# Gibbs free energy and entropy inconsistency

• MexChemE
In summary: So, in summary, for the given reaction, at a temperature of 27°C (300.15 K), the values for ΔS and ΔH are 25.76 cal K-1 and 11495.45 cal, respectively. The signs of ΔG and ΔS do not necessarily have to be opposite for a reaction to be spontaneous, as it depends on the change in entropy of the surroundings.

## Homework Statement

For a certain reaction, ΔG = 13580 + 16.1 T log10(T) - 72.59 T. Find ΔS and ΔH for the reaction at 298.15 K.

## Homework Equations

ΔG = ΔH - TΔS
$$\left[\frac{\partial (\Delta G)}{\partial T} \right]_P = - \Delta S$$

## The Attempt at a Solution

For the sake of this thread's length I won't write too much details, I'm having a very specific question about the solutions of this problem.

First I calculated ΔG plugging T = 298.15 K into the given function and got ΔG = 3815.11 cal. Now, this result is telling me the reaction is non-spontaneous. Fine.

Then I calculated ΔS by differentiating the ΔG function and plugged T = 298.15 K in order to get ΔS = 25.76 cal K-1. This result is telling me the reaction is spontaneous. Both results are given by the textbook and are correct. I also plugged the numeric values of ΔS and ΔG into ΔH = ΔG + TΔS and got ΔH = 11495.45 cal, which is also a correct solution according to the textbook.

Aren't the signs of ΔG and ΔS supposed to be opposite, according to the spontaneity criteria? Thanks in advance for any input!

MexChemE said:
signs of ΔG and ΔS supposed to be opposite
A reaction can be "entropically driven," or, it may be "enthalpically driven." No big deal. Entropically driven examples, vaporization, solution, mmmm ---- what else? Enthalpically driven, oxidation, solidification, anything that gets hot. Throw sulfuric acid into water and watch enthalpy and entropy at work. Dilute a concentrated sodium chloride solution and watch entropy at work and enthalpy opposing the process (it cools, at room T).

MexChemE
A reaction is spontaneous if it results in an increase in the entropy of the universe (i.e. the system and its surroundings). The ΔS in the equation reflects only the change in entropy of the system. For a reaction at constant temp and pressure, the enthalpy will be proportional to the change in entropy of the surroundings (with more negative ΔH leading to a larger increase in entropy). Thus, if a reaction increases the entropy of the system at the expense of the entropy of the surroundings (by converting thermal energy into chemical potential energy), the reaction can still be non-spontaneous overall.

MexChemE and Bystander
Ygggdrasil said:
The ΔS in the equation reflects only the change in entropy of the system.

I was ignoring this little detail, now I can be at peace again. Thank you both!

Bystander
In my question the temperature given is 27°C.. should I just go ahead with the same temperature or should I convert it into Kelvin?

If you are given an empirical equation like this:
MexChemE said:
ΔG = 13580 + 16.1 T log10(T) - 72.59 T.
the source should tell you whether T is in °C or K. Sometimes it's one, sometimes the other. If the question asks "Find ΔS and ΔH for the reaction at 298.15 K" then presumably T is in K for this equation.
For fundamental thermodynamic equations like ΔG = ΔH - TΔS, T is always in K.

## What is Gibbs free energy and entropy inconsistency?

Gibbs free energy and entropy inconsistency refers to a discrepancy between the predicted change in Gibbs free energy and the actual change in entropy during a chemical reaction or physical process. This inconsistency can occur when calculating the change in free energy using different methods, or when experimental measurements do not match predicted values.

## What causes Gibbs free energy and entropy inconsistency?

Several factors can contribute to Gibbs free energy and entropy inconsistency, including errors in experimental measurements, incomplete or inaccurate data, and assumptions made in the calculation methods. Additionally, changes in temperature and pressure can also affect the relationship between Gibbs free energy and entropy.

## How is Gibbs free energy and entropy inconsistency resolved?

To resolve Gibbs free energy and entropy inconsistency, it is important to carefully analyze and evaluate the data and methods used in the calculations. This may involve making adjustments to experimental procedures, using more accurate measurement techniques, or re-evaluating assumptions made in the calculations. Additionally, it may be necessary to consider other factors, such as changes in temperature and pressure, to fully understand the inconsistency.

## What are the implications of Gibbs free energy and entropy inconsistency?

Gibbs free energy and entropy inconsistency can have significant implications for predicting and understanding chemical reactions and physical processes. Inaccurate calculations can lead to incorrect predictions and interpretations of experimental results, which can hinder progress in scientific research and development.

## How can Gibbs free energy and entropy inconsistency be prevented?

To prevent Gibbs free energy and entropy inconsistency, it is important to carefully design experiments and use accurate measurement techniques. It is also crucial to understand the limitations and assumptions of different calculation methods and to validate results using multiple approaches. Additionally, regularly reviewing and updating data and procedures can help prevent inconsistencies from occurring.