Biochemistry Chapter Energy Calculations

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Questions and Answers

What is the value of ΔG for the combustion of glucose at 25 °C?

2.943 J

-20 kJ mol-1

-2828 kJ mol-1 (correct)

-31 kJ mol-1

How is the energy required for a bird to fly 10 m above the ground calculated?

By calculating the total metabolic rate of the bird

By using the formula $mgh$ (correct)

By considering only the height without mass

By using only the mass of the bird

What happens to the energy released from ATP hydrolysis if it is not utilized for work?

It is stored as potential energy

It is dissipated into the environment

It is released as heat (correct)

It is converted back into glucose

What is the ΔG value for the formation of glutamine from glutamate?

+14.2 kJ mol-1 Signup and view all the answers

What is the result of coupling ATP hydrolysis with the reaction that has a positive ΔG?

It allows favorable reactions to occur despite their positive ΔG Signup and view all the answers

Which statement accurately describes the relationship between enthalpy and chemical bonding?

Enthalpy changes are associated with forming new, stronger bonds. Signup and view all the answers

What happens to the contribution of entropy at higher temperatures?

Entropy has a larger contribution to free energy. Signup and view all the answers

Which term describes the energy associated with the movement of an object?

Kinetic energy Signup and view all the answers

According to the laws of thermodynamics, energy can be:

Transferred in various forms without being lost from the universe. Signup and view all the answers

What characterizes an isolated system?

Exchanges neither energy nor matter with its surroundings. Signup and view all the answers

Which of the following accurately describes the role of NADH in chemical reactions?

It serves as a reduced species in oxidation reactions. Signup and view all the answers

What does the formula $G = H - TS$ represent?

The Gibbs free energy in terms of enthalpy and entropy. Signup and view all the answers

In thermodynamics, the term 'surroundings' refers to which of the following?

The external environment where observations are made. Signup and view all the answers

What happens to the internal energy of an isolated system?

It remains constant. Signup and view all the answers

What is the relationship between work and heat for isothermal expansion of a perfect gas?

q = -w Signup and view all the answers

How is the change in internal energy (ΔU) measured at constant volume?

ΔU = qV Signup and view all the answers

What does the term 'enthalpy' (H) represent?

The sum of internal energy and pressure-volume work. Signup and view all the answers

For a perfect gas at 25 °C, what is the added term to the internal energy to calculate the molar enthalpy?

RT Signup and view all the answers

Under constant pressure conditions, how is the change in enthalpy (ΔH) expressed?

ΔH = ΔU + pΔV Signup and view all the answers

What occurs during the reaction of oxidation of tristearin in a biological system?

The atmosphere does work upon the system. Signup and view all the answers

What is true about the internal energy of a perfect gas?

It remains independent of the volume it occupies. Signup and view all the answers

What is the overall standard enthalpy change for the process converting glucose to lactic acid?

-120 Signup and view all the answers

Which formula represents the standard enthalpy of combustion of sucrose?

12 Signup and view all the answers

How is the standard enthalpy change for a reaction calculated?

By taking the difference of the enthalpy of products and reactants weighted by stoichiometry. Signup and view all the answers

What is the standard enthalpy of formation for water in its liquid state?

-286 Signup and view all the answers

Which statement about standard enthalpies of formation is correct?

They can be negative if the compound is stable. Signup and view all the answers

What is the experimental value of the standard enthalpy of combustion of sucrose?

-5645 Signup and view all the answers

In what context do standard enthalpies of formation have a value of zero?

For elements in their most stable form. Signup and view all the answers

What defines a spontaneous process among the examples given?

It is a natural change that occurs without intervention. Signup and view all the answers

What is the standard reaction entropy change for the hydration of carbon dioxide catalyzed by carbonic anhydrase?

-96.3 J K-1 mol-1 Signup and view all the answers

How does the binding of NAD+ to lactate dehydrogenase occur spontaneously despite a negative ΔrS∅?

The entropy of the surroundings increases. Signup and view all the answers

What is the relationship between Gibbs Energy and entropy for spontaneous processes?

Gibbs Energy decreases while entropy increases. Signup and view all the answers

According to the 2nd Law of Thermodynamics, when do processes occur spontaneously?

When the overall entropy of the universe is increased. Signup and view all the answers

What is the formula for calculating Gibbs Free Energy?

G = H - TS Signup and view all the answers

What is the implication of ΔSuniv being greater than zero?

The process is spontaneous. Signup and view all the answers

What happens to the absolute entropy of all perfectly crystalline substances at absolute zero?

It is zero. Signup and view all the answers

What does the equation ΔSsur = -ΔH/T signify in thermodynamics?

The change in enthalpy of the surroundings. Signup and view all the answers

What is the overall enthalpy change for the reaction converting 2H2O2(l) to O2(g) and H2O(l)?

-172 Signup and view all the answers

Which fuel provides the highest energy output per gram?

Hydrocarbon fuels (48 kJ g-1) Signup and view all the answers

What does Hess's Law state about the standard enthalpy of a reaction?

It is the sum of the enthalpies of the separate reactions Signup and view all the answers

What happens to glucose during vigorous exercise due to oxygen deprivation?

It is broken down to lactic acid Signup and view all the answers

What is the standard enthalpy of combustion for methane (CH4)?

-890 kJ mol-1 Signup and view all the answers

What is the primary reason for using fats for energy storage in mammals?

They provide insulation Signup and view all the answers

What does ΔH represent in thermodynamic equations?

Enthalpy change Signup and view all the answers

What energy output does fasting provide compared to when carbohydrates are burned?

Less than carbohydrates Signup and view all the answers

Study Notes

MPharm Programme Thermodynamics

The MPharm programme covers thermodynamics.
Topics include kinetics and thermodynamics, the law of conservation of energy, the first, second and third laws of thermodynamics
Also included are internal energy, enthalpy, entropy, Hess's law, equilibria, Gibbs free energy and non-covalent forces & binding.
Recommended texts are "why chemical reactions happen" by James Keeler & Peter Wothers (Oxford University Press 2003) and "Physical Chemistry for the Life Sciences" by Peter Atkins & Julio de Paula (OUP 2006).

Overview

Thermodynamics bridges kinetics and thermodynamics.
The law of conservation of energy is a fundamental concept.
The first, second and third laws of thermodynamics have wide applications.
Internal energy, enthalpy, and entropy concepts are key to understanding thermodynamic processes.
Hess's law simplifies calculations involving enthalpy changes.
Equilibrium and Gibbs free energy are crucial aspects
Non-covalent forces and binding are essential in biological systems.

Free Energy (G)

Free Energy (Gibbs Free Energy) comprises enthalpy and entropy.
The formula for Gibbs Free Energy: G = H - TS
The formula for change in Gibbs Free Energy: ΔG = ΔH - TΔS
Enthalpy changes relate to chemical bonding or non-covalent interactions.
negative ΔH values indicate favorable bonding/interactions.
A favorable solvent interaction (non-covalent) also involves a negative ΔH.
Entropy changes relate to order/disorder in a process.
Higher temperatures favor entropy's contribution to Gibbs Free Energy more.
Enthalpy has a larger contribution at lower temperatures

Energy Types

Energy exists in two primary forms: kinetic and potential energy.
Kinetic energy is associated with movement, calculated classically as Ek = ½ mv².
Potential energy is due to position, and calculated classically as Ep = mgh.
Total Energy, E is the sum, E=Ek +Ep.

Conservation of Energy

Energy cannot be created or destroyed, only transferred.
Energy transfer from the sun takes many forms.
Energy dissipates as heat, which is non-usable, with high entropy

Important Molecules

NADH is a highly reduced species, used in oxidation reactions.
ATP releases energy in phosphate hydrolysis reactions.

Systems and Surroundings (Thermodynamic Systems)

The system under study is a focus.
Examples include reaction flasks, biological cells, or whole animals.
The surroundings are external to the system.
Data for measurements is obtained from the surroundings.
Surroundings are kept at a constant volume or pressure.

System Types

Open systems can exchange matter and energy with the surroundings.
Closed systems can exchange energy, but not matter, with the surrounding.
Isolated systems exchange neither matter nor energy with the surroundings.

Heating

Heating is energy transfer between a system and its surroundings.
Diathermic barriers (e.g., metals, skin, biological membranes) facilitate energy transfer.
Adiabatic barriers impede energy transfer.

Zeroth Law

If system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A is in thermal equilibrium with system C.

Work and Heat

Work is considered useful, ordered energy.
Heat is non-useful, random energy.

Work Calculations

Work (w) = mass x gravity x height (mgh)
In thermodynamics calculations, work has the symbol w and heat q.

Sign Conventions

Negative work (w < 0) indicates work done by the system.
Positive work (w > 0) indicates work done on the system.
Negative heat (q < 0) indicates heat lost from the system.
Positive heat (q > 0) indicates heat gained by the system.

Work Associated with Gas Expansion

p_extA is the opposing force
Work = h x p_extA
The work is negative (w = -p_extΔV), indicating the system is doing work.

Exhaling Air

Work required to push air from lungs against atmospheric pressure (typically 12-20 times/minute).
Consider exhaling 0.5 L (5.0 x 10^-4 m³) against atmospheric pressure; w = -51 J.
This is roughly equivalent to lifting 7 kg off the ground through a height of 75 cm.

Expansions and Mechanical Equilibrium

System does no work if there's no opposing force (w = 0).
Maximum work during expansion occurs when opposing pressure is infinitesimally less than internal pressure.
Maximum work is possible with reversible changes.
The change in work in infinitesimal terms is dw = -p_extdV ≈ pdV.
Work performed, w, is calculated using the formula w = -nRT In(V_f/V_i), where V_f is final volume and V_i is initial volume

Measuring Heat

Heat capacity (C) = q/ΔT
Calculate transferred heat using the formula q = CAT, given the heat capacity and change in temperature.
Common materials have specific heat capacity (C_s; J K^-1 g^-1) or molar heat capacity (C_m; J K^-1 mol^-1).
Constant pressure (Cp) or constant volume (Cv) are important concepts.

Reversible Isothermal Expansion of a Perfect Gas

Temperature remains constant throughout the process.
Kinetic energy remains constant (speed of molecules doesn't change).
Potential energy of a perfect gas is zero, therefore total energy only depends on kinetic energy.
Heat (q) from surroundings equals negative work done by surroundings in this reversible process.
q = -w and q = nRT In(Vf/Vi).

The Internal Energy, U

Internal energy (U) is the total energy of the atoms, molecules and ions
It's impossible to measure U directly, only changes in U can be determined.
ΔU = w + q, where w is work and q is heat exchange.

Perfect Gases Again

For isothermal expansion of a perfect gas, ΔU = 0.
Internal energy of a perfect gas is independent of volume at a constant temperature.
Changes to the distance between moving atoms/molecules cause changes to internal energy.

The First Law of Thermodynamics

Isolated systems cannot exchange heat or perform work on their surroundings.
Their internal energy stays constant.
Perpetual motion devices are impossible because they would require a constant drop in the system's internal energy without replenishment of energy.

Measuring ΔU

Carry out reaction in constant volume vessel for calculating ΔU.
When no expansion work is possible w = 0; in that case ΔU = q_v (heat generation in the closed system).
Heat capacity at constant volume is, Cv=ΔU/ΔT.

Enthalpy

Most biological systems operate at constant pressure.
Enthalpy (H) accounting factor: H = U + pV
When dealing with constant pressure, we are concerned with enthalpy changes.
ΔH = ΔU + pΔV

Molar Enthalpies

Molar Enthalpy is defined as Hm = H/n for 1 mole of a gas.
for a perfect gas at 25 °C., RT = 2.5 kJ mol^-1.
At constant pressure for an open system the enthalpy change is equal to the heat transferred, or ΔΗ= q_P.

Exothermic and Endothermic

Exothermic processes release energy (q<0 , ΔH <0).
Endothermic processes absorb energy (q>0, ΔH >0.)
The heat capacity at constant pressure is given by Cp = ΔH/ΔT

Phase Transitions

Pure substances in their standard state (with 1bar) often have a temperature of 25°C.
Substances don't have to be in their most stable form for standard conditions.
Substances can have multiple phases (eg. ice, water, vapor).

Standard Enthalpies of Transition

Data on freezing and boiling points, Δ_fusH°, and Δ_vapH^o, for various substances are tabulated.

Thermochemical Equations

Water's high vaporization enthalpy stems from hydrogen bonding.
Melting has easier enthalpy change as molecules remain close.
The changes in enthalpy involved in freezing and melting are equal and opposite.

General Enthalpy Changes

Forwards and backward processes exhibit equal and opposite enthalpy changes

Sublimation and Vapour Deposition

Sublimation is the direct conversion of a solid to a vapor (eg., frost vanishing).
The overall enthalpy change for a process can be calculated by summing enthalpy changes of steps into which the process is hypothetical divided.
All enthalpy values must be determined at the temperature of interest for valid calculations.

Measuring Phase Changes

Differential Scanning Calorimetry (DSC) measures the difference in heat transferred between a sample and a reference material.
Useful for characterizing materials such as Proteins, micelles, lipids, nucleic acids, and pharmaceuticals.

Chemical Change: Bond Enthalpies

Energy change associated with bond dissociation is the bond enthalpy.
Breaking bonds is endothermic, while creating bonds is exothermic.

Selected Bond Enthalpies

Diatomic and polyatomic molecules have tabulated bond enthalpies.
The exact value depends on the environment of the atoms.
Textbooks often provide mean bond enthalpy tables for common compounds in the gas phase

Using Mean Bond Enthalpies

Estimation of enthalpy change for reactions (e.g., hydrogen peroxide decomposition).
Necessary to take into account phase changes (melting, vaporization, sublimation) in gas phase calculations.

Solution (Hydrogen Peroxide Decomposition)

Numerical calculation of overall enthalpy change during hydrogen peroxide decomposition steps.

Standard Enthalpies of Combustion

Standard enthalpy of combustion is the change of enthalpy per mole of a combustible substance.
Use a correction for gases, ΔH = ΔU + Δ(pV) = ΔU +nRTΔV, taking into account molar volumes, Δ V_gasRT

Biological Fuels

Humans' energy needs depend on age, sex and activity.
Carbohydrates generally provide 17kJ/g.
Fats provide 38kJ/g.
Hydrocarbons provide 48kJ/g.
More oxidized fuels release less energy combustion.

Hess's Law

The standard enthalpy of a reaction is the sum of the standard enthalpies of the reactions into which the overall reactions may be divided.

Using Hess's Law:

Calculate Enthalpy changes in various processes (eg glycolysis, using tabulated data for glucose and lactic acid reactions).

Standard Reaction Enthalpies

Difference between the standard molar enthalpies of products and reactants.
Each reactant and product calculation is made under standard conditions (1 bar and its standard temperature).

Standard Enthalpy of Formation

Standard enthalpy of formation is the enthalpy change when one mole of a substance is formed from its constituent elements in their most stable states.

Applying Standard Enthalpies of Formation

Estimation of standard enthalpy of combustion of sucrose.

Spontaneity

Spontaneity is the tendency of chemical reactions to proceed without input of energy.
Spontaneous processes that disperse energy and matter tends to have higher entropy.

Spontaneity and Energy

Spontaneous processes are not necessarily associated with lower energy.
Isothermal expansion of a perfect gas into a vacuum has no overall change in the energy of the system, just a change in the spacing between atoms/molecules.

The Direction of Spontaneous Change

Matter and energy tend to disperse.
Gas molecules spread out randomly and the probability of them staying in one corner is negligible.
Energy is transferred between atoms or molecules during collisions.

The Second Law of Thermodynamics

The overall entropy of an isolated system tends to increase.
Entropy is a measure of dispersal of matter and energy.

Entropy- Spread of Energy

Entropy as a tendency for energy to spread out.
There is a higher probability of a hot/cold bar system changing to disperse energy equally within each block rather than them remaining separate in their blocks.

Entropy- Hot and Cold Bars

The example demonstrates entropy increase occurs when hot and cold bars are placed together and collide.

Entropy- Hot and Cold Packet Distributions

Probability calculation for different distributions of energy packets across the hot and cold metal bars confirms that systems tend towards a state with maximum entropy

Entropy - Energy Packet Distributions

The graph showing combinations of energy packets distribution supports the idea that the high entropy state is the most probable for the energy packets distribution.

Entropy- Energy in Heating/Cooling

Entropy calculation for heating and cooling water.
Entropy calculation shows that the entropy increases during heating and decreases during cooling.

Entropy Changes Accompanying Heating

Calculation of entropy changes associated with temperature changes in systems with constant or variable heat capacities.

Entropy Change Accompanying Phase Transitions

Phase transitions (e.g., melting, boiling) involve entropy increase due to increased molecular freedom.
Changes in entropy accompany phase transitions in biological macromolecules (e.g, unfolding of proteins).

Entropies of Vaporisation

Table of vaporization entropies at 1 atmosphere pressure and at normal boiling point for certain substances.

Entropy of Vaporization of Water

Calculation of the entropy of vaporization of water at 25 °C.
It involves calculations of heating of water up to boiling temperature plus the entropy change during transition (vaporization) plus cooling back to 25 °C.

Metabolism and Entropy

Summary of metabolic processes and their effect on entropy in a resting human.

Ok, but why should we be bothered about that?

Heat transfer to/from the surroundings is equal and opposite to heat absorbed/released by the system.
Relationship between energy change (ΔU) in the systems and entropy change (ΔS) in the surroundings during the reaction.
At constant pressure, ΔS_sur = -ΔH_sys/T

Focusing on the System

Combining the system and surroundings for the change in total entropy.
Relating the ΔS_sur with ΔrG° is possible due to the equality of the amount of heat transferred.

The Gibbs Energy (Gibbs Free Energy)

The Gibbs Free energy is associated with temperature, enthalpy, and entropy changes during chemical reactions and processes.
G = H -TS
When T is constant, we can calculate ΔG=ΔH - TΔS

Work and The Gibbs Energy Change

The Gibbs energy change, ΔG, for any process is equal to the maximum non-expansion work that can be extracted from the process under constant temperature and pressure.
Non-expansion work include electrical work, mechanical work, redox chemistry occurring in a cell or within contracting muscles.
ΔG=w_max

Changes in Gibbs Energy and Metabolism

Calculate the amount of glucose used during a bird's flight by determining the Gibbs energy change (ΔG) that accompanies glucose's combustion when the bird raises its body 10m above the surface.

Solution

Determination of energy required by a bird using the formula Work = mgh, where m is mass in kg, g is acceleration due to gravity (9.81 m/s²), and h is height in m.
Calculation of moles of glucose needed using the relationship between energy extracted and free energy per mole.

ATP Hydrolysis

ATP (adenosine triphosphate) hydrolysis provides energy for unfavorable biochemical reactions.

Coupling ATP Hydrolysis

Coupled ATP hydrolysis supplies sufficient driving energy to form glutamine from glutamate.

The Standard Reaction Gibbs Energy

Standard reaction Gibbs Energy can be calculated by combining the standard Gibbs energies of formation for products and reactants.

Calculating Standard Reaction Gibbs Energy for Reaction Catalysed By Carbonic Anhydrase

Numerical calculation of ΔH° and ΔS° to calculate ArG° of CO2(g)+H2O(l)→H2CO3(aq) at 25 °C

Tabulated Standard Reaction Gibbs Energies of Formation

Provides a guide for combining standard enthalpies and entropies to determine Gibbs energies of formation at 298K.
Calculation showing how constituent elements form products and reactants using their standard states, and subsequently determining the Gibbs free energy change for a given process (eg combustion of sucrose).

The Gibbs Energy and Equilibria

Standard reaction Gibbs energy to determine the equilibrium constant (K) using the equation ΔG° = -RT In K.

Temperature and Reaction Feasibility

Reactions are feasible when ΔG° < 0 under constant temperature and pressure.
Temperature of feasibility is calculated when ΔG° = 0; T= ΔH°/ΔS°

Calculation Example (Thermodynamic Spontaneity for Decomposition of Calcium Carbonate)

Calculating the temperature at which decomposition of Calcium Carbonate becomes energetically favorable (spontaneous).

Summary of Thermodynamic Reaction Spontaneity

Summary of thermodynamic conditions under which a reaction is spontaneous depending on enthalpy and entropy change factors.

Where We Got To in Our Discussion of Entropy

Emphasizes the significance of overall entropy change of the universe to determine spontaneous processes
The need that the total entropy change (ΔS_univ) of both the system and surroundings for a given reaction must be greater than zero for the process to be thermodynamically feasible.