Q20.109CP In the process of respiration, g... [FREE SOLUTION]

Chapter 20: Q20.109CP (page 921)

In the process of respiration, glucose is oxidized completely. In fermentation, $O_{2}$ is absent and glucose is broken down to ethanol and ${CO}_{2}$ . Ethanol is oxidized to ${CO}_{2}$ and $H_{2} O$ .
Balance the following equations for these processes:
Respiration: $C_{6} H_{12} O_{6} (s) + O_{2} (g) 鈫� {CO}_{2} (g) + H_{2} O (l)$
Fermentation: $C_{6} H_{12} O_{6} (s) 鈫� C_{2} H_{5} OH (l) + C O_{2} (g)$
Ethanol oxidation: $C_{2} H_{5} OH (l) + O_{2} (g) 鈫� {CO}_{2} (g) + H_{2} O (l)$
Calculate ${螖骋}_{rxn}^{o}$ for respiration of $1.00 g$ glucose.
Calculate ${螖骋}_{rxn}^{o}$ for fermentation of $1.00 g$ glucose.
Calculate ${螖骋}_{rxn}^{o}$ for oxidation of the ethanol from part (c).

Short Answer

Expert verified

a) The reactions that are balanced are:

$\begin{array}{rcl} C_{6} H_{12} O_{6} (s) + 6 O_{2} (g) & 鈫� & 6 {CO}_{2} (g) + 6 H_{2} O (l) \\ C_{6} H_{12} O_{6} (s) & 鈫� & 2 C_{2} H_{5} OH (l) + 2 C O_{2} (g) \\ C_{2} H_{5} OH (l) + 2 O_{2} (g) & 鈫� & 2 {CO}_{2} (g) + 3 H_{2} O (l) \end{array}$

b) For 1 g of glucose respiration, the Gibbs energy is $- 15.981 kJ$ .

c) For 1 g of glucose fermentation, the Gibbs energy is $- 1.26468 kJ$ .

d) From 1 g of glucose fermentation, Gibb's energy for ethanol oxidation is $- 12.0827 kJ$ .

Step by step solution

Definition of Oxidation

The loss of electrons by a molecule, atom, or ion during a reaction is known as oxidation. When the oxidation state of a molecule, atom, or ion is enhanced, it is called oxidation.

Balancing the equations for Respiration, fermentation, and ethanol oxidation

The reactions that are balanced are:

Respiration: $C_{6} H_{12} O_{6} (s) + 6 O_{2} (g) 鈫� 6 {CO}_{2} (g) + 6 H_{2} O (l)$
Fermentation: $C_{6} H_{12} O_{6} (s) 鈫� 2 C_{2} H_{5} OH (l) + 2 C O_{2} (g)$
Ethanol oxidation: $C_{2} H_{5} OH (l) + 2 O_{2} (g) 鈫� 2 {CO}_{2} (g) + 3 H_{2} O (l)$

Calculating ΔGrxno for respiration(b)

To compute the ${螖骋}_{rxn}^{o}$ per 1 mol of glucose, first, calculate the ${螖骋}_{rxn}^{o}$ per 1 mol of glucose.

Calculate the reaction's Gibbs change under standard conditions (298 K),

$\begin{array}{rcl} {螖骋}_{rxn}^{o} & = & {鈭�}_{}^{} {螖骋}_{products}^{o} - {鈭�}_{}^{} {螖骋}_{reactants}^{o} \\ {螖骋}_{rxn}^{o} & = & [{6 mol 脳螖骋}_{{CO}_{2} (g)}^{o} {+ 6 mol 脳螖骋}_{H_{2} O (l)}^{o}] - [{1 mol 脳螖骋}_{C_{6} H_{12} O_{6} (s)}^{o} {+ 6 mol 脳螖骋}_{O_{2} (g)}^{o}] \\ \begin{array}{l} {螖骋}_{rxn}^{o} = [6 mol 脳 (- 394 . 40 kJ / mol) + 6 mol 脳 (- 237 . 192 kJ / mol)] - [1 mol 脳 (- 910 . 56 kJ / mol + 6 mol 脳 (0 . 00 kJ / mol)] \\ {螖骋}_{rxn}^{o} = - 2878.992 kJ / mol \end{array} \end{array}$

Now, convert 1 g of glucose to grams of material.

$\begin{array}{rcl} n (C_{6} H_{12} O_{6}) & = & \frac{m}{M_{R}} = \frac{1 g}{180.156 g / mol} \\ n (C_{6} H_{12} O_{6}) & = & 5.55075 脳 10^{- 3} mol \end{array}$

Finally, 1 g of glucose equals

${螖骋}_{rxn}^{o} = 5.55075 脳 10^{- 3} mol 脳 (- 2878.992 kJ / mol) {螖骋}_{rxn}^{o} = - 15.981 kJ$

For 1 g of glucose respiration, the Gibbs energy is $- 15.981 kJ$ .

Calculating ΔGrxno for fermentation

${螖骋}_{rxn}^{o} = [{2 mol 脳螖骋}_{{CO}_{2} (g)}^{o} {+ 2 mol 脳螖骋}_{C_{2} H_{o} H (l)}^{o}] - [{1 mol 脳螖骋}_{C_{6} H_{12} O_{6} (s)}^{o}]$

Using Appendix B as a guide,

${螖骋}_{rxn}^{o} = [2 mol 脳 (- 394 . 40 kJ / mol) + 2 mol 脳 (- 174 . 80 kJ / mol)] - [1 mol 脳 (- 910 . 56 kJ / mol] {螖骋}_{rxn}^{o} = - 227.84 kJ / mol$

Now that you know that 1 g of glucose equals $5.55075 脳 10^{- 3} mol$ ,

${螖骋}_{rxn}^{o} = 5.55075 脳 10^{- 3} mol 脳 (- 227.84 kJ / mol) {螖骋}_{rxn}^{o} = - 1.26468 kJ$

For 1 g of glucose fermentation, Gibb's energy is $- 1.26468 kJ$ .

Calculating ΔGrxno for oxidation of ethanol

(d) Finally,when it comes to ethanol oxidation,

${螖骋}_{rxn}^{o} {= 2 mol 脳螖骋}_{{CO}_{2} (g)}^{o} {+ 3 mol 脳螖骋}_{H_{2} O (l)}^{o} - [{1 mol 脳螖骋}_{C_{2} H_{5} OH (l)}^{o} {+ 2 mol 脳螖骋}_{O_{2} (g)}^{o}]$

Using Appendix B as a guide,

${螖骋}_{rxn}^{o} = [2 mol 脳 (- 394 . 40 kJ / mol) + 2 mol 脳 (- 237 . 192 kJ / mol)] - [1 mol 脳 (- 174 . 80 kJ / mol + 2 mol 脳 (0 . 00 kJ / mol] {螖骋}_{rxn}^{o} = - 1088.384 kJ / mol$

Now that we know that the ethanol obtained from glucose is further oxidized, the ethanol gained from the reaction above is:

$n (C_{2} H_{5} OH) = 2 脳 n (C_{6} H_{12} O_{6}) = 1.11015 脳 10^{- 2} mol$

As a result, Gibb's energy

${螖骋}_{rxn}^{o} = 1.11015 脳 10^{- 2} mol 脳 (- 1088.384 kJ / mol) {螖骋}_{rxn}^{o} = - 12.0827 kJ$

Gibb's energy for ethanol oxidation is $- 12.0827 kJ$ , which is obtained from 1 g of glucose fermentation.

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Short Answer

Step by step solution

Definition of Oxidation

Balancing the equations for Respiration, fermentation, and ethanol oxidation

Calculating ΔGrxno for respiration(b)

Calculating ΔGrxno for fermentation

Calculating ΔGrxno for oxidation of ethanol

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