91Ó°ÊÓ

The equilibrium constant, often denoted as \(K_{\mathrm{eq}}\), is a crucial concept in understanding chemical reactions. It helps predict the extent to which a reaction will proceed. The value of \(K_{\mathrm{eq}}\) reflects the ratio of the concentrations of products to reactants at equilibrium. A high \(K_{\mathrm{eq}}\) (greater than 1) means products are favored, while a low value (less than 1) suggests reactants are favored.

In the context of exergonic reactions, a large \(K_{\mathrm{eq}}\) indicates a greater tendency for the reaction to occur spontaneously and release energy. In the exercise, \(K_{\mathrm{eq}} = 1000\) is much higher than \(K_{\mathrm{eq}} = 0.001\), so it suggests more products are formed, thus releasing more energy (exergonic).

• Large \(K_{\mathrm{eq}}\): Reaction favors products, more exergonic
• Small \(K_{\mathrm{eq}}\): Reaction favors reactants, less exergonic

Gibbs free energy, symbolized as \(\Delta G\), is a measure of the maximum reversible work obtainable from a system at constant temperature and pressure. The change in Gibbs free energy, \(\Delta G^\circ\), determines whether a reaction occurs spontaneously. The key relationship to understand here is:

\[ \Delta G^\circ = -RT \times \ln(K_{\mathrm{eq}}) \]

Where \(R\) is the universal gas constant and \(T\) is the temperature in Kelvin.

This equation shows that when \(K_{\mathrm{eq}}\) is greater than 1, \(\Delta G^\circ\) becomes negative, indicating that the reaction releases free energy (exergonic). Conversely, when \(K_{\mathrm{eq}}\) is less than 1, \(\Delta G^\circ\) is positive, suggesting that the reaction absorbs energy (endergonic). Thus, the reaction with \(K_{\mathrm{eq}} = 1000\) is exergonic, while \(K_{\mathrm{eq}} = 0.001\) is endergonic.

• Negative \(\Delta G^\circ\): Exergonic, releases energy
• Positive \(\Delta G^\circ\): Endergonic, absorbs energy

Spontaneous processes are crucial to understanding chemical reactions. A reaction is said to be spontaneous if it occurs naturally without needing to be driven by an external energy source. Whether a reaction is spontaneous is determined by the sign of \(\Delta G^\circ\).

If \(\Delta G^\circ\) is negative, the process can occur spontaneously, often with a release of energy, making it exergonic. These reactions typically favor the formation of products, as demonstrated in the exercise where the reaction with \(K_{\mathrm{eq}} = 1000\) is more likely to be spontaneous.

When \(\Delta G^\circ\) is positive, the reaction is non-spontaneous. It requires an input of energy to proceed, and such reactions are endergonic, favoring reactants over products.

• Spontaneous: \(\Delta G^\circ\) is negative, products are formed
• Non-spontaneous: \(\Delta G^\circ\) is positive, needs energy input