Question

Why is it more convenient to predict the direction of a reaction in terms of \(\Delta G_{\mathrm{sys}}\) instead of \(\Delta S_{\text {univ }}\) ? Under what conditions can \(\Delta G_{\mathrm{sys}}\) be used to predict the spontaneity of a reaction?

Short answer

\( \Delta G_{\mathrm{sys}} \) predicts reaction direction more directly. It works under constant temperature and pressure.

Step-by-step solution

Understanding \\Delta G_{\mathrm{sys}} and \\Delta S_{\text {univ }}

The Gibbs free energy change \( \Delta G_{\mathrm{sys}} \) is a thermodynamic quantity that combines enthalpy \( \Delta H \) and entropy \( \Delta S \) changes of a system. In contrast, \( \Delta S_{\text {univ }} \) represents the change in entropy of the universe, combining both the system and surroundings. \( \Delta G_{\mathrm{sys}} \) directly relates to the tendencies of a reaction under constant temperature and pressure conditions, whereas \( \Delta S_{\text {univ }} \) is broader and less practical for immediate predictions.

Using \( \Delta G_{\mathrm{sys}} \) for Direction Prediction

Predictions made using \( \Delta G_{\mathrm{sys}} \) are more convenient because it simplifies the assessment: a negative \( \Delta G_{\mathrm{sys}} \) indicates a spontaneous reaction, whereas a positive \( \Delta G_{\mathrm{sys}} \) indicates non-spontaneity. This criterion is more direct than calculating \( \Delta S_{\text {univ }} \) because it doesn't require the separate calculation of entropy changes in both the system and surroundings.

Conditions for \( \Delta G_{\mathrm{sys}} \) Usage

\( \Delta G_{\mathrm{sys}} \) can be used to predict the spontaneity of a reaction under conditions where temperature and pressure are constant. This is typically applicable in many laboratory and industrial settings, allowing for straightforward determinations of whether a reaction will occur spontaneously.

Key concepts

Thermodynamics

Thermodynamics is a fundamental concept that deals with energy and its transformations. In the context of chemical reactions, it explains how and why reactions occur. There are three main laws of thermodynamics, but in chemical reactions, we focus mainly on the first and second laws.

• The first law is about energy conservation, implying energy cannot be created or destroyed, only transformed.
• The second law introduces the concept of entropy, a measure of disorder or randomness, indicating that systems naturally progress toward greater disorder.

These principles help us understand how energy changes during reactions and why certain processes happen spontaneously while others do not.
Thermodynamics offers a framework to predict whether a reaction is energetically favorable based on energy changes within the system.

Spontaneity Prediction

Predicting whether a reaction will happen spontaneously is crucial in chemistry. We use the Gibbs free energy change (\( \Delta G_{\mathrm{sys}} \)) to make this prediction easily. This value tells us about the energy available to do work during a reaction.

• If \( \Delta G_{\mathrm{sys}} \) is negative, the reaction is spontaneous, meaning it can occur without external input.
• If it is positive, the reaction is non-spontaneous, requiring energy from an external source.

This method simplifies the process because it directly relates to conditions where temperature and pressure are constant. This makes \( \Delta G_{\mathrm{sys}} \) a more practical tool than calculating the universal entropy change \( \Delta S_{\text{univ}} \).
Gibbs free energy is an all-in-one measure that delights chemists by streamlining calculations and predictions.

Enthalpy and Entropy

The concepts of enthalpy and entropy are intertwined with Gibbs free energy. Enthalpy (\( \Delta H \)) refers to the total heat content of a system and is crucial for energy balance.

• Positive \( \Delta H \) indicates the reaction absorbs heat (endothermic).
• Negative \( \Delta H \) indicates the reaction releases heat (exothermic).

Entropy (\( \Delta S \)), on the other hand, is about disorder. A positive \( \Delta S \) means increased disorder, adding to the spontaneity.
Incorporating both into \( \Delta G \) with the equation:\[\Delta G = \Delta H - T \Delta S\]allows for a comprehensive assessment of a reaction's likelihood to proceed spontaneously.
Understanding how these variables interact provides valuable insight into the energetic feasibility of chemical processes.