Question

Consider the equation \(\Delta G=\Delta H-T(\Delta S)\). Why is it necessary to specify the temperature when making a table listing \(\Delta G\) values?

Short answer

Temperature must be specified because \(\Delta G\) depends on it via the term \(T(\Delta S)\).

Step-by-step solution

Identify the Variables

Note the variables in the equation \(\Delta G = \Delta H - T(\Delta S)\). Here, \(\Delta G\) is the change in Gibbs free energy, \(\Delta H\) is the change in enthalpy, \(T\) is the temperature, and \(\Delta S\) is the change in entropy.

Understand the Temperature Dependence

Realize that the term \(T(\Delta S)\) involves temperature (T). This means that \(\Delta G\) is dependent on the value of the temperature, T.

Evaluate Effect of Temperature

If temperature is not specified, the value of \(\Delta G\) can vary significantly because the term \(T(\Delta S)\) will change with different temperatures.

Specify Temperature for Consistency

To ensure consistency and comparability of the \(\Delta G\) values, it is necessary to specify the temperature. This keeps the \(T\) term constant and allows for meaningful interpretation of the \(\Delta G\) values.

Key concepts

thermodynamics

Thermodynamics is a branch of physics that deals with the relationships between heat, work, temperature, and energy. It helps us understand how energy is transferred between systems and how it affects the physical properties of substances. One important part of thermodynamics is Gibbs Free Energy, which can predict whether a reaction will happen spontaneously. In this context, Gibbs Free Energy is given by the equation \( \Delta G = \Delta H - T(\Delta S) \). Here, \( \Delta G \) represents the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature, and \( \Delta S \) is the change in entropy.

enthalpy

Enthalpy (\( H \)) is a measure of the total energy of a thermodynamic system, including internal energy and the product of pressure and volume. It's important in chemical reactions because it helps us understand heat changes at constant pressure. In the Gibbs Free Energy equation, \( \Delta H \) represents the change in enthalpy. If \( \Delta H \) is negative, the reaction releases heat (exothermic). If it's positive, the reaction absorbs heat (endothermic). Clearly specifying the temperature when listing \( \Delta G \) values ensures that we account for the heat changes accurately and keep our comparisons meaningful.

entropy

Entropy (\( S \)) measures the disorder or randomness in a system. A higher entropy means greater disorder. In chemical reactions, entropy change (\( \Delta S \)) plays a crucial role. If \( \Delta S \) is positive, the system becomes more disordered; if negative, it becomes more ordered. In the Gibbs Free Energy equation, the term \( T(\Delta S) \) shows that the effect of entropy on \( \Delta G \) depends on temperature. Why? Because temperature acts as a multiplier. This is why it’s crucial to specify the temperature; otherwise, the effect of entropy on \( \Delta G \) can vary widely.

temperature dependence

Temperature plays a pivotal role in determining the Gibbs Free Energy (\( \Delta G \)) of a reaction. The term \( T(\Delta S) \) in the equation \( \Delta G = \Delta H - T(\Delta S) \) directly influences how \( \Delta G \) changes with temperature. Think of temperature as a scaling factor for entropy effects.
At high temperatures, entropy changes significantly impact \( \Delta G \). For example:

• If \( \Delta S \) is positive, \( \Delta G \) becomes more negative, favoring spontaneity.
• If \( \Delta S \) is negative, \( \Delta G \) becomes more positive, reducing spontaneity.

Therefore, without specifying temperature, we can't correctly predict or compare \( \Delta G \) values. So, always mention the temperature for accurate thermodynamic analysis.