Chapter 17, Problem 99A

Interpretation Introduction

Interpretation:

The sign of Gibbs free energy for a spontaneous reaction is to be explained..

Concept introduction:

The Gibbs free energy is the maximum amount of energy available to a system during a process that can be converted into useful work.

It is denoted by a symbol G

$\text{G = H-TS}$

Where $\text{H }$ = enthalpy of the system

$\text{T}$ = is the absolute temperature

$\text{S}$ = entropy of the system

Answer to Problem 99A

The sign of Gibbs free energy for a spontaneous reaction is negative.

Explanation of Solution

The total entropy change during a process is given as

$\text{ΔStotal}\text{=ΔSsys+ΔSsurr}$

If the system is in thermal equilibrium with the surroundings, then the temperature of the surroundings is the same as temperature of the system. So, increase in enthalpy of the surroundings is equal to decrease in enthalpy of the system. when reaction is carried out at constant temperature and pressure the heat evolved is equal to enthalpy change. if a reaction is carried out at constant pressure and temperature and heat {q} is given out to the surroundings reversibly, then

The change in Gibbs energy of the system is expressed as,

$\text{ ΔG = ΔH - TΔS}$

When energy and entropy factors are favorable which means that the change in entropy is negative and $\text{TΔS}$ is positive then

$\text{ ΔG = -ve}$

Hence, the free energy is negative for a spontaneous reaction.

Conclusion

The sign of Gibbs free energy for a spontaneous reaction is negative.