Chapter 21, Problem 130AE

(a)

Interpretation Introduction

Interpretation: By using given bond energies the enthalpy $\Delta H$ for the reaction of two molecules of glycine to form a peptide linkage is to be estimated. The entropy $\Delta S$ to favor the formation of peptide linkages between two molecules of glycine is to be predicted. Also, the formation of proteins is a spontaneous process or not is to be predicted.

Concept introduction: When two or more amino acids are linked in a chain, a compound called peptide is formed in which the carboxyl group of each acid is joined to the amino group of the next forming a $\text{-OC-NH-}$ bond, known as peptide bond. Glycine is an amino acid with a single hydrogen atom present in its side chain. The chemical formula of glycine is $\left({\text{C}}_{\text{2}}{\text{H}}_{\text{5}}{\text{NO}}_{\text{2}}\right)$. When two molecules of glycine joined through a peptide linkage a dipeptide is formed.

To determine: The $\Delta H$ for the reaction of two molecules of glycine to form a peptide linkage by using bond energies.

Answer to Problem 130AE

Answer

The $\Delta H$ for the reaction is $\underset{\_}{1302KJ}$. Hence, the reaction is an endothermic reaction.

Explanation of Solution

Explanation

The enthalpy $\Delta H$ for the reaction is $\underset{\_}{1302KJ}$. Hence, the reaction is an endothermic reaction.

The reaction between two molecules of glycine to form peptide linkage is,

Figure 1

The enthalpy of the reaction is calculated by using the formula,

$\Delta H_{rxn}^{\text{ο}}\text{=}{\displaystyle \sum \text{D}}\left(\text{bonds broken}\right)\text{-}{\displaystyle \sum \text{D}\left(\text{bonds formed}\right)}$

In the given reaction shown in Figure 1 bonds are broken and formed during peptide formation and energy is absorbed and released. The bond energies are shown in (Table 3-3) respectively.

Therefore, the energy required to break the bonds is calculated as,

$\begin{array}{l}\text{2 moles of 2N-H bonds = 4×391 KJ = 1564 KJ}\\ \text{2 moles of C-N bonds = 2×305 KJ = 610 KJ}\\ \text{2 moles of 2C-H bonds = 4×413 KJ = 1652 KJ}\\ \text{2 moles of C-C bonds = 2×347 KJ = 694 KJ}\end{array}$

$\begin{array}{l}\text{2 moles of C=O bonds = 2×745 KJ = 1490 KJ}\\ \text{2 moles of C-O bonds = 2×358 KJ = 716 KJ}\\ \text{2 moles of O-H bonds = 2×467 KJ = 934 KJ}\\ \text{Total energy required to break the bonds = 7660 KJ}\end{array}$

Similarly, the energy released when the bonds are formed are calculated as,

$\begin{array}{l}\text{3 N-H bonds = 2×392 KJ = 782 KJ}\\ \text{3 C-N bonds = 3×305 KJ = 915 KJ}\\ \text{4 C-H bonds = 4×413 KJ = 1652 KJ}\\ \text{2 C-C bonds = 2×347 KJ = 694 KJ}\end{array}$

$\begin{array}{l}\text{2 C=O bonds = 2×745 KJ = 1490 KJ}\\ \text{1 C-O bond = 1×358 KJ = 358 KJ}\\ \text{1 O-H bond = 1×467 KJ = 467 KJ}\\ \text{Total energy released to form the bonds = 6358 KJ}\end{array}$

Therefore, the total enthalpy for the reaction is calculated by using the formula,

$\begin{array}{c}\Delta H_{rxn}^{\text{ο}}\text{=}{\displaystyle \sum \text{D}}\left(\text{bonds broken}\right)\text{-}{\displaystyle \sum \text{D}\left(\text{bonds formed}\right)}\\ \text{= 7660 KJ - 6358 KJ}\\ \text{= }\underset{\_}{1302KJ}\end{array}$

Hence, the total enthalpy of formation for the reaction of two molecules of glycine to form a peptide linkage is positive. It is an endothermic reaction.

(b)

Interpretation Introduction

Interpretation: By using given bond energies the enthalpy $\Delta H$ for the reaction of two molecules of glycine to form a peptide linkage is to be estimated. The entropy $\Delta S$ to favor the formation of peptide linkages between two molecules of glycine is to be predicted. Also, the formation of proteins is a spontaneous process or not is to be predicted.

Concept introduction: When two or more amino acids are linked in a chain, a compound called peptide is formed in which the carboxyl group of each acid is joined to the amino group of the next forming a $\text{-OC-NH-}$ bond, known as peptide bond. Glycine is an amino acid with a single hydrogen atom present in its side chain. The chemical formula of glycine is $\left({\text{C}}_{\text{2}}{\text{H}}_{\text{5}}{\text{NO}}_{\text{2}}\right)$. When two molecules of glycine joined through a peptide linkage a dipeptide is formed.

To determine: The entropy $\Delta S$ to favor the formation of peptide linkages between two molecules of glycine.

Answer to Problem 130AE

Answer

The entropy $\Delta S$ for the reaction is negative. Hence, the reaction is non-spontaneous.

Explanation of Solution

Explanation

The entropy $\Delta S$ to favor the formation of peptide linkages between two molecules of glycine is negative.

The reaction between two molecules of glycine to form a peptide linkage is found to be an endothermic process because of the positive value of enthalpy. In the system an endothermic process absorbs heat from the surrounding and therefore, decreases the entropy of the surrounding because the molecular motion in the surrounding decreases. Therefore, for the given reaction $\Delta S$ becomes negative and the reaction is non-spontaneous with respect to the entropy $\Delta S$.

(c)

Interpretation Introduction

Interpretation: By using given bond energies the enthalpy $\Delta H$ for the reaction of two molecules of glycine to form a peptide linkage is to be estimated. The entropy $\Delta S$ to favor the formation of peptide linkages between two molecules of glycine is to be predicted. Also, the formation of proteins is a spontaneous process or not is to be predicted.

Concept introduction: When two or more amino acids are linked in a chain, a compound called peptide is formed in which the carboxyl group of each acid is joined to the amino group of the next forming a $\text{-OC-NH-}$ bond, known as peptide bond. Glycine is an amino acid with a single hydrogen atom present in its side chain. The chemical formula of glycine is $\left({\text{C}}_{\text{2}}{\text{H}}_{\text{5}}{\text{NO}}_{\text{2}}\right)$. When two molecules of glycine joined through a peptide linkage a dipeptide is formed.

To determine: The formation of proteins is a spontaneous process or not.

Answer to Problem 130AE

Answer

Formation of proteins is a non-spontaneous process.

Explanation of Solution

Explanation

The formation of proteins is a non-spontaneous process.

The formation of proteins occurs when large numbers of amino acids are joined through peptide linkage. The formation of peptide linkage is a non-spontaneous process as stated above due to the negative value of $\Delta S$. Hence, formation of proteins is a non-spontaneous process.