Chapter 18, Problem 18.56QP

Interpretation Introduction

Interpretation:

The crystallization of sodium acetate from a super saturated solution occurs spontaneously.  Entropy $(\Delta S)$ and Enthalpy $(\Delta {\rm H})$ sign should be identified.

Concept Introduction:

Spontaneous process: A process which is initiated by itself, without the help of external energy source is called spontaneous process.  All spontaneous process is associated with the decrease in free energy in the system.

Thermodynamics is the branch of science that relates heat and energy in a system.  The four laws of thermodynamics explains the fundamental quantities such as temperature, energy and randomness in a system.  Entropy is the measure of randomness in a system.  For a spontaneous process there is always a positive change in entropy. The second law of thermodynamics says that entropy of the universe is increasing. The change in entropy in the universe is given by the summation of entropy change in the system and surroundings.

${\text{ΔS}}_{\text{univ}}{\text{=ΔS}}_{\text{sys}}{\text{+ΔS}}_{\text{surr}}$

In thermodynamics, free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.

The equation given below helps us to calculate the change in free energy in a system.

$\text{ΔG = }\Delta {\rm H}\text{- T}\Delta \text{S}$