Chapter 17, Problem 17.74QP

Interpretation Introduction

Interpretation:

The temperature ($K$) values has to be calculated given the $MgC{O}_3$ decomposition reaction.

Concept Introduction:

Thermodynamics is the branch of science that relates heat and energy in a system.  The four 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

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 $\text{G}$.  All spontaneous process is associated with the decrease of free energy in the system.  The free energy change ${\text{(ΔG}}_{\text{rxn}})$ is the difference in free energy of the reactants and products in their standard state.

${\text{ΔG}}_{\text{rxn}}\text{=}\sum {\text{nΔG}}_{\text{f}}\text{(Products)-}\sum {\text{nΔG}}_{\text{f}}\text{(Reactants)}$

Enthalpy is

${\text{ΔH}}_{\text{rxn}}\text{=}\sum {\text{nΔH}}_{\text{f}}\text{(Products)-}\sum {\text{nΔH}}_{\text{f}}\text{(Reactants)}$

Decomposition reaction: The reaction breaking down compounds (such as carbonates, nitrates or hydroxides) by heating them is called thermal decomposition.

For example,

$CaC{O}_{3(s)}\underset{}{\to }Ca{O}_{(s)}+C{O}_2{}_{(g)}$