Chapter 16, Problem 23P

Interpretation Introduction

Interpretation:

Balanced equation for the conversion of glucose to lactate should be written.

Concept introduction:

The reactions for those the numbers of atoms of each element in the reactant and in the product side are equal. Such reactions are said to be a balanced chemical equation.

Answer to Problem 23P

$\text{Glucose+2ADP+2P}\to \text{2Lactate+2ADP}$

Explanation of Solution

During glycolysis, two molecules of pyruvate are formed. The reaction is as follows:

${\text{Glucose+2ADP+2NAD}}^{+}+2\text{P}\to {\text{2Pyruvate+2ATP+2NADH+2H}}^{+}\text{-------- equation 1}$

When muscles undergo intense exercise, then due to lack of oxygen, pyruvate is converted to lactic acid. This process is termed as lactic acid fermentation. The reaction is as follows:

${\text{2Pyruvate+2NADH+2H}}^{+}\to 2{\text{Lactate+2NAD}}^{+}\text{--------- equation 2}$

Adding equation 1 and 2, we get,

$\text{Glucose+2ADP+2P}\to \text{2Lactate+2ADP ------- equation 3}$

So, this is the balanced conversion of glucose into lactic acid.

Interpretation Introduction

Interpretation:

The standard free-energy change for the conversion of glucose into lactate.

Concept introduction:

Glycolysis is the process that occurs in the cytoplasm of the cell. It is the breakdown of one molecule of glucose into two molecules of pyruvic acid. During this process energy is released in the form of two moles of ATP. The purpose of glycolysis is to maintain the blood glucose level.

Answer to Problem 23P

$\Delta {\text{G for conversion of glucose to lactate = -114 kJmol}}^{-1}$.

Explanation of Solution

Given:

$\begin{array}{l}\text{[glucose] = 5 mM}\\ \text{[lactate]=0}\text{.05 mM}\\ \text{[ATP]=2 mM}\\ \text{[ADP]=0}\text{.2 mM}\\ \text{[P]=1 mM}\end{array}$

Standard Gibbs free energy for the formation of pyruvate:

${\text{Glucose+2ADP+2NAD}}^{+}+2\text{P}\to {\text{2Pyruvate+2ATP+2NADH+2H}}^{+}\text{-------- equation 1},\Delta {\text{G}}_1^{\circ }=-73.3{\text{kJmol}}^{-1}$

Standard Gibbs free energy for the formation of lactate from pyruvate:

${\text{2Pyruvate+2NADH+2H}}^{+}\to 2{\text{Lactate+2NAD}}^{+}\text{--------- equation 2},\Delta {\text{G}}_2^{\circ }=-50{\text{kJmol}}^{-1}$

Adding equation 1 and 2,

$\begin{array}{l}\text{Glucose+2ADP+2P}\to \text{2Lactate+2ADP ------- equation 3, }\\ \Delta {\text{G}}_3^{\circ }=\Delta {\text{G}}_1^{\circ }+\Delta {\text{G}}_2^{\circ }\\ \Delta {\text{G}}_3^{\circ }=-73.{\text{3 kJmol}}^{-1}+-5{\text{0 kJmol}}^{-1}\\ \Delta {\text{G}}_3^{\circ }=-123.{\text{3 kJmol}}^{-1}\end{array}$

According to free energy change equation,

$\begin{array}{l}\Delta \text{G}=\Delta {\text{G}}^{\circ }+\text{RTlnQ}\\ \text{Where, Q = reaction quotient, R = gas constant, and T = temperature}\end{array}$

$\begin{array}{l}\text{Q = }\frac{{[\text{Lactate]}}^2\times {[\text{ATP]}}^2}{[\text{Glucose]}\times {\text{[ADP]}}^2\times {[\text{P]}}^2}=\frac{{\text{[0}\text{.05}\text{mM]}}^2\times {[2\text{mM]}}^2}{[5\text{mM]}\times {\text{[0}\text{.2}\text{mM]}}^2\times {[1\text{mM]}}^2}=5\text{0 M}\\ \text{lnQ = ln 50 = 3}\text{.9}\end{array}$

For equation 3,

$\begin{array}{l}\Delta {\text{G}}_3^{\circ }=-123.{\text{3 kJmol}}^{-1}\\ \text{R = 0}\text{.0083 kJ/mol K}\\ \text{T = 298 K}\end{array}$

$\begin{array}{l}\Delta {\text{G}}_3\text{=}\Delta {\text{G}}_3^{\circ }+\text{RTlnQ}\\ \Delta {\text{G}}_3\text{=}-123.3{\text{kJmol}}^{-1}+0.0083\text{kJ/mol K}\times \text{298}\text{K}\times \text{3}\text{.9}\\ \Delta {\text{G}}_3=-114{\text{kJmol}}^{-1}\end{array}$