What is the difference between \(\Delta G\) and \(\Delta G^{\circ}\) for a chemical change?

Understanding chemical spontaneity is essential for predicting the behavior of chemical reactions. In thermodynamics, spontaneity refers to the likelihood of a process to occur without the need for external energy input. A spontaneous process can perform work on the surroundings, and it is characterized by a negative Gibbs free energy change, denoted as \(\Delta G\).

The sign of \(\Delta G\) is what indicates whether a process is spontaneous or not. Specifically:

• If \(\Delta G < 0\), the process is spontaneous and may proceed on its own.
• If \(\Delta G = 0\), the system is in equilibrium, and no net change occurs over time.
• If \(\Delta G > 0\), the process is non-spontaneous, meaning it will not occur without an input of energy.

When \(\Delta G\) is calculated for a reaction, it takes into account the current conditions, such as temperature, pressure, and concentrations of reactants and products. This flexibility means that a reaction's spontaneity may vary with changes in these conditions. In contrast, \(\Delta G^\circ\), used for standard conditions, provides a reference point for comparing the spontaneity of reactions under defined, stable scenarios.

The concept of standard conditions is fundamental when discussing Gibbs free energy and chemical spontaneity. The term \(\Delta G^\circ\) represents the Gibbs free energy change under 'standard state' conditions. These conditions serve as a baseline for comparison in thermodynamics and consist of a pressure of 1 bar, a concentration of 1 M for each solute in solution, and pure solids or liquids in their most stable forms. All these parameters need to be measured at a specified common temperature, often set at 298 K (approximately 25°C).

Under these standard conditions, the properties of substances can be tabulated, enabling us to calculate the standard Gibbs free energy change for a variety of chemical reactions. This standardized approach simplifies the evaluation of reaction spontaneity and allows for the tabulation of standard Gibbs free energies of formation \(\Delta G_f^\circ\), which are useful reference values for predicting reaction behavior in a 'standard' chemical environment.

The reaction quotient, represented by the symbol \(Q\), is a dimensionless number that provides a snapshot of a reaction's status by comparing the concentrations of reactants and products at any point during the reaction. It is defined as the ratio of the concentrations of products raised to their stoichiometric coefficients to the concentrations of reactants raised to their stoichiometric coefficients, as seen in the general reaction equation:

• The reaction quotient for a reaction: aA + bB \(\rightleftharpoons\) cC + dD is given by \(Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\) where brackets denote concentrations.

When the reactant and product concentrations satisfy the equilibrium condition, \(Q\) becomes the equilibrium constant, \(K\). The reaction quotient is especially significant when relating \(\Delta G\) to \(\Delta G^\circ\) through the expression \(\Delta G = \Delta G^\circ + RT\ln(Q)\). At equilibrium, \(\Delta G = 0\), and \(Q = K\), which leads to the equation \(\Delta G^\circ = -RT\ln(K)\), linking standard Gibbs free energy change to the equilibrium constant. \(Q\) thus acts as a guide; if \(QK\), the reaction will move in the reverse direction to regain equilibrium.