Medical ChemistryLecture 3 2007 (J.S.)

Kinetics of chemical reactions

Chemical equilibrium

Energy in chemical reactionsFree Gibbs energy – the driving force of chemical reactions

2

]S[

t–v 1

ν]P[

t1ν

v =c–t

Because , velocity is expressed in mol × l–1 × s–1

The fundamental terms in reaction kineticsKinetics studies the rates (and mechanisms) of chemical reactions.

The term velocity (symbol v) is the reaction rate expressed in terms of change in the concentrations of reactants:

For the simple reaction S P, the velocity is defined as

S – substrate, P – product,ν – reaction stoichiometric coefficients (if there are any)

Factors affecting velocities of reactions: temperature, concentrations of reactants, catalysts or inhibitors.

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Velocity depends on the concentrations of reactants

This dependence is described in the velocity equation:

For the reaction mA + nB xC,

v = k [A]m [B]n

where k is the kinetic constant that includes the specific reaction features as well as the temperature term ( k = A × e–Ea I RT ).

Due to decreasing concentrations of reactants, there must bealways a gradual decrease of reaction velocity in closedsystems till the reaction reaches the equilibrium.

The sum of all exponents in velocity equations (m + n + ….) indicates the reaction order.The equation mentioned above is a (m+n)th-order reaction.

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Progress curves (kinetic curves)

The progress - the time course of a reaction - is shown bya plot of the concentration of any of the substrates or products against time.

The instantaneous velocity vx

at any particular time tx is then

given by the slope of the tangent to the curve at that time.

For the first-order reactions

[S]t = [S]0 e– k t or vt = v0 e– k t

[S]0 – initial concentration of S, v0 – initial velocity, in the first moments of the reaction

Example: Both curves hold for the reaction S P. It is a first-order reaction according to the velocity equation v = k [S] .

[S]

t

x

tg α = d[S] / dt = vx

α

tx

[P]

t

[S]

t

(equilibrium)

At equilibrium the net reactionvelocity is zero.

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First-order reactionsare most commonly decomposition reactions, radioactive decay,isomerization and rearrangements, and simple enzyme-catalyzedreactions involving a single substrate at low concentration.

The kinetic constant k of a first-order reaction can be found from the

slope of the straight line in the plot of log [S] versus time.

The half-life t½ of a first-order reaction is the time it takes forone-half of a reactant to undergo a reaction. The half-lifeof a first-order reaction is independent of the concentrationof the reactant and equals t½ = 0,69 / k .

[S]0

t

[S]0/2

[S]0/4

t½ 2t½

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Second- and higher-order reactionswill not be discussed in this course.

Zero-order reactions

[S]

t

Zero-order kinetics

First- orhigher-orderkinetics

The velocity of a zero-order reaction does not depend on the reactant concentration, it is constant ( v = k [S]0 = k ).

The velocity of such reactions iscontrolled by other factors than bycollisions of the reactants involved.In enzyme-catalyzed reactions, thevelocity depends on the concentration ofthe enzyme-substrate complex. If thesubstrate concentration is higher thanrequired for the full enzyme saturation, the reaction is zero order for some time.However, after the concentration decreasesand the enzyme is not fully saturated, thereaction becomes first- or higher-order.

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If v1 = v2 in equilibrium state, then there exists a constant ratio for

the particular reaction – the equilibrium constant K :

Chemical equilibrium

In closed systems, the reactions proceed to certain point and thenapparently stop and leave considerable amounts of unaffected reactants.

A dynamic, chemical equilibrium is reached because thevelocities of the forward and reverse reactions are equal.

Reversible reactions do not go to completion.

Basically, every reaction (even a "irreversible“) can be viewed as the formationof the equilibrium between the starting reactants and the reaction products.

The forward reaction rate v1 = k1 [A]m [B]n

The reverse reaction rate v2 = k2 [C]p [D]q

Reversible reaction mA + nB pC + qDv1

v2

k1

k2

[ ]C

Kc = [ ] [ ]

[ ] [ ]n

eq

m

eq

q

eq

p

eq

BADC

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The law of chemical equilibrium (Guldberg and Waage, 1867)

For any reversible reaction at chemical equilibrium andparticular temperature, there exist a fixed ratio among concentrations of products and reactants expressed asthe equilibrium constant K.

When a closed system is at equilibrium, it will remain inthis state indefinitely unless the equilibrium is affectedin some manner by external factors.

"Position“ of the equilibrium:

K » 1 – the equilibrium is "on the right“, it favours the reaction products

K « 1 – the equilibrium is established "on the left“ favouring the reactantsK ≈ 1 – the reaction is "perfectly reversible“

Catalysts do not change the value of K,they cause a system to reach equilibrium more quickly.

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External factors upsetting equilibria

Changes in equilibrium concentrationsby adding more of the reactants or by removing of some of the productschange the reaction rates: the rates of the forward and reverse reactionswill continue to change until equilibrium that corresponds to the value ofequilibrium constant K is reached again. The value of K does not change; at restored equilibrium, the concentrations of the reactants and products will be different from those before the change.

Changes in temperaturechange the value of the constant K: An increase in temperaturefavours the endothermic reaction (which may be either the forward or thereverse reaction), a decrease favours the exothermic reaction.

Changes in pressurecause significant changes in equilibria only where the number of moles ofgaseous products and reactants differ. An increase in pressure shifts anequilibrium in the direction that produces the smaller number of moleculesin the gas phase. The value of the constant K remains unchanged.

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The general principle that underlies all changes in equilibria is

Le Chatelier´s principle:

If a system in equilibrium is subjected to a change inconcentration, temperature, and pressure, the systemwill react in a way that tends to relieve the change.

Energy in chemical reactionsThe driving force of reactions

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The fundamental terms in chemical thermodynamics

Energy can be defined as ability of producing heat or doing work.Energy takes any of several forms, such as mechanical, thermal,chemical, osmotic, electrical.

Energy release or consumption accompanying chemical reactions isa consequence of bonds cleavage and formation.

System is a portion of universe under study, surroundings is everythingthat is not part of a system under study.

Insulated systems – without any communication withtheir surroundings (no exchange of matter nor energy)

Closed systems – can release or absorb energy fromthe surroundings but no exchange of matter is possible.

Open systems exchange energy, matter, even information) withthe surroundings.

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The internal energy U

is the sum of all the energy of all atoms, molecules, or ions that comprise a chemical system.

The total internal energy U of a system cannot be determined.However, the internal energy change of a system ΔU canbe both measured and calculated. It is the amount of energyexchanged with the surroundings during a chemical or physicalchange of the system.

U = Ufinal – Uinitial or U = U2 – U1

U > 0 an increase in the internal energy of the systemU < 0 a decrease of the internal energy of the system

An increase in the internal energy of a chemical system can result– in the temperature increase,– in melting, vaporization or a change in crystalline form, resp.,– in a endothermic chemical reaction.

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The first law of thermodynamics

The energy of the insulated system is constant.Energy can be converted to one form to another, butcannot be destroyed.In the interaction between a closed system and itssurroundings, the internal energy change of the systemequals the heat exchanged by the system plus the workdone on or by the system.

U = q + wworkheat

Heat lost by a system or work done by a systemon the surroundings are given negative values.

Although work can be transformed completely into heat, itdoes not follow that heat can be transformed completely to work.Then heat is taken as a less utilizable form of energy.

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In this course of chemistry, the only two kinds of work will be discussed– the work when a gas expands or contracts (pressure-volume work)and work associated with electrochemical changes in galvanic cells.

For a gas expanding against a constant external pressure, the work equals w = – p ΔV .

Chemical reactions realized at constant external pressure,most often atmospheric pressure, are very common. In thosereactions, the internal energy change equals U = q – p V.

This reaction heat q is defined as a quantity called enthalpy H and then the enthalpy change H = U + p V

Most reactions in living systems (in aqueous environment)are realized without any pressure-volume work or thecontribution of pΔV is negligable; then H = U

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The enthalpy change ΔH is equal to the heat of reaction.It expresses the difference in bond energy of reactionproducts and reactants.

H < 0 exothermic reaction, the enthalpy of the reaction products is lower (the bonds are more stable) than that of the reactants

H > 0 endothermic reaction, the enthalpy of the products is higher than that of reactants.

Standard enthalpy changes are expressed as the quantity of heat

per one mole of the substance or substances in question in the standard state and at specified temperature (usually

at 298 K, i.e. 25 °C). Then the symbol is ΔH° or simply ΔH° .

Example:

H2(g) + ½O2(g)    H2O(l) H° =  286 kJ mol1

the reaction is strongly exothermic

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The standard stateof any substance is the physical state at which it is most stable atatmospheric pressure (101.3 kPa) and a specified temperature. Theusual specified temperature is 298 K (25 °C, roughly room temperature).

For some specific processes, the standard enthalpy change ΔH°is named specifically, e.g.the standard enthalpy change of (or heat of) formation ΔH°f (of a substance from elements), combustion ΔH°c (substance + oxygen(g) → combustion products),

neutralization ΔH°neutralization (acid + base → salt(aq) + H2O(l) ), solution ΔH°soln (1 mol solute + n mol solvent → 1 mol solute in solvent).

ΔH of a reaction is the same whether the reaction takes placein one step or several steps (Hess´s law for combining ΔH values).

ΔH for a reaction in one direction is equal in magnitude to ΔHfor the reaction in the reverse direction, but is opposite in sign.

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Animals use the energy released by the oxidative breakdown of nutrients to H2O and CO2 (proteins give also nitrogenous catabolites). Chemical energy of nutrients corresponds with the heat of combustion.

Energetic yield of nutrients(heat of combustion) in per one gram of a pure nutrient:

Saccharides 17 kJ / g (4.1 kcal / g)

Triacylglycerols (fat) 38 kJ / g (9.1 kcal / g)

Proteins 24 kJ / g (5.7 kcal / g)when combusted to H2O, CO2, and N2 in a calorimeter,

17 kJ / g (4.1 kcal / g) in human bodies (catabolism to H2O, CO2, and urea CO(NH2)2

Remember that the heat evolved in going from the initial state to the final state is the same no matter by what route the reaction takes place, whether in calorimeter or within living cells.

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Spontaneous chemical reactions or physical changes,defined better as "thermodynamically favourable", arethose that can happen without any continuing outside influence.

The second law of thermodynamics

Every spontaneous chemical and physical change increasesthe entropy of the universe as a whole.

In insulated systems only such processes can proceedwhich tend to less organization, to more simple compounds,which result in total entropy increase.

Entropy is a thermodynamic property, a measure of disorder.It is defined as the amount of energy (heat) in the system that cannot be

transformed to work: S = Qrev / T . A change in entropy is ΔS = S2 – S1 .

The opposite to entropy is information (a negative entropy), a measureof order or organization.

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If ΔSsystem decreases (ΔS of a negative value), this change must be

accompanied by a simultaneous and larger increase in ΔSsurroundings,

because the condition for spontaneous process expressed by the second law of thermodynamics is

ΔSuniverse = ΔSsystem + ΔSsurroundings > 0

In contrast to insulated systems, in spontaneous processes in closed and open systems the entropy can either increase or decrease.

Ssurroundings is proportional to the heat that the system under study releases

into the surroundings or absorbs from it. Because also the enthalpy change ΔH of the system (reaction heat) must be taken into account , the mere entropy change ΔSsystem is not the best criterion of the spontaneity of

a given chemical reaction in closed and open systems..

Increase in entropy (ΔS of a positive value) is the driving force of processes in the universe as a wholeand also in insulated systems under study.

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The entropy change of a system ΔSsystem

Entropy increases

Increasing temperature

Melting a solid

Evaporating a liquid

Dissolving a solid in a liquid

Mixing two substances in the same phase

Increasing the number of particles during a reaction (e.g., decompositions of molecules)

Entropy decreases

Decreasing temperature

Freezing a liquid

Condensing a gas

Precipitation of a product in a solution

Separating two substances in the same phase

Decreasing the number of particles during a reaction

(e.g., syntheses)

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If ΔG is negative, the reaction can proceed spontaneously and the value of ΔG represents the maximal amount of useful energy (work) that the system can perform in the reaction at constant temperature and pressure.

In closed and open systems, the driving force of chemical

reactions or physical changes is the free energy change ΔG.

The Gibbs free energy G of a system is the energy that is available to do useful work as the result of chemical or physical change at constant temperature and pressure.

The free energy change ΔG (= G2 – G1) is defined as

G = H – T S

useful work heat lost or absorbed dueto entropy change

enthalpy change(reaction heat)

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G the criterion of process feasibility

G < 0 exergonic reaction prone to proceed spontaneously G > 0 endergonic reaction that cannot proceed spontaneously under given circumstances

(the reverse reaction is spontaneous) G = 0 the system is at the equilibrium state

There is no relation between ΔG and the velocity of a reaction !!

H the heat of reaction H < 0 exothermic reaction H > 0 endothermic reaction

S the entropy change S > 0 the final state is very probable S < 0 a very low probability of the final state

The meaning of thermodynamic functions

T S the product (the entropic member) is critically dependent on the temperature T

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– the entropy of the system increases and heat is released,– the chemical change is endothermic but accompanied

with a marked entropy increase, and/or– the change is highly exothermic in spite of it is accompanied

with an entropy decrease.

Spontaneous chemical changes take place In closed systems when

Reactions can occur spontaneously (i.e. without any continuing outside influence) only if they are exergonic –only if the free energy change G is of negative value.

ΔS –ΔS ΔH ΔG = ΔH – TΔSpositive(decompositions)

negative negative(exothermic)

always negative; the reaction isspontaneous, practically irreversible

positive(endothermic)

as far as TΔS > ΔH (at higher temperatures),the reaction becomes spontaneous (morefavourable)

negative(syntheses)

positive negative(exothermic)

as far as TΔS < ΔH (at lower temperatures),the reaction becomes more favourable

positive(endothermic)

positive at all temperatures; the forwardreaction cannot be spontaneous(the reverse reaction is always spontaneous)

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This state is reached in spontaneous chemical reactions by means of – the evolution or absorption of heat (ΔH),

– the changes in entropy (more simple products),resulting in the changes in concentrations of the substances in the system so as to comply with the value of the

equilibrium constant K.

The general tendency of any spontaneous process isto reach an equilibrium state – a state of the most thermodynamic stability.

The more far-apart are the concentrations of participantsfrom the equilibrium concentrations, the higher is the ΔG.

At constant temperature and pressure, a closed system atthe equilibrium state has its minimum of Gibbs free energy,at equilibrium the free energy change ΔG = 0 .

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ΔG is a measure of disagreement between the initialconcentrations of reactants and products of the reactionand their equilibrium concentrations.

The expression takes the same form as the equilibrium constant but is used for a initial state, not for a reaction at equilibrium.

The initial non-equilibrium concentrations of the substancestaking part in reaction a A + b B c C + d D are usedto calculate the reaction quotient Q :

[A]ai [B]b

i

[C]ci [D]d

iQ =

The equilibrium state is defined as K =[A]a

eq [B]beq

[C]ceq [D]d

eq

The value of Q indicates what changes will occur in reaching equilibrium:When Q < K , the reaction has a chance to proceed in the forward direction.When Q > K , the reaction has a chance to proceed in the reverse direction.

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betweenthe system that exists at the beginning of the processin its standard state (the reaction quotient Q = 1),

i.e. all reactants, both reactants and products are of unit activity, in aqueous solution their concentration c = 1 mol l–1

(if H+ is a reactant, then also [H+] = 1, pH = 0), at specified temperature (usually 25 °C equal to 298 K), and atmospheric pressure 101.3 kPa,

and the reaching the state with a minimal G value,that is the equilibrium state of the system in which the reactants and products has reached the concentrations corresponding with the equilibrium constant K.

Standard Gibbs free energy change ΔG°for a reversible process represents the free energy change

(In biological systems, the standard state is defined by pH = 7,0 ;then the free energy changes are marked as ΔG°´.)

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ΔG = ΔGº + RT ln [A]a

i [B]bi

[C]ci [D]d

i

The ΔG of a reaction depends on the particular kind of reaction (expressed by the ΔGº term) and the initial concentrations of reactants and products (expressed by the second term equal to Q).

a A + b B c C + d DThe relation between free energy and equilibriumfor any reaction (here the type isused) is given by the mathematical expression

If the equilibrium concentrations are put in as initial ones, the system is in its equilibrium state, G = 0 :

0 = G + RT ln K and G = – RT ln K

The relationship is sometimes written in the form G = RT ln K + RT ln Q

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If the reaction starts in the standard state (all concentrations [A], [B], [C], and [D] equal 1 mol l–1), the second term equals zeroso that the definition of ΔG° is obtained:

G = G + RT ln 1 = G

Values of G are very important characteristics of chemicalreactions, but they should be never overemphasized.

Even though the value of G is negative, the spontaneousreaction could proceed in the reverse direction (positive ΔGvalue) due to the high reaction quotient Q at high initialconcentration of the reaction products.

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Transformation of energy in living organisms

Living organisms are open systems that have to receivepermanently nutrients – compounds of high enthalpy(energy) and low entropy (due to their complex structure).

Nutrients are transformed into waste metabolites of lowenthalpy and high entropy (simplified structures).

The part of free energy gained by exergonic breakdown ofnutrients drives endergonic reactions and processes(synthesis of complex molecules, performance of mechanicalor osmotic work, etc.).

The remaining part of acquired energy is released as heatinto the surroundings.

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Endergonic reaction cannot proceed spontaneously,but these thermodynamically unfavourable reactions are driven by exergonic reactions to which they are coupled.

Coupling occurs because the two reactions share a common reactant or intermediate.

Example:

The overall net free energy change is negative (ΔGº´ = – 13.4 kJ mol–1), the conversion of malate to aspartate is exergonic.

MalateFumarate

H2ONH3

AspartateΔGº´1 = + 2 kJ mol–1

ΔGº´2 = – 15.4 kJ mol–1

Energetic coupling in open systems

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ATP + H2O ADP + Pi G°´ (at pH 7) = – 30.5 kJ mol–1

O

OH OH

2

O

O

CHOPOP

O

O

O ~ P

O

O

O ~

+ H+H

N

N

N

N

NH2

ATP

+ P O

O

O

HO2O

O

OH OH

N

N

N

N

NH2

2

ADP

P

O

O

O CHOP

O

O

O~

Adenosine triphosphate (ATP)

is a high-energy compound that serves as the "universal currency" of free energy in biological systems. ATP hydrolysis drives metabolism

by shifting the equilibrium of coupled reactions.

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The reaction which is used to drive endergonic ones is very oft the hydrolysis of ATP.

Example:

Glucose Glucose 6-phosphate

ATP ADP

Go´ = + 13.8 kJ mol–1

Go´ = – 30.5 kJ mol–1

= – 16.7 kJ mol–1

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Examples of high-energy phosphatesand ΔG´ of the hydrolysis

– 30.5

– 62

– 50

– 52

– 43

acid anhydride

ester

mixed acid anhydride*

mixed acid anhydride*

amid

ATP

Phosphoenolpyruvate

1,3-Bisphosphoglycerate

Carbamoyl phosphate

Creatine phosphate

ΔG ´kJ mol–1Phosphate derivative High-energy phosphate

* acyl phosphate

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Photosyntheticautotrophs Heterotrophs

CO2

H2O

O2

Nutrients rich in H

hν

4 H4 H+

O2 2 O2–

CO2Biological oxidations(dehydrogenations)

Decarboxylations

Reducing equivalents(reducing power)

4 e–2 H2O

Nutrients rich in H

Heterotrophs:

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Fatty acids of fats are a more efficient fuel source than saccharidessuch as glucose because the carbon in fatty acids is more reduced

Most of the Gibbs´ free energy in the body originates in the exergonicsynthesis of water (2H2 + O2 2H2O, 25 °C): ΔG° = – 474.3 kJ mol–1

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A steady state of an open system

is a dynamic state of an open system which receivesand gives off, within a given interval, the same amountof substances and energy so that the concentration ofintermediates in the system remains unchanged.

Nutrients richin hydrogen

Oxygen

Water

Heat and work

Low-energymetabolites