Question

Recall Is there a connection between the free-energy change for a reaction and its equilibrium constant? If there is a connection, what is it?

Short answer

\( \Delta G \) is related to \( K \) by \( \Delta G = -RT \ln K \). Spontaneous reactions have \( \Delta G < 0 \) and \( K > 1 \). Non-spontaneous reactions have \( \Delta G > 0 \) and \( K < 1 \).

Step-by-step solution

Understanding Free Energy Change

Free energy change \( \Delta G \) is a measure of the amount of work a thermodynamic system can perform. It shows whether a reaction is spontaneous or not. If \( \Delta G < 0 \), the reaction is spontaneous; if \( \Delta G > 0 \), it is non-spontaneous.

Equilibrium Constant Defined

The equilibrium constant \( K \) is a ratio of the concentrations of products to reactants at equilibrium. It indicates the extent to which a reaction proceeds before reaching equilibrium.

Connection Between \( \Delta G \) and \( K \)

There is a connection between the free-energy change \( \Delta G \) and the equilibrium constant \( K \). This connection is given by the equation: \( \Delta G = -RT \ln K \), where \( R \) is the gas constant and \( T \) is the temperature in Kelvin.

Implications of the Equation

From the equation \( \Delta G = -RT \ln K \), if \( K > 1 \), \( \ln K \) is positive, making \( \Delta G \) negative, which implies the reaction is spontaneous. If \( K < 1 \), \( \ln K \) is negative, making \( \Delta G \) positive, which implies the reaction is non-spontaneous.

Key concepts

Free Energy Change

Free Energy Change, denoted as \( \Delta G \), is a crucial concept in thermodynamics. It evaluates the amount of work a system can perform in a reaction. The sign and magnitude of \( \Delta G \) tell us whether a process is spontaneous or not. If \( \Delta G \) is less than zero (\( \Delta G < 0 \)), the reaction is spontaneous, meaning it can occur without external input of energy. If \( \Delta G > 0 \), the reaction is non-spontaneous and requires energy to proceed. This criterion helps chemists determine the feasibility of reactions.

Equilibrium Constant

The Equilibrium Constant \( K \) is a ratio that shows the relationship between the concentrations of products and reactants at equilibrium. It provides insight into the direction and extent to which a chemical reaction proceeds. If \( K \) is greater than 1, products are favored at equilibrium, while if \( K \) is less than 1, reactants are favored. For a given reaction: \[ K = \frac{[products]}{[reactants]} \]. Knowing the value of \( K \) allows scientists to predict the position of equilibrium and understand the reaction's dynamics.

Thermodynamic Spontaneity

Thermodynamic Spontaneity pertains to the natural tendency of a process to occur without external influence. It's often determined by evaluating the Free Energy Change. A spontaneous process, where \( \Delta G < 0 \), happens naturally, whereas a non-spontaneous process (\