Chapter 27, Problem 12P

Interpretation Introduction

(a)

Interpretation:

The conversion of rate of energy expenditure from $\text{70}\text{watt}$ to kilojoules per second and to kilocalories per second is to be stated.

Concept introduction:

The set of complex compounds which are responsible for migration of the electrons from the electron donors to the acceptors of the electrons with help of the redox reactions is known as electron transport chain. This electron transport chain also helps in the coupling of transferred electrons with protons transfer inside and outside the cell membrane.

Answer to Problem 12P

The conversion of rate of energy expenditure from $\text{70}\text{watt}$ to kilojoules per second and to kilocalories per second is $\text{0}\text{.07}\text{kJ/s}$ and $0.017\text{kcal/s}$ respectively.

Explanation of Solution

The given rate of energy expenditure corresponding to a $\text{70}\text{kg}$ person at resting position is $\text{70}\text{watt}$.

The conversion of watt into kilojoules per second is done below.

$1\text{watt}=0.001\text{kJ/s}$

So, the value of rate of energy expenditure in kilojoules per second becomes $\begin{array}{c}\text{70}\text{watt}=\text{70}\times 0.001\text{kJ/s}\\ =\text{0}\text{.07}\text{kJ/s}\end{array}$.

The conversion of watt into kilocalories per second is done below.

$1\text{watt}=0.00024\text{kcal/s}$

So, the value of rate of energy expenditure in kilocalories per second becomes $\begin{array}{c}\text{70}\text{watt}=\text{70}\times 0.00024\text{kcal/s}\\ =\text{0}\text{.0168}\text{kcal/s}\\ =0.017\text{kcal/s}\end{array}$.

Therefore, the value of rate of energy expenditure, that is $\text{70}\text{watt}$, in kilojoules per second is $\text{0}\text{.07}\text{kJ/s}$ and in kilocalories per second is $0.017\text{kcal/s}$.

Interpretation Introduction

(b)

Interpretation:

The total number of electrons which flows through the mitochondrial electron-transport chain per second under the mentioned conditions is to be stated.

Concept introduction:

The set of complex compounds which are responsible for migration of the electrons from the electron donors to the acceptors of the electrons with help of the redox reactions is known as electron transport chain. This electron transport chain also helps in the coupling of transferred electrons with protons transfer inside and outside the cell membrane.

Answer to Problem 12P

The total number of electrons which flows through the mitochondrial electron-transport chain per second under the mentioned conditions is $3.86\times {10}^{20}{e}^{-}\text{/s}$.

Explanation of Solution

The given rate of energy expenditure corresponding to a $\text{70}\text{kg}$ person at resting position is $\text{70}\text{watt}$.

According to the unit concept, one watt equals to one ampere as watt is used for the measurement of current flow. The half-reactions that takes place during the mitochondrial electron-transport chain is given below.

$\begin{array}{l}\text{NADH}+{\text{H}}^{+}\to {\text{NAD}}^{+}+2{\text{H}}^{+}+2e^{-}E°=0.320\text{V}\\ \frac{1}{2}{\text{O}}_{\text{2}}+2{\text{H}}^{+}+2e^{-}\to {\text{H}}_{\text{2}}\text{O}E°=0.816\text{V}\end{array}$

So, the total potential difference of the two half-reactions is $\begin{array}{c}E°=0.320\text{V}+0.816\text{V}\\ =\text{1}\text{.14}\text{V}\end{array}$.

The relation between watt $\left(W\right)$, volt $\left(V\right)$ and electric current $\left(I\right)$ is given below.

$\begin{array}{c}W=I\times V\\ I=\frac{W}{V}\end{array}$

Substitute the value of watt and volt in the above expression.

$\begin{array}{c}I=\frac{70\text{watt}}{1.14V}\\ =61.4\text{watt/V}\\ =\text{61}\text{.4}\text{A}\\ =\text{61}\text{.4}\text{C}{\text{s}}^{-1}\end{array}$

As $1\text{ampere}$ equals to one coulomb per second and $1\text{coulomb}=6.28\times {10}^{18}{e}^{-}$. So, the total number of electrons in $\text{61}\text{.4}\text{C}{\text{s}}^{-1}$ is $\frac{\text{61}\text{.4}\text{C}{\text{s}}^{-1}\times 6.28\times {10}^{18}{e}^{-}}{1\text{C}}=3.86\times {10}^{20}{e}^{-}\text{/s}$

Therefore, the total number of electrons which flows through the mitochondrial electron-transport chain per second is $3.86\times {10}^{20}{e}^{-}\text{/s}$.

Interpretation Introduction

(c)

Interpretation:

The corresponding rate of ATP production is to be stated.

Concept introduction:

The molecule which helps in the migration of energy produced during the breakdown of food to the other processes of cells is known adenosine triphosphate or ATP molecule. ATP contains adenine as nitrogenous base, a ribose sugar and three phosphate groups.

Answer to Problem 12P

The corresponding rate of ATP production is $\text{0}\text{.801}\text{mmol}\text{ATP/s}$.

Explanation of Solution

The given rate of energy expenditure corresponding to a $\text{70}\text{kg}$ person at resting position is $\text{70}\text{watt}$.

The relation between the total numbers of electrons moving through electron transport chain and the total number of ATP molecules produced is that $\text{NADH}$ forms $2.5$ ATP and evolves two electrons in the electron transport chain. So, approximately $1.25$ ATP is produced by one electron.

Thus, the total number of ATP molecules produced by $3.86\times {10}^{20}{e}^{-}\text{/s}$ number of electrons is $3.86\times {10}^{20}{e}^{-}\text{/s}\times \frac{1.25\text{ATP}}{1e^{-}}=4.83\times {10}^{20}\text{ATP/s}$

The molar concentration of ATP molecules is calculated by the expression given below.

$\text{Molar concentration of ATP}=\frac{\text{Number}\text{of}\text{ATP}\text{molecules/s}}{\text{Avogadro's}\text{number}}$

Substitute number of molecules and Avogadro’s number in above formula.

$\begin{array}{c}\text{Molar concentration of ATP}=\frac{4.83\times {10}^{20}\text{ATP/s}}{\text{6}\text{.023}\times {10}^{23}\text{ATP}}\times {10}^3\text{mmol}\\ =\text{0}\text{.801}\text{mmol}\text{ATP/s}\end{array}$

Therefore, the corresponding rate of ATP production is $\text{0}\text{.801}\text{mmol}\text{ATP/s}$.

Interpretation Introduction

(d)

Interpretation:

The total time in which an ATP molecule turns over in a person at rest is to be stated.

Concept introduction:

The molecule which helps in the migration of energy produced during the breakdown of food to the other processes of cells is known adenosine triphosphate or ATP molecule. ATP contains adenine as nitrogenous base, a ribose sugar and three phosphate groups.

Answer to Problem 12P

The total time in which an ATP molecule turns over in a person at rest is $123\text{s}$.

Explanation of Solution

The total given ATP content of the body is $\text{50}\text{g}$.

The rate of ATP production is $\text{0}\text{.801}\text{mmol}\text{ATP/s}$.

The molar mass of ATP is $507.18\text{mg/mmol}$.

The mass of ATP is calculated by the expression given below.

$\text{Mass}=\text{Moles}\times \text{molar}\text{mass}$

Substitute the value of moles and molar mass of TAP in the above expression.

$\begin{array}{c}\text{Mass}=\text{0}\text{.801}\text{mmol}\text{ATP/s}\times 507.18\text{mg/mmol}\\ =\text{406}\text{mg}\text{ATP/s}\end{array}$

The conversion of $\text{mg}$ into $\text{g}$ is done below.

$\text{1}\text{mg}={10}^{-3}\text{g}$

Therefore, the mass of ATP becomes, $\text{406}\text{mg}\text{ATP/s}=\text{406}\times {\text{10}}^{-3}\text{g}\text{ATP/s}$

The total time for ATP turn over is calculated by dividing the given mass of TAP content in body with $\text{406}\times {\text{10}}^{-3}\text{g}\text{ATP/s}$ as follows.

$\frac{50\text{g}}{\text{406}\times {\text{10}}^{-3}\text{g}\text{ATP/s}}=123\text{s}$

Therefore, the total time in which an ATP molecule turns over in a person at rest is $123\text{s}$.