Chapter 5, Problem 5C.1E

(a)

Interpretation Introduction

Interpretation:

The standard enthalpy for the reaction in which the K value is doubled at the given condition that T is increased by $10K$ at $298K$ has to be calculated.

Concept Introduction:

Gibbs free energy can be used to calculate the maximum amount of reversible work performed by a thermodynamic system at constant temperature and pressure. Symbol = G, Unit = Joule (J)/mol.

$\Delta G=\Delta G^0+RT\ln Q\boxed{\begin{array}{l}here,\Delta G=Gibbsfreeenergy\\ \Delta G^0=ChangeinGibbsfreeenergy\\ R=Gas\text{constant}\\ \text{T}\text{=}\text{Temperature}\end{array}}$

Concentration of the solution can also expressed by mole fraction. Mole fraction is equal to moles of the component divided by total moles of the mixture.

$\text{Mole fraction =}\frac{\text{moles of a component}}{\text{total moles}}$

Generally, the van’t Hoff equation is used to determine the equilibrium constant value at some temperature with having known equilibrium constant value for some other temperature.

$\begin{array}{l}van\text{'}tHoffequation\Rightarrow \ln \frac{K\text{'}}{K}=\frac{{\Delta }_{r}H}{R}\left(\frac{1}{T}-\frac{1}{T\text{'}}\right)\\ \boxed{\begin{array}{c}here,{\Delta }_{r}H=enthalpychange\\ R=gascons\text{tant}\\ T\&T\text{'}=differenttemperatures\\ K\text{'}=Equilibrium\text{constant}valueatT\text{'}\\ K=Equilibrium\text{constant}valueatT\end{array}}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The standard enthalpy for the reaction in which the K value is halved at the given condition that T is increased by $10K$ at $298K$ has to be calculated.

Concept Introduction:

Gibbs free energy can be used to calculate the maximum amount of reversible work performed by a thermodynamic system at constant temperature and pressure. Symbol = G, Unit = Joule (J)/mol.

$\Delta G=\Delta G^0+RT\ln Q\boxed{\begin{array}{l}here,\Delta G=Gibbsfreeenergy\\ \Delta G^0=ChangeinGibbsfreeenergy\\ R=Gas\text{constant}\\ \text{T}\text{=}\text{Temperature}\end{array}}$

Concentration of the solution can also expressed by mole fraction. Mole fraction is equal to moles of the component divided by total moles of the mixture.

$\text{Mole fraction =}\frac{\text{moles of a component}}{\text{total moles}}$

Generally, the Van’t Hoff equation is used to determine the equilibrium constant value at some temperature with having known equilibrium constant value for some other temperature.

$\begin{array}{l}van\text{'}tHoffequation\Rightarrow \ln \frac{K\text{'}}{K}=\frac{{\Delta }_{r}H}{R}\left(\frac{1}{T}-\frac{1}{T\text{'}}\right)\\ \boxed{\begin{array}{c}here,{\Delta }_{r}H=enthalpychange\\ R=gascons\text{tant}\\ T\&T\text{'}=differenttemperatures\\ K\text{'}=Equilibrium\text{constant}valueatT\text{'}\\ K=Equilibrium\text{constant}valueatT\end{array}}\end{array}$