Question

Explain the relationship between temperature and the tendency for reactions to occur spontaneously.

Short answer

A reaction is more likely to occur spontaneously at high temperatures if \(\triangle S > 0\), and at low temperatures if \(\triangle S < 0\).

Step-by-step solution

Understanding Spontaneity and Gibbs Free Energy

Spontaneity of a reaction is determined by Gibbs free energy, denoted as \(\triangle G\). A reaction is spontaneous if \(\triangle G < 0\). Gibbs free energy takes into account enthalpy (heat content, \(\triangle H\)), entropy (disorder, \(\triangle S\)), and temperature (T). The relationship is given by the equation \[ \triangle G = \triangle H - T \triangle S \]

Identifying the Influence of Temperature

Analyze the equation \(\triangle G = \triangle H - T \triangle S\). Temperature (T) directly affects the \(- T \triangle S\) term. At higher temperatures, this term becomes more significant, influencing the value of \(\triangle G\).

High Temperature Effects

For reactions where \(\triangle S > 0 \) (positive entropy change), increasing temperature typically makes \(\triangle G\) more negative. Thus, reactions with positive entropy changes are more likely to be spontaneous at higher temperatures.

Low Temperature Effects

For reactions where \(\triangle S < 0 \) (negative entropy change), increasing temperature typically makes \(\triangle G\) more positive. These reactions tend to be spontaneous only at lower temperatures.

Temperature's Role Summary

In summary: If \(\triangle S > 0\), high temperature favors spontaneity. If \(\triangle S < 0\), low temperature favors spontaneity. Temperature can shift the spontaneity of a reaction depending on the sign of entropy change.

Key concepts

Gibbs Free Energy

To understand the spontaneity of chemical reactions, we need to delve into the concept of Gibbs free energy. Gibbs free energy, denoted by \( \triangle G \), is a thermodynamic potential that helps predict the direction of a chemical reaction and its feasibility. The formula for Gibbs free energy is \[ \triangle G = \triangle H - T \triangle S \]. Here, \( \triangle H \) represents the enthalpy change (the heat content of the system), \( T \) is the temperature in Kelvin, and \( \triangle S \) denotes the entropy change (a measure of disorder or randomness). If \( \triangle G \) is negative, the reaction occurs spontaneously. Conversely, if \( \triangle G \) is positive, the reaction is non-spontaneous.

Entropy

Entropy is a fundamental concept in thermodynamics, symbolized by \( S \). It represents the degree of disorder or randomness in a system. A greater number of microstates corresponds to higher entropy because the system is more disordered. Entropy plays a crucial role in determining reaction spontaneity. The sign of \( \triangle S \), the entropy change, can influence whether a reaction becomes spontaneous under certain conditions. For example, when \( \triangle S \) is positive, the system gains disorder, favoring spontaneity at higher temperatures. On the other hand, when \( \triangle S \) is negative, implying a loss of disorder, the reaction may only be spontaneous under lower temperatures. Understanding entropy helps predict how energy disperses and how molecules are distributed in a reaction.

Temperature Effects on Reactions

Temperature significantly influences the spontaneity of chemical reactions by affecting the Gibbs free energy through the \[ -T \triangle S \] term. For reactions where \( \triangle S > 0 \), an increase in temperature makes \( -T \triangle S \) more negative, thereby reducing \( \triangle G \) and making the reaction more likely to be spontaneous. This is because the positive entropy change is amplified by the temperature, enhancing the disorder and driving the reaction forward.
Conversely, for reactions where \( \triangle S < 0 \), increasing the temperature makes \( -T \triangle S \) more positive, increasing the value of \( \triangle G \), and making the reaction less likely to be spontaneous. In such cases, the loss of disorder is emphasized by the temperature, making the reaction unfavorable. Hence, temperature can be a determining factor in whether a reaction will proceed spontaneously based on the nature of the entropy change.