Chapter 18, Problem 18.28QP

(a)

Interpretation Introduction

Interpretation:

Given the chemical equilibrium reaction, standard free energy $\Delta G°$ value has to be calculate at $2000K$

Concept Information:

Thermodynamics is the branch of science that relates heat and energy in a system.  The laws of thermodynamics explain 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. 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 is associated with the decrease of free energy in the system.  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

The equilibrium constant is related to the to the standard free energy change, the equation can be written as

$\begin{array}{l}{\text{ΔG}}^{\text{0}}\text{=-RTln}\text{K----------[1]}\\ \text{ΔG}=\text{Free energy}\\ \text{Δ}{\text{G}}^{\text{0}}\text{=}\text{Standard}\text{state free energy}\\ \text{R}\text{=}\text{Gas}\text{Constant}\\ T=\text{Temprature}\text{273}\text{K}\\ \text{K=}\text{Equlibrium}\text{Constant}{\text{(K}}_{\text{P}}\text{and}{\text{K}}_{\text{C}}\text{)}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The free energy $(\text{ΔG)}\text{}$ value has to be calculated given the equilibrium reaction under given pressure.

Concept Information:

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.

Relationship of $K_c$ and$K_p$: Subsisting $P=[A]RT$ into the expression for $Kp$ for each substance, the relationship between $K_c$ and becomes $K_P=K_c{(RT)}^{\Delta n}$