Question

How does the value of \(\Delta G^{\circ}\) for a reaction relate to the equilibrium constant for the reaction? What does a negative \(\Delta G^{\circ}\) for a reaction imply about \(K\) for the reaction? A positive \(\Delta G^{\circ}\) ?

Short answer

A negative gular brackets .ngular brackets .ngular brackets .ngular brackets indicate a favorable reaction (K > 1), whereas a positive gular brackets .ngular brackets .ngular brackets .ngular brackets indicates an unfavorable reaction (K < 1).

Step-by-step solution

Understanding the Relationship

The value of standard Gibbs free energy change, gular brackets gular brackets respectively represent standard conditions, is related to the equilibrium constant of a reaction, represented as K, through the equation (gular brackets)(9.314 J/(mol*K) gular brackets within brackets. T is the temperature in Kelvin. Therefore, the sign of gular brackets (gular brackets of K.

Interpreting Negative gular brackets gular brackets for a Reaction

When gular brackets gular brackets (J/mol gular bracketsgabel brackets, according to the equation, this results in a positive exponent on the right side of the equation since -1 multiplied by a negative number is positive. Therefore, e raised to a positive power is greater than one, which implies that K is greater than one, indicating a reaction that favorably proceeds towards products at standard conditions.

Key concepts

Equilibrium Constant

The equilibrium constant, represented as K, is a vital concept in thermodynamics and signifies the ratio of the concentrations of the products to the reactants each raised to the power of their stoichiometric coefficients in a balanced chemical equation at equilibrium. It is a dimensionless value that provides insight into the position of equilibrium; a larger K value (>1) indicates a preference for the formation of products, while a smaller K value (<1) reflects a reaction that favors the reactants.

For a given temperature, K remains constant and can predict the direction of the chemical reaction. Whether a reaction tends to go to completion or remains predominantly as reactants can be deduced from the magnitude of K. In a dynamic equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, maintaining the concentrations of reactants and products constant over time.

Thermodynamics in Chemistry

In the realm of thermodynamics in chemistry, Gibbs free energy, denoted as \( \Delta G \), plays a pivotal role. It is the maximum amount of work that can be extracted from a closed thermodynamic system at a constant temperature and pressure. \( \Delta G \), when coupled with the equilibrium constant (K), allows for the prediction of whether or not a chemical reaction will occur spontaneously under standard state conditions.

The equation \( \Delta G^\circ = -RT\ln(K) \) bridges the gap between thermodynamics and equilibrium. Here \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, and \( K \) is the equilibrium constant. A negative \( \Delta G^\circ \) implies that a reaction is exergonic, releasing energy, and proceeds spontaneously, leading to a K greater than one. Conversely, a positive \( \Delta G^\circ \) indicates that the reaction is endergonic, requiring an input of energy to occur, and resulting in a K less than one.

Standard State Conditions

Standard state conditions are reference points used in chemistry to report thermodynamic properties, such as Gibbs free energy, allowing for consistent comparisons between different substances and reactions. These conditions are defined as 1 bar for pressure and a specified temperature, usually 298 K (25°C), with concentrations of all solutes at 1 M.

In thermodynamics, when we refer to \( \Delta G^\circ \) or K at 'standard state' or 'standard conditions', it means the Gibbs free energy change or equilibrium constant, respectively, has been measured or calculated under these standardized conditions. It is crucial to understand that these are purely conventional terms meant to provide a common baseline. Keeping temperature, pressure, and concentration constant simplifies calculations and comparisons but does not necessarily reflect the conditions a reaction would encounter in a real-world or biological system.