔG° and K as follows:

0 = ΔG°+ RT ln K

ΔG°= ?RT ln K

The equation ΔG° = - RT ln K is the Gibbs free energy change of a reaction at standard temperature and pressure (298 K and 1 atm) when the reaction quotient, Q, equals the equilibrium constant, K. This equation relates the free energy change of a reaction to the equilibrium constant of the reaction, where R is the gas constant, T is the temperature in Kelvin, and ln k is the natural logarithm of the equilibrium constant.

Two terms [1] reaction quotient and [2] equilibrium constant will be often used in the post.

What do they mean?

Reaction quotient

Let's consider the generic chemical reaction: aA + bB ? cC + dD In this reaction, moles of species A react with b moles of species B to form c moles of species C and d moles of species D. The reaction quotient, Q, for this reaction, is defined as the concentration of products raised to their stoichiometric coefficients divided by the concentration of reactants raised to their stoichiometric coefficients: Q = [C]^c[D]^d / [A]^a[B]^b

Equilibrium constant

The equilibrium constant, K, for the reaction, is the ratio of the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients when the reaction reaches equilibrium. K = [C]^c[D]^d / [A]^a[B]^b

Difference between reaction quotient and equilibrium constant

The reaction quotient (Q) is a ratio that can be calculated at any point during a reaction, while the equilibrium constant (K) is specifically a ratio calculated at equilibrium. The reaction quotient, Q, is calculated using the same formula as the equilibrium constant, K, but it is calculated at a point in time when the reaction has not yet reached equilibrium. It allows us to determine if a reaction is at equilibrium, moving towards equilibrium, or away from equilibrium.

By comparing Q to K, we can predict the direction in which the reaction will proceed to reach equilibrium.

On the other hand, the equilibrium constant, K, is a specific ratio that is calculated when the reaction has reached a state of equilibrium. It represents the concentrations of products and reactants at equilibrium and is a constant value under a given set of conditions.

The equilibrium constant provides insight into the composition of the equilibrium mixture and the position of the equilibrium state.

Explanation

As said above, the reaction quotient, Q, is a measure of the relative concentrations of products and reactants in a chemical reaction at a given point in time, while the equilibrium constant, K, is a measure of the concentrations of products and reactants at equilibrium. At equilibrium, the reaction quotient Q is equal to the equilibrium constant K.

The relationship between Q and K can be expressed as follows:

Q and K show the direction of the reaction

- If Q < K, it means that the concentration of products is lower than what is required at equilibrium. In this case, the reaction will proceed from left to right to reach equilibrium.

- If Q = K, it means that the concentrations of products and reactants are at equilibrium. The reaction is at equilibrium, and there is no net change in the concentrations of reactants and products.

- If Q > K, it means that the concentration of products is higher than what is required at equilibrium. In this case, the reaction will proceed from right to left to reach equilibrium.

Gibbs free energy change also shows the direction of the reaction

?If the Gibbs free energy change is negative (dG < 0), the reaction is spontaneous in the forward direction. If dG is positive (dG > 0), the reaction is non-spontaneous and will proceed in the reverse direction. If dG = 0, the reaction is at equilibrium.

Therefore, the relationship between the Gibbs free energy change, ΔG°, and the equilibrium constant, K, ΔG° = - RT ln K is a combination of the reaction quotient, Q. equilibrium constant K, and the free energy change, ΔG°

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