Chapter 18, Problem 18.24QP

Interpretation Introduction

Interpretation:

The given autoionization reaction standard entropy $({\text{ΔG}}^0)$ value has to be calculated.

Concept Introduction:

In thermodynamics a process is spontaneous if it is taking place by itself without the help of external energy.  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. All spontaneous process will have highly energetic initial state than the final state. This indicates that while the process occurs, there is a decrease in free energy of the system. The increase in randomness also favors the spontaneity of a process.  In nonspontaneous process, there is a requirement of external energy source. The free energy of the system increases.  The entropy decreases in non-spontaneous process.

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

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

Where,

  $\text{ΔG }$ is the change in free energy of the system.

  $\Delta {\rm H}$ is the change in enthalpy of the system.

  $\text{T}$ is the absolute value of the temperature.

  $\Delta \text{S}$ is the change in entropy in the system.

Free energy$({\text{ΔG}}^0)$: The entropy is second law of thermodynamics it indicated for $({\text{ΔG}}^0)$ symbol, the many of chemical reactions cause changes in entropy and it plays on important role in determining in which direction (forward and backward) a chemical reaction spontaneously proceeds.

Kw: The self-ionization of water (also autoionization of water, and auto dissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, $H_{2}O$, deprotonates (loses the nucleus of one of its hydrogen atoms) to become a hydroxide ion, $O{H}^{-}$.