Biochemistry Chapter Energy Calculations

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.

Focusing on the System

• Deriving the relationship between the Gibbs free energy change, ΔG° of a system and the total change in entropy of the universe.
• Summarizes how to calculate spontaneity entirely based on the system properties alone.

References

• Not included.