Medical Chemistry Lecture 3 2007 (J.S.) Kinetics of chemical reactions Chemical equilibrium Energy in chemical reactions Free Gibbs energy – the driving force of chemical reactions
The fundamental terms in reaction kinetics Kinetics 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. ] S [ t – v 1 ν ] P [ t 1 ν v = c – t Because , velocity is expressed in mol × l –1 × s –1
where k is the kinetic constant that includes the specific reaction features as well as the temperature term ( k = A × e –Ea I R T ) . Due to decreasing concentrations of reactants, there must be always a gradual decrease of reaction velocity in closed systems 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. 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
Progress curves ( kinetic curves ) The progress - the time course of a reaction - is shown by a plot of the concentration of any of the substrates or products against time. The instantaneous velocity v x at any particular time t x 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 v t = v 0 e – k t [S] 0 – initial concentration of S, v 0 – 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] . At equilibrium the net reaction velocity is zero. [ S ] t x tg α = d [S] / d t = v x α t x [ P ] t [ S ] t (equilibrium)
First-order reactions are most commonly decomposition reactions, radioactive decay, isomerization and rearrangements, and simple enzyme-catalyzed reactions 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 t ½ of a first-order reaction is the time it takes for one-half of a reactant to undergo a reaction. The half-life of a first-order reaction is independent of the concentration of the reactant and equals t ½ = 0,69 / k . [S] 0 t [S] 0 /2 [S] 0 /4 t ½ 2 t ½
Second- and higher-order reactions will not be discussed in this course. Zero-order reactions 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 is controlled by other factors than by collisions of the reactants involved. In enzyme-catalyzed reactions , the velocity depends on the concentration of the enzyme-substrate complex. If the substrate concentration is higher than required for the full enzyme saturation, the reaction is zero order for some time . However, after the concentration decreases and the enzyme is not fully saturated, the reaction becomes first- or higher-order. [ S ] t Zero-order kinetics First- or higher-order kinetics
If v 1 = v 2 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 then apparently stop and leave considerable amounts of unaffected reactants. A dynamic, chemical equilibrium is reached because the velocities 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 formation of the equilibrium between the starting reactants and the reaction products. The forward reaction rate v 1 = k 1 [A] m [B] n The reverse reaction rate v 2 = k 2 [C] p [D] q Reversible reaction m A + n B p C + q D v 1 v 2 k 1 k 2 K c =
The law of chemical equilibrium (Guldberg and Waage, 1867) When a closed system is at equilibrium, it will remain in this state indefinitely unless the equilibrium is affected in 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 reactants K ≈ 1 – the reaction is "perfectly reversible“ Catalysts do not change the value of K , they cause a system to reach equilibrium more quickly. For any reversible reaction at chemical equilibrium and particular temperature, there exist a fixed ratio among concentrations of products and reactants expressed as the equilibrium constant K .
External factors upsetting equilibria Changes in equilibrium concentrations by adding more of the reactants or by removing of some of the products change the reaction rates: the rates of the forward and reverse reactions will continue to change until equilibrium that corresponds to the value of equilibrium 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 temperature change the value of the constant K : An increase in temperature favours the endothermic reaction (which may be either the forward or the reverse reaction), a decrease favours the exothermic reaction. Changes in pressure cause significant changes in equilibria only where the number of moles of gaseous products and reactants differ. An increase in pressure shifts an equilibrium in the direction that produces the smaller number of molecules in the gas phase. The value of the constant K remains unchanged .
The general principle that underlies all changes in equilibria is Le Chatelier´s principle: If a system in equilibrium is subjected to a change in concentration, temperature, and pressure, the system will react in a way that tends to relieve the change.
Energy in chemical reactions The driving force of reactions
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 is a consequence of bonds cleavage and formation. System is a portion of universe under study, surroundings is everything that is not part of a system under study. Insulated systems – without any communication with their surroundings (no exchange of matter nor energy) Closed systems – can release or absorb energy from the surroundings but no exchange of matter is possible. Open systems exchange energy, matter, even information) with the surroundings.
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 Δ U can be both measured and calculated. It is the amount of energy exchanged with the surroundings during a chemical or physical change of the system. U = U final – U initial or U = U 2 – U 1 U > 0 an increase in the internal energy of the system U < 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.
The first law of thermodynamics U = q + w work heat Heat lost by a system or work done by a system on the surroundings are given negative values. Although work can be transformed completely into heat, it does not follow that heat can be transformed completely to work. Then heat is taken as a less utilizable form of energy . The energy of the insulated system is constant. Energy can be converted to one form to another, but cannot be destroyed. In the interaction between a closed system and its surroundings, the internal energy change of the system equals the heat exchanged by the system plus the work done on or by the system.
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 Δ V . Chemical reactions realized at constant external pressure , most often atmospheric pressure, are very common. In those reactions, 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 the contribution of p Δ V is negligable; then H = U
The enthalpy change Δ H is equal to the heat of reaction . It expresses the difference in bond energy of reaction products 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 Δ H ° or simply Δ H ° . Example: H 2 ( g ) + ½O 2 ( g ) H 2 O (l ) H ° = 286 kJ mol 1 the reaction is strongly exothermic
The standard state of any substance is the physical state at which it is most stable at atmospheric pressure (101.3 kPa) and a specified temperature. The usual specified temperature is 298 K (25 °C , roughly room temperature). For some specific processes, the standard enthalpy change Δ H ° is named specifically, e.g. the standard enthalpy change of (or heat of) formation Δ H ° f (of a substance from elements), combustion Δ H ° c (substance + oxygen( g ) -> combustion products), neutralization Δ H ° neutralization (acid + base -> salt( aq ) + H 2 O( l ) ), solution Δ H ° soln (1 mol solute + n mol solvent -> 1 mol solute in solvent). Δ H of a reaction is the same whether the reaction takes place in one step or several steps (Hess´s law for combining Δ H values). Δ H for a reaction in one direction is equal in magnitude to Δ H for the reaction in the reverse direction, but is opposite in sign .
Animals use the energy released by the oxidative breakdown of nutrients to H 2 O and CO 2 (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 H 2 O, CO 2 , and N 2 in a calorimeter, 17 kJ / g (4.1 kcal / g) in human bodies (catabolism to H 2 O, CO 2 , and urea CO(NH 2 ) 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.
Spontaneous chemical reactions or physical changes, defined better as " thermodynamically favourable ", are those that can happen without any continuing outside influence. In insulated systems only such processes can proceed which 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 = Q rev / T . A change in entropy is Δ S = S 2 – S 1 . The opposite to entropy is information (a negative entropy), a measure of order or organization. The second law of thermodynamics Every spontaneous chemical and physical change increases the entropy of the universe as a whole.
If Δ S system decreases ( Δ S of a negative value), this change must be accompanied by a simultaneous and larger increase in Δ S surroundings , because the condition for spontaneous process expressed by the second law of thermodynamics is Δ S universe = Δ S system + Δ S surroundings > 0 In contrast to insulated systems, in spontaneous processes in closed and open systems the entropy can either increase or decrease . S surroundings is proportional to the heat that the system under study releases into the surroundings or absorbs from it. Because also the enthalpy change Δ H of the system (reaction heat) must be taken into account , the mere entropy change Δ S system is not the best criterion of the spontaneity of a given chemical reaction in closed and open systems.. Increase in entropy (Δ S of a positive value) is the driving force of processes in the universe as a whole and also in insulated systems under study.
The entropy change of a system Δ S system 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)
If Δ G is negative , the reaction can proceed spontaneously and the value of Δ G represents the maximal amount of useful energy (work) that the system can perform in the reaction at constant temperature and pressure. 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 Δ G (= G 2 – G 1 ) is defined as In closed and open systems , the driving force of chemical reactions or physical changes is the free energy change Δ G . G = H – T S useful work heat lost or absorbed due to entropy change enthalpy change (reaction heat)
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 Δ G 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
– 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 . positive at all temperatures; the forward reaction cannot be spontaneous (the reverse re a ction is always spontaneous) positive (endothermic) as far as T Δ S < Δ H (at lower temperatures), the reaction becomes more favourable negative (exothermic) positive negative (syntheses) as far as T Δ S > Δ H (at higher temperatures), the reaction becomes spontaneous (more favourable) positive (endothermic) always negative; the reaction is spontaneous, practically irreversible negative (exothermic) negative positive (decompositions) Δ G = Δ H – T Δ S Δ H – Δ S Δ S
This state is reached in spontaneous chemical reactions by means of – the evolution or absorption of heat ( Δ H ) , – 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 is to reach an equilibrium state – a state of the most thermodynamic stability. The more far-apart are the concentrations of participants from the equilibrium concentrations, the higher is the Δ G. At constant temperature and pressure, a closed system at the equilibrium state has its minimum of Gibbs free energy , at equilibrium the free energy change Δ G = 0 .
Δ G is a measure of disagreement between the initial concentrations of reactants and products of the reaction and 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 substances taking part in reaction a A + b B c C + d D are used to calculate the reaction quotient Q : The equilibrium state is defined as 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. [A] a i [B] b i [C ] c i [D] d i Q = K = [A] a eq [B] b eq [C ] c eq [D] d eq
between the system that exists at the beginning of the process in 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 Δ G ° 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 Δ G °´ .)
The Δ G of a reaction depends on the particular kind of reaction (expressed by the Δ G º term) and the initial concentrations of reactants and products (expressed by the second term equal to Q ). 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 Δ G = Δ G º + RT ln [A] a i [B] b i [C ] c i [D] d i a A + b B c C + d D The relation between free energy and equilibrium for any reaction (here the type is used) is given by the mathematical expression
If the reaction starts in the standard state (all concentrations [A], [B], [C], and [D] equal 1 mol l –1 ), the second term equals zero so that the definition of Δ G ° is obtained: G = G + RT ln 1 = G Values of G are very important characteristics of chemical reactions, but they should be never overemphasized. Even though the value of G is negative, the spontaneous reaction could proceed in the reverse direction (positive Δ G value) due to the high reaction quotient Q at high initial concentration of the reaction products.
Transformation of energy in living organisms Living organisms are open systems that have to receive permanently nutrients – compounds of high enthalpy (energy) and low entropy (due to their complex structure). Nutrients are transformed into waste metabolites of low enthalpy and high entropy (simplified structures). The part of free energy gained by exergonic breakdown of nutrients drives endergonic reactions and processes (synthesis of complex molecules, performance of mechanical or osmotic work, etc.). The remaining part of acquired energy is released as heat into the surroundings.
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 ( Δ G º´ = – 13.4 kJ mol –1 ), the conversion of malate to aspartate is exergonic. Energetic coupling in open systems Malate Fumarate H 2 O NH 3 Aspartate Δ G º´ 1 = + 2 kJ mol –1 Δ G º´ 2 = – 15.4 kJ mol –1
ATP + H 2 O ADP + Pi G °´ (at pH 7) = – 30.5 kJ mol –1 O O H O H 2 O O C H O P O P O O O ~ P O O O ~ + H + H N N N N N H 2 ATP + P O O O H O 2 O O O H O H N N N N N H 2 2 ADP P O O O C H O P 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 .
The reaction which is used to drive endergonic ones is very oft the hydrolysis of ATP. Example: Glucose Glucose 6-phosphate ATP ADP G o ´ = + 13.8 kJ mol –1 G o ´ = – 30.5 kJ mol –1 = – 16.7 kJ mol –1
Examples of high-energy phosphates and Δ G ´ 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 Δ G ´ kJ mol –1 Phosphate derivative High-energy phosphate * acyl phosphate
Photosynthetic autotrophs Heterotrophs CO 2 H 2 O O 2 Nutrients rich in H hν 4 H 4 H + O 2 2 O 2– CO 2 Biological oxidations (dehydrogenations) Decarboxylations Reducing equivalents (reducing power) 4 e – 2 H 2 O Nutrients rich in H Heterotrophs:
Most of the Gibbs´ free energy in the body originates in the exergonic synthesis of water (2H 2 + O 2 2H 2 O, 25 °C ) : Δ G ° = – 474.3 kJ mol –1 Fatty acids of fats are a more efficient fuel source than saccharides such as glucose because the carbon in fatty acids is more reduced
A steady state of an open system is a dynamic state of an open system which receives and gives off, within a given interval, the same amount of substances and energy so that the concentration of intermediates in the system remains unchanged . Nutrients rich in hydrogen Oxygen Water Heat and work Low-energy metabolites