Chapter 20, Problem 20.104P

(a)

Interpretation Introduction

Interpretation:

For the following metabolic reaction, the $\text{ΔG}$ value should be calculated at $298K$, using the given equilibrium value.

Concept introduction:

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 standard free energy change ${\text{(ΔG}}^{\text{°}}{}_{\text{rxn}})$ is the difference in free energy of the reactants and products in their standard state.

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

Free energy change$\text{ΔG}$: change in the free energy takes place while reactants convert to product where both are in standard state. It depends on the equilibrium constant $\text{K}$

$\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{o}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ \\ {\text{ΔG}}^{\text{o}}\text{=- RT}\ln \left(\text{K}\right)\end{array}$

Where,

$\text{T}$ is the temperature

$\text{ΔG}$ is the free energy

${\text{ΔG}}^{\text{o}}$, ${\text{ΔH}}^{\text{o}}$ and ${\text{ΔS}}^{\text{o}}$ is standard free energy, enthalpy and entropy values.

(b)

Interpretation Introduction

Interpretation:

For the following metabolic reaction, the $\text{ΔG}$ value should be calculated at $298K$, using the given $Q$ value.

The value of free change should be calculated when the reaction quotient $Q=10.$

Concept introduction:

Free energy change$\text{ΔG}$: change in the free energy takes place while reactants convert to product where both are in standard state. It depends on the equilibrium constant $\text{K}$,

$\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{o}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ \\ {\text{ΔG}}^{\text{o}}\text{=- RT}\ln \left(\text{K}\right)\end{array}$

Where,

$\text{T}$ is the temperature

$\text{ΔG}$ is the free energy

${\text{ΔG}}^{\text{o}}$, ${\text{ΔH}}^{\text{o}}$ and ${\text{ΔS}}^{\text{o}}$ is standard free energy, enthalpy and entropy values.

Reaction quotient$\left(Q\right)$: Reaction quotient and equilibrium constant has same expression.  Reaction quotient is also the ratio between the concentrations of the reactant to product, but these concentrations are not necessarily the equilibrium concentrations.

        $Q=\frac{\left[\text{Product}\right]}{\left[\text{Reactant}\right]}$

The reaction quotient $\left(Q\right)$ is helpful in predicting the direction of the reaction.

• When $\text{Q}\text{>}{\text{K}}_{\text{c}}$, the reaction proceeds towards left to increase the concentration of the reactants.
• When $\text{Q}<{\text{K}}_{\text{c}}$, the reaction proceeds towards right to increase the concentration of the products.
• When $\text{Q}={\text{K}}_{\text{c}}$, the reaction is at equilibrium.

(c)

Interpretation Introduction

Interpretation:

For the following metabolic reaction, the $\text{ΔG}$ value should be calculated at $298K$, using the given $Q$ value.

The value of free change should be calculated when reaction quotient $Q=\mathrm{0.100.}$

Concept introduction:

Reaction quotient$\left(Q\right)$: Reaction quotient and equilibrium constant has same expression.  Reaction quotient is also the ratio between the concentrations of the reactant to product, but these concentrations are not necessarily the equilibrium concentrations.

        $Q=\frac{\left[\text{Product}\right]}{\left[\text{Reactant}\right]}$

The reaction quotient $\left(Q\right)$ is helpful in predicting the direction of the reaction.

• When $\text{Q}\text{>}{\text{K}}_{\text{c}}$, the reaction proceeds towards left to increase the concentration of the reactants.
• When $\text{Q}<{\text{K}}_{\text{c}}$, the reaction proceeds towards right to increase the concentration of the products.
• When $\text{Q}={\text{K}}_{\text{c}}$, the reaction is at equilibrium.

Free energy change$\text{ΔG}$: change in the free energy takes place while reactants convert to product where both are in standard state. It depends on the equilibrium constant $\text{K}$,

$\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{o}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ \\ {\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}-{\text{TΔS}}^{\text{o}}\end{array}$

Where,

$\text{T}$ is the temperature

$\text{ΔG}$ is the free energy

${\text{ΔG}}^{\text{o}}$, ${\text{ΔH}}^{\text{o}}$ and ${\text{ΔS}}^{\text{o}}$ is standard free energy, enthalpy and entropy values.

(d)

Interpretation Introduction

Interpretation:

For the following metabolic reaction, the reaction quotient $Q$ value should be calculated at $298K$, when $\Delta G=-2.50kJ/mol.$

Concept introduction:

Free energy change$\text{ΔG}$: change in the free energy takes place while reactants convert to product where both are in standard state. It depends on the equilibrium constant $\text{K}$,

$\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{o}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ \\ {\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}-{\text{TΔS}}^{\text{o}}\end{array}$

Where,

$\text{T}$ is the temperature

$\text{ΔG}$ is the free energy

${\text{ΔG}}^{\text{o}}$, ${\text{ΔH}}^{\text{o}}$ and ${\text{ΔS}}^{\text{o}}$ is standard free energy, enthalpy and entropy values.

Reaction quotient$\left(Q\right)$: Reaction quotient and equilibrium constant has same expression.  Reaction quotient is also the ratio between the concentrations of the reactant to product, but these concentrations are not necessarily the equilibrium concentrations.

        $Q=\frac{\left[\text{Product}\right]}{\left[\text{Reactant}\right]}$

The reaction quotient $\left(Q\right)$ is helpful in predicting the direction of the reaction.

• When $\text{Q}\text{>}{\text{K}}_{\text{c}}$, the reaction proceeds towards left to increase the concentration of the reactants.
• When $\text{Q}<{\text{K}}_{\text{c}}$, the reaction proceeds towards right to increase the concentration of the products.
• When $\text{Q}={\text{K}}_{\text{c}}$, the reaction is at equilibrium.