Thermodynamics Units 15-18 PDF

Units 15 10 17 18 Thermodynamics Prof. Tamas Janaky  Chemical reaction — energy change Physical and chemical changes usually involve the use or production of energy. The energy change involved in the combustion of fuels like kerosene, coal, wood, natural...

Units 15 10 17 18 Thermodynamics Prof. Tamas Janaky  Chemical reaction — energy change Physical and chemical changes usually involve the use or production of energy. The energy change involved in the combustion of fuels like kerosene, coal, wood, natural gas, etc., takes the form of heat and light. Electrical energy is obtained from chemical reactions in batteries. The formation of glucose, C6H12O6 by the process of photosynthesis requires the absorption of light energy from the sun.  Types of energy ELECTRIC, ELECTROMAGNETIC Any object may possess multiple types of energy.  Conversion of energy: transfer and transform Energy can be transferred (move from one location to another) and it can change (transform) from one type to another – but the total amount of energy is always conserved, i.e. it stays the same (law of conservation of energy). The Sun transforms Our bodies An electric fan Lightning converts nuclear energy into convert chemical transforms electrical energy heat and light energy in our food electrical energy into light, heat energy into mechanical into kinetic and sound energy energy for us to energy move  Thermodynamics Thermodynamics is one branch of knowledge that all of those who deals with natural science must have a grasp of. Thermodynamics can be considered as a ‘system level’ science, that is it deals with descriptions of the whole system and not with interactions at the level of individual particles. Thermodynamics puts before us some fundamental laws which are universal in nature (and hence applicable to fields across disciplines).  Thermodynamics Thermodynamics is the study of the relations between heat, work, temperature, and energy. The laws of thermodynamics describe how the energy in a system changes and whether the system can perform useful work on its surroundings.  Chemical thermodynamics Chemical thermodynamics deals with the laws of energy changes accompanying chemical reactions, as well as the changes of physical states of the chemical species. Among the variety of energy changes, heat energy (heat absorption or heat release) stands out, which usually manifests itself in a change in temperature. In addition to energy changes, chemical thermo- dynamics also deals with the predictions of the potential, direction and equilibrium of chemical processes.  Biological thermodynamics Thermodynamics can provide a useful way of thinking about biological processes and is indispensable when considering molecular and cellular mechanisms. Thermodynamics of biological systems explains the nature and general laws of thermodynamic processes occurring in living organisms that convert the energy of the Sun and food into other types of energy. The nonequilibrium thermodynamic state of living organisms is ensured by the continuous alternation of cycles of controlled biochemical reactions, accompanied by the release and absorption of energy. Definitions important to thermodynamics System: is region where we focus our attention; the part of the universe that is of interest, separated from the surroundings by a boundary. Surroundings: is everything in the universe that is not part of the system. Universe = System + Surroundings  Types of system Open system – can exchange both energy and matter with the surroundings Closed system – exchanges energy but NOT matter with the surroundings Isolated system – neither energy nor matter can be exchanged with the surroundings (a closed vacuum ‘thermos’ flask can be considered as isolated). Fundamental terms in thermodynamics Energy (E) Work (w) Heat (q) Temperature (T)  Energy Energy is defined as capacity (ability) of a system to do work (to move matter) and supply heat. Etotal = Ekinetic + Epotential + Einternal macroscopic forms of microscopic forms of energy: energy: whole system possesses relate to the system on a with respect to a fixed molecular or atomic level external reference v Einternal = U Ekin gas molecules Epot container  Internal energy Etotal = Ekinetic + Epotential + Einternal Internal energy is the sum of the kinetic energies and potential energies (all the various forms of microscopic energies) of all the particles in the system. The total internal energy of a sample of matter depends on the temperature, the type of particles, and the number of particles in the sample.  Internal energy Kinetic energy is the energy of motion at particle level: translational, rotational, vibrational energies Potential energy: energy due to the interactions between particles. It includes intermolecular forces, chemical bonds, and other interactions. (Chemical energy is a form of potential energy stored in the bonds between atoms and molecules. This energy is released or absorbed during chemical reactions when these bonds are broken or formed.)  Law of conservation of energy All forms of energy can be transformed into all other forms of energy through one or more steps, but cannot be created or destroyed. During most processes, energy is exchanged between the system and the surroundings. If the system loses a certain amount of energy, than same amount of energy is gained by the surroundings. If the system gains a certain amount of energy, that energy is supplied by the surroundings, that is, the energy of the universe is constant. Euniverse = Esystem + Esurroundings = 0  Units of Energy The SI unit of energy is the joule (J). 1 J = 1 kgm2/s2 A calorie (cal) is the quantity of energy required to raise the temperature of 1.00 g of pure liquid water by 1 degree Celsius. Calorie (nutritional) is unit of energy that a food or drink provides. 1 kilocalorie (kcal) = 1000 cal = 1 Calorie One cal is exactly 4.184 J 1 cal = 4.184 J = 4.184 kgm2/s2  Energy flow to/from a system The internal energy of the system (at given state variables) cannot be determined, but its change (E) can be measured or calculated. E = Efinal - Einitial When a chemical system changes from reactants to products, the internal energy of the system changes: E = Eproducts - Ereactants Energy is an extensive property. (Extensive properties depend on the mass of a system (m, V, U, H, S) while intensive properties are independent (T, d).  Internal energy is a state function Internal energy is a state function: its value depend on the exact state the system (n, p, V, T...). State functions: their changes do not depend on the path, but only depend on the initial and final states. ΔE = Efinal – Einitial Other state functions: enthalpy, entropy, Gibbs free energy. Work and heat are not state functions (path functions)!  State functions Afinal Afinal A: altitude A = Af - Ai Ainitial solid gas liquid  First law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy. It states that energy can be converted from one form to another, but it cannot be created nor destroyed. In all closed system the change in the internal energy (E) of the system equals the sum of heat (q) and work (w). E = q + w This exchange can occur in only two ways: Heat (q) may be transferred to (+) or from (–) the system. The system may do work (w) on its surroundings (–) or have work done on it (+).  Work (w) When work occurs, something moves or changes. During these changes, energy moves from place to place or changes form. In chemistry there are two main types of work that are of interest: Electrical Mechanical work by expanding gases, the pressure-volume (expansion) work.  ΔE = q + w Pressure-volume (expansion) work Chemical reactions sometimes accompanied by formation of gas or phase-transition, where the volume changes. At constant pressure: w = –pV If V > 0 w0 If V = 0 w=0  E = q closed  ΔE = q + w Heat (q) Heat: the energy that flows into or out of a system because of a difference in temperature between the thermodynamic system and its surroundings until thermal equilibrium. Heat always flows from a hotter to a colder object until they have the same temperature. q > 0 heat transferred INTO a system q < 0 heat transferred OUT of a system Heat can be converted to and from other forms of energy.  Temperature Temperature (T ) is an intensive parameter which describes the state of a system. Energy in a substance is stored in the randomized motion of the molecules. This stored energy is called heat. Temperature is a measure of the random motions or heat in a substance.. Temperature is "a measure of the average kinetic energy of the particles”. The faster the atoms or molecules move, the higher the temperature. Unit: Kelvin (K)  Enthalpy The enthalpy (heat content) of reaction equals the heat evolved/absorbed in a reaction (heat of reaction) at constant pressure (qp):  H = qp H is a state function and an extensive property. H = Hfinal - Hinitial = qp Signs on ΔH + heat is taken in by system ΔH > 0 Endothermic – heat is given off by system ΔH < 0 Exothermic  Heat of reaction The total amount of heat that is evolved or absorbed by a system in a chemical reaction (qp). Exothermic reaction energy is produced in reaction 2 Al(s) + Fe2O3 (s)  heat evolved, flows out of system Al2O3 (s) + 2 Fe(s) –1000 kJ (q < 0, H negative) the system warms up Endothermic reaction energy is consumed by the reaction Ba(OH)2. 8H2O(s) + 2 NH4SCN(s)  heat absorbed, flows into the system Ba(SCN)2(aq) + 2 NH3(g) + 10 H2O(l) (q > 0, H positive) + 100 kJ the system cools down Heat produced or consumed in a chemical reaction can be measured by calorimetry.  Enthalpies of reaction The energy changes in a chemical reaction are a result of energy changes in breaking and forming of bonds. The enthalpy change that accompanies a reaction is called: heat of reaction Hrxn = S Hproducts – SHreactants final initial Thermochemical equation: exothermic 2H2(g) + O2(g) 2H2O(g) H = – 483.6 kJ Balanced equation H associated with the reaction Coefficients in balanced equation = no. of moles of reactant/product producing associated H (extensive)  Standard enthalpy changes (Ho) The characteristic data of chemical reactions is the enthalpy change, but it is not necessary to know the absolute enthalpy value of the participating substances. However, we need a reference value, a standard state, to which we can relate the enthalpy changes. The standard state of elements and compounds means the most stable physical form of the respective substance at 0.1 MPa and 298 K. Standard enthalpies (ΔH°) are enthalpy changes that occur in chemical reactions with all materials in their standard states.  Standard enthalpies of formation Standard enthalpy of formation (Hfo) is the change in enthalpy for the reaction that forms one mol of a substance from its elements in their standard states (0.1 MPa of pressure and 298 K). Units: kJ/mol The standard entahalpy of formation of elements in their most stable form eqals zero. 2H2(g) + O2(g) 2H2O(g) Hf° = – 483.6 kJ Standard enthalpies of formation (Hfo) Enthalpies of reaction under standard conditions Enthalpies of reaction can be calculated from tabulated data of standard enthalpies of formation (Hfo):  Hrxn = S n  Hf(products) ‒ S m  Hf(reagents) stoichiometric coefficients The standard enthalpy change of formation is equal to the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants.  Enthalpy of reaction in biochemistry Glucose + ATP ADP + Glucose-6-phosphate Substance Hfo (kJ/mol) ATP –2981.8 ADP –2000.2 Glucose –1267.1 Glucose-6-phosphate –2279.1 Specific conditions: 298K, 0.1 MPa, pH=7.0, cMg 0.001M and an ionic strength of 0.25 M H  = HfADP + HfG6P ‒ HfG ‒ HfATP H  = –30.4 kJ/mol  Hess’s law (low of heat summation) The total enthalpy change during a chemical reaction is independent of the number and the nature of the intermediate steps. The heat exchange is independent of the path. Reaction occurs in CH4(g) + 2O2(g) CH4(g) + 2O2(g) two steps but H is Enthalpy H =-607kJ the same. Enthalpy CO(g) + 2H2O(g)+1/2O2(g) H = -890kJ H = -283kJ CO2(g) + 2 H2O(g) CO2(g) + 2 H2O(g) Changing of enthalpy at phase transfer (physical change) Total enthalpy change from solid gas = sum of enthalpy change for solid liquid + liquid gas solid liquid Hmelt liquid gas Hvap solid gas Hsub= Hmelt+ Hvap Thank you very much for your attention! Please stay a few more minutes and answer the questions. Thermodynamics – entropy, Gibbs free energy Prof. Tamas Janaky Spontaneity One of the basic goals of chemistry is to predict whether or not a reaction will occur when substances are brought together; that is, whether the reaction is spontaneous, or not. Spontaneous processes are physical or chemical changes that occur without outside intervention. They have a definite direction. In a spontaneous process, the path between reactants and products is irreversible. The reverse process is not spontaneous. Temperature has an impact on spontaneity. Spontaneous Physical Processes spontaneous nonspontaneous X Spontaneous Physical and Chemical Processes A lump of sugar dissolves in a cup of coffee. Heat flows from a hotter object to a colder object. A gas expands in an evacuated bulb. Iron exposed to oxygen and water forms rust. Why are some processes spontaneous and others not? The spontaneity of a process may depend upon the temperature of the system. e.g. T > 0oC ice melts spontaneous at this temperature H2O (s) H2O (l) T < 0oC water freezes spontaneous at this temperature H2O (l) H2O (s) T = 0oC water and ice are in equilibrium H2O (l) H2O (s) some chemical reactions can also exhibit temperature dependent spontaneities Spontaneity and H Majority of the exothermic reactions are spontaneous because there is decrease in energy. Combustion of methane ‒ SPONTANEOUS! CH4(g) + 2O2(g) → CO2(g) + 2 H2O(g)  H = ‒890 kJ/mol Reaction of sodium with water ‒ SPONTANEOUS! 2Na(s) + H2O(l) → 2NaOH(aq) + H2(g)  H = ‒368.6 kJ/mol But! There are endothermic and spontaneous reactions! 2 N2O5(s) → 4NO2(g) + O2(g)  H = +109.5 kJ/mol SPONTANEOUS! NH4NO3(s) NH4+(aq) + NO3‒(aq)  H = +25.7 kJ/mol A process does not have to be inevitably exothermic to be spontaneous!  Spontaneity and H Any enthalpy change in a particular direction, positive or negative, cannot be the only factor to decide if a chemical reaction would take place? There must be some additional factors. CH4(g) + 2O2(g) → CO2(g) + 2 H2O(g) 2Na(s) + H2O(l) → 2NaOH(aq) + H2(g) 2 N2O5(s) → 4NO2(g) + O2(g) NH4NO3(s) NH4+(aq) + NO3‒(aq) The common factor in all these four cases of spontaneous reactions is a transition of the system from an ordered arrangement of particles to less ordered arrangement. Entropy the measure of the randomness or disorder in a system; the measure of how dispersed the energy of a system is among the different possible ways that system can contain energy more disordered  larger entropy Low entropy High entropy  Ice, at 0oC  Water, at 0oC  A diamond, at 0oC  Carbon vapor at 1,000,000K A protein molecule  The same protein molecule in its regular native state in unfolded state  A bank manager’s desk  A professor’s desk Enthropy and disorder Order is less probable than disorder (statistically there are many more ways of having disorder than there are of having order). work work work Work is generally required to produce order out of disorder, so energy must be used to produce a highly ordered state. Entropy is a state function S = Sfinal - Sinitial when heat (q) transfers at temperature T, the system's entropy changes by S = q/T S = H/T (R. Clausius, 1864) Unit: J/K-1mol-1 Entropy is an extensive property.  Processes where entropy increases (S > 0) heat heat heat heat Ssolid < Sliquid 0 process is spontaneous If Suniv = 0 process is at equilibrium Thus Suniv is continually increasing! Suniverse must increase during a spontaneous process, even if Ssystem decreases. Change in entropy as a function of temperature Entropy is directly related to the heat added to the system and, as such, is related to the extent of molecular movement. Decrease Increase inintemperature temperature  decrease inthermal increase in thermalenergy energy  decrease intranslational, increase in translational, vibrational and rotational energy  decrease inentropy increase in entropy As the temp keeps decreasing, these motions “shut down” reaches a point of perfect order. S 0 as T 0 Third law of thermodynamics The entropy of a pure crystalline substance at T=0 (absolute zero) is zero. W=1 W>1 Perfect crystal at 0 K Crystal deforms at T > 0 K (L. Boltzmann, 1877) W: the number of real microstates statistical approach S = kB lnW (probability) kB: Boltzmann constant relationship between entropy and the number of ways the atoms or molecules of a thermodynamic system can be arranged Standard molar entropy (S o) Standard molar entropy (S°) is defined as the entropy gained when converting one mole of a substance from a perfect crystal at 0K to 0.1 MPa and 298K. Entropy change for a reaction The entropy usually increases in the following situations: A reaction in which a molecule is broken into two or more smaller molecules. A reaction in which there is an increase in moles of gases. A process in which a solid changes to a liquid or a liquid changes to a gas. m1 R1(a) + m2 R2(a) + … → n1P1(a) + n2P2(a) + …  S rxn =  n  S(products) ‒  m  S(reagents) stoichiometric coefficients Predicting spontaneity of reactions Rx’s that have a large and negative H tend to occur spontaneously. Spontaneous reactions result in an increase in entropy in the universe. Spontaneity depends on enthalpy, entropy, and temperature. Gibbs Free Energy Provides a way to predict the spontaneity of a reaction using a combination of enthalpy and entropy of a reaction.  Gibbs free energy (G) Unifying the first and second law of thermodynamics, the Gibbs free energy G can be defined (provided, p and T are constant). G = H ‒ TS G = H – TS G is also a state function and an extensive quantity. Gibbs free energy is the maximum work that may be performed by a system at a constant temperature and pressure. (J.W. Gibbs, 1878) Spontaneous reactions (usually) can be used to obtain useful work: wmax = –G Spontaneity and G The change in the Gibbs free energy (G) allows us to predict whether a process is spontaneous or not (thermodynamically possible or not). Grxn =  Gproducts – Greactants G < 0  spontaneous in forward direction (exergonic process) G > 0  non-spontaneous in forward direction spontaneous in reverse direction (endergonic process) G = 0  at equilibrium Standard Gibbs free energy The standard free-energy change, ∆G °, is the free-energy change that occurs when reactants in their standard states are converted to products in their standard states.  G° =  H° – T  S°  G° is the free energy change for reactants and products at 298 K and 0.1 MPa. Standard states: Gas ‒ 0.1 MPa Solid ‒ pure substance Solution ‒ concentration = 1 mol/dm3 Standard Gibbs free energy of formation (Gfº) Gfº is the free-energy change that occurs when 1 mol of substance is formed from its elements in their reference forms (usually the stablest states) at 0.1 MPa and at 298K. Gfo = 0 kJ/mol for elements in their standard states  Grxn =  n  G(products) ‒  m  G(reagents)  Gibbs Free Energy and Temperature How is change in free energy affected by change in temperature? G o = H – TS o o Ho So Go – + – Exergonic rxn, spontaneous at all temp. + – + Endergonic rxn, nonspontaneous at all temp Endothermic rxn, spontaneous if + + +/ – T > H/S; higher T is favourable. Exothermic rxn, spontaneous if – – +/ – T < H/S; lower T is favourable. Using the equation we can calculate the temperature at which a reaction changes from nonspontaneous to spontaneous under standard conditions. At this temperature, ∆G° equals zero.  Gibbs Free Energy and Temperature NH4NO3(s) → NH4+(aq) + NO3–(aq) ∆H° = +28 kJ/mol ∆S° = +109 J/K mol  G° =  H° – T  S° ∆G° = 28 – 298(+0.109) = –4.5 kJ/mol at 298K spontenous reaction in equilibrium:  G° = 0 =  H° – T  S°  H° = T  S° T = H°/ S° above T = 28 / 0.109 = 256.9K the reaction is spontaneous Free energy and equilibrium aA + bB cC + dD Keq = ([C]c [D]d/[A]a[B]b) G° and the chemical equilibrium For a reaction at conditions which are not standard state, the following equation has been derived: G = Go + RT ln Q Q: reaction quotient Q= (cC×cD)/(cA×cB) cA, cB … non-equilibrium concentrations at equilibrium G = 0; Q = K Then 0 = Go + RT ln K Go = – RT ln K –Go/RT K=e The first part of the lecture is over. Electrochemistry Prof. Tamas Janaky  Electrochemisty Electrochemistry deals with chemical reactions that produce electricity (electric current) and the changes associated with the passage of electrical current through matter.  Electrochemistry  Importance of electrochemistry use a mobile phone use a laptop starting your car, electric car fuel cell electric vehicles corrosion of iron preparation of important industrial materials …  Electrochemisty  Oxidation, reduction, redox reaction  Oxidation number  Electrochemical cell  Voltaic or galvanic cell  Cell notation  Emf  Electrode and cell potential  Standard electrode potential  Free energy and cell potential  Nernst equation  Application of emf measurement  Oxidation-reduction  Traditionally oxidation was regarded as a chemical reaction when oxygen was added to a substance e.g. Mg(s) + ½O2(g) → MgO(s)  Whilst reduction was when a metal was produced from its ore and this usually involved removing oxygen, or addition of hydrogen. e.g. HgO(s) → Hg(l) + ½O2(g) ZnO(s) + H2(g) → Zn(s) + H2O(l) However, it was soon recognised that there were many similar reactions that did not involve oxygen or hydrogen. Oxidation-reduction or redox reactions The chemical changes that occur when electrons are transferred between reactants are called oxidation – reduction (or redox) reactions.  Oxidation-Reduction Reactions Oxidation = loss of electrons (LEO: loss of electrons = oxidation) (OIL: oxidation is loss of electron) Reduction = gain of electrons (GER: gain of electrons = reduction) (RIG: reduction is gain of electron) Reduction (gaining electrons) can’t happen without an oxidation to provide the electrons. Oxidation and reduction always go hand in hand.  Terminology for Redox Reactions Oxidation = loss of electrons An oxidizing agent is a substance that causes oxidation, taking electrons from the species being oxidized. Reduction = gain of electrons A reducing agent is a substance that causes reduction, giving electrons to the substance being reduced. Oxidation-reduction  Redox Reactions  Oxidation (electron loss) always accompanies reduction (electron gain). oxidation Zn( s )  Cu 2 ( aq) Zn 2 ( aq)  Cu( s ) reduction  The number of electrons gained by the oxidizing agent always equals the number of electrons lost by the reducing agent. Loss of 2 e- Zn( s )  Cu 2 ( aq) Zn 2 ( aq)  Cu( s ) Gain of 2 e-  Concepts in Oxidation-Reduction We never ”see” electrons in the final balanced chemical equation: 2 2 Zn( s )  Cu ( aq ) Zn ( aq )  Cu( s ) Zn → Zn2+ + 2e¯ oxidation half reaction (copper ion is the oxidizing agent) Cu2+ + 2e¯ → Cu reduction half reaction (zinc is the reducing agent)  Oxidation number (oxidation state) The charges on the species in a redox reaction are called oxidation numbers (or oxidation states), since they tell how many electrons have been gained or lost from the neutral state of the elements. The oxidation number is the ionic charge on a monatomic ion, or the charge of an atom (in a covalently bonded species) would have if all the bonding electrons belonged to the more electro- negative atom in the group. +1 –1 +4 –2 NaCl SO2  Oxidation numbers  Atoms in elementary form is zero (since neutral)  Ions equal to charge of the ion  Group 1 metals +1  Group 2 metals +2  Nonmetals O –2 (peroxides –1 & superoxides –½) H +1 (when bonded to other nonmetals) –1 (when bonded to metals: hydrides) F –1 X –1 except when combined with oxygen Sum of the oxidation numbers equals zero or the charge of the polyatomic ion.  Oxidation numbers After a redox reaction the oxidized substance has a higher (more positive, less negative) oxidation number, while the reduced one has a lower (less positive, more negative) one. 0 +2 +2 0 2 2 Zn( s )  Cu ( aq ) Zn ( aq )  Cu( s )  Balancing redox reactions What species is being oxidized (or, what is the reducing agent)? What species is being reduced (or, what is the oxidizing agent)? What species result from the oxidation and reduction? Does the reaction occur in acidic or basic solution? Methods for balancing redox reactions: Half-reaction method Oxidation number method  Balancing redox reactions – Half-reaction method I. The equation is separated to two half reactions: oxidation and reduction. The half reactions are balanced and then combined to attain the balanced equation for the overall reaction. Let’s consider the reaction of Fe2+ ions with permanganate in acidic solution. H+ Fe2+(aq) + MnO4−(aq)  Fe3+(aq) + Mn2+(aq)  Balancing redox reactions – Half-reaction method II. The oxidation half reaction: Fe2+  Fe3+ To balance the charge, we must add 1 electron to the right side. Fe2+  Fe3+ + 1 e−  Balancing redox reactions – Half-reaction method III. The reduction half reaction: MnO4−  Mn2+ The manganese is balanced; to balance the oxygen, we must add 4 molecules of water to the right side. MnO4−  Mn2+ + 4 H2O To balance the hydrogen, we add 8 H+ to the left side. 8 H+ + MnO4−  Mn2+ + 4 H2O To balance the charge, we add 5 e− to the left side. 5 e− + 8 H+ + MnO4−  Mn2+ + 4 H2O  Balancing redox reactions – Half-reaction method IV. Fe2+  Fe3+ + 1 e− 5 e− + 8 H+ + MnO4−  Mn2+ + 4 H2O Let’s multiply the first reaction by 5 to attain the same number of electrons on each side. 5 Fe2+  5 Fe3+ + 5 e− 5 e− + 8 H+ + MnO4−  Mn2+ + 4 H2O Now let’s add these together and substract the electrons. 5 Fe2+ + MnO4− + 8 H+  5 Fe3+ + Mn2+ + 4 H2O  Balancing redox reactions – Oxidation-number method I. The increase in oxidation number for the atoms that are oxidized must equal the absolute value of the decrease in oxidation number for the atoms that are reduced. Consider the following equation: I2 + HNO3 HIO3 + NO2 + H2O not balanced Assign the oxidation numbers. 0 +5 +5 +4 I2 + HNO3 HIO3 + NO2 + H2O  Balancing redox reactions – Oxidation-number method II. Let’s calculate the change in the oxidation numbers. 1 e– gained 0 +5 +5 +4 I2 + HNO3 HIO3 + NO2 + H2O 5 e– lost  Balancing redox reactions – Oxidation-number method III. The number of electrons lost must equal the number of electrons gained. 10 e– gained 0 +5 +5 +4 I2 + 10 HNO3 2 HIO3 + 10 NO2 + H2O 10 e– lost The remaining atoms are balanced by inspection. I2 + 10 HNO3 2 HIO3 + 10 NO2 + 4 H2O  Redox Reactions Direct Redox Reaction Indirect Redox Reaction Oxidizing and reducing A battery functions by trans- agents in direct contact. ferring electrons through an Cu(s) + 2 Ag+(aq) external wire from the reducing agent to the Cu2+(aq) + 2 Ag(s) oxidizing agent.  Oxidation-reduction oxidation Zn( s )  Cu 2 ( aq) Zn 2 ( aq)  Cu( s ) reduction Oxidation and reduction always go hand in hand. The separation of oxidation and reduction reactions in time is not possible but in space it is.  Electrochemical Cells An electrochemical cell is a system consisting of electrodes that dip into an electrolyte and in which a chemical reaction either uses or generates an electric current. voltaic, or galvanic cell is an electrochemical cell in which a spontaneous reaction generates an electric current. electrolytic cell is an electrochemical cell in which an electric current drives an otherwise nonspontaneous reaction. Alessandro Volta, 1799 Luigi Galvani, 1780  Voltaic or galvanic cell anode cathode oxidation reduction negative positive spontaneous redox reaction  Electrodes Zinc Copper  Salt bridge A salt bridge is a tube of an electrolyte (KCl, NaNO3) in gel that is connected to the two half-cells of a voltaic cell. It allows the flow of ions but prevents the mixing of the different solutions that would allow direct reaction of the cell reactants.  Notation for Voltaic Cells It is convenient to have a shorthand way of designating particular voltaic cells. Zn(s) | Zn2+ (1M) || Cu2+ (1M) | Cu(s) anode cathode Shorthand rules: Anode reaction – left; reduced form first. Cathode reaction – right; oxidized form first. Vertical line drawn between different phases (including reaction of gases at metal electrode.) Double vertical drawn where salt bridge separates two half-reactions.  Type of electrodes  Metal electrode Zn(s) | Zn 2+ (1M)  Gas electrode H+ (1M) | H2 (1 atm) | Pt(s)  Metal/precipitate electrode Ag(s) | AgCl | Cl¯  Redox electrode Pt(s) | Fe2+/Fe3+  Standard electrodes A standard electrode is an electrode in which the molarities of ions is equal to 1M and the pressure of gas is equal to 0.1MPa at 298K. Standard hydrogen electrode: H+ (1M) | H2 (0.1MPa) | Pt(s)  Electrode potentials anode cathode metal Zn metal Cu ------------ ++++++++++++ ++++++++++++++  -----------  solution Zn2+ solution Cu2+ Electrode reactions consist of an exchange of electrons or ions between species in the two phases at the metal/electrolyte boundary. The driving force of such an exchange is the difference in energy of the species (electrons or ions) in the two phases. The source of driving force is the formation of electric double layer and is proportional to the so-called electrode potential. Electric double layer Double layer potential ≡ ELECTRODE POTENTIAL  Electrode potentials  In a voltaic cell the anode is at low potential and the cathode is at higher potential. Electrons flow in an external circuit from low to higher potential.  The potential difference between two electrodes is the driving force that propels electrons from the anode (pushes the electron) to the cathode (pulls the electron).  Standard reduction potential The potential of one electrode can not be measured directly. Only the potential difference between two electrodes can be measured. We need a reference value to which the potentials of other electrodes can be compared. Reference: standard hydrogen electrode (SHE) 2 H+(aq, 1 M) + 2e-  H2(g, 0.1 MPa) E o = 0.00 V  Electromotive force (EMF) maximal potential difference between electrodes Ecell = EMF = Ecathode – Eanode Ecell > 0 so Ecathode > Eanode E°cell = standard cell potential E°cell = E°cathode – E°anode E° - standard reduction potential of each half-cell (the tendency for reduction to occur at the electrode)  Standard Electrode Potentials Ecell 0 = 0.76 V anode cathode Standard emf (E0cell) o o o Ecell= Ecathode - Eanode Zn (s) | Zn2+ (1M) || H+ (1M) | H2 (1 atm) | Pt (s) E0cell = EH 0/H 0 + – EZn 2+ 2 /Zn 0.76 V = 0 – EZn0 2+/Zn EZn0 2+/Zn = – 0.76 V Zn2+ (1 M) + 2e- Zn E0 = – 0.76 V  Standard reduction potential (E°) Standard reduction potential is the voltage associated with a reduction reaction at an electrode when all solutes are 1 M, all gases are at 0.1 MPa and the temperature is 298 K. Thank you for your attention! Please stay a few more minutes and answer the questions. Electrochemistry (continuation) Prof. Tamas Janaky  Voltaic or galvanic cell anode cathode oxidation reduction negative positive spontaneous redox reaction  Electrode potentials anode cathode metal Zn metal Cu ------------ ++++++++++++ ++++++++++++++  -----------  solution Zn2+ solution Cu2+ Electrode reactions consist of an exchange of electrons or ions between species in the two phases at the metal/electrolyte boundary. The driving force of such an exchange is the difference in energy of the species (electrons or ions) in the two phases. The source of driving force is the formation of electric double layer and is proportional to the so-called electrode potential. Electric double layer Double layer potential ≡ ELECTRODE POTENTIAL  Electrode potentials In a voltaic cell the anode is at low potential and the cathode is at higher potential. Electrons flow in an external circuit from low to higher potential. The potential difference between two electrodes is the driving force that propels electrons from the anode (pushes the electron) to the cathode (pulls the electron).  Standard potential The potential of one electrode can not be measured directly. Only the potential difference between two electrodes can be measured. We need a reference value to which the potentials of other electrodes can be compared. Reference: standard hydrogen electrode (SHE) 2 H+(aq, 1 M) + 2e-  H2(g, 0.1 MPa) E° = 0.00 V  Electromotive force (EMF) maximal potential difference between electrodes Ecell = EMF = Ecathode – Eanode Ecell > 0 so Ecathode > Eanode E°cell = standard cell potential E°cell = E°cathode – E°anode E° - standard reduction potential of each half-cell (the tendency for reduction to occur at the electrode)  Standard Electrode Potentials ° = 0.76 V Ecell anode cathode o Standard emf (E cell ) o o o E cell = Ecathode – Eanode Zn (s) | Zn2+ (1M) || H+ (1M) | H2 (1 atm) | Pt (s) o o o Ecell = EH /H + 2 – EZn2+/Zn o 0.76 V = 0 – EZn2+/Zn o EZn 2+/Zn = – 0.76 V o Zn2+ (1M) + 2e— Zn E = – 0.76 V  Standard reduction potential (E°) Standard reduction potential is the voltage associated with a reduction reaction at an electrode when all solutes are 1 M, all gases are at 0.1 MPa and the temperature is 298 K. Electromotive force  Electromotive force Zn(s) + Cu2+(aq) Zn2+(aq) + Cu(s) Zn(s) | Zn2+ (1M) || Cu2+ (1M) | Cu(s) anode cathode Zn2+(aq) + 2e— Zn(s) E°Zn = –0.76V Cu2+(aq) + 2e— Cu(s) E°Cu = 0.34V E°cell = E°Cu - E°Zn = 0.34 –(– 0.76) = 1.10 V  Standard redox potential Most negative value Li+(aq) + e– Li(s) Strongest reducing Increasing strength of oxidizing agent agent Increasing strength of reducing agent 2H+(aq) + 2e– H2(g) Most positive value F2 (g) + 2e– 2F–(aq) Strongest oxidizing agent  Spontaneity of redox reactions The more positive the E° value for a half- reaction the greater the tendency for the substance to be reduced (oxidizing agent). The more negative the E° value, the greater the tendency for the substance to be oxidized (reducing agent). In a system the more negative electrode will be oxidized and the less negative (more positive) will be reduced.  Standard redox potentials A species which is lower down Cathode (Reduction) Half-Reaction E° (volts) Li+(aq) + e- -> Li(s) -3.04 in the table (more positive) K+(aq) + e- -> K(s) -2.92 will spontaneously oxidize a Ca2+(aq) + 2e- -> Ca(s) -2.76 species that is higher (less Na+(aq) + e- -> Na(s) -2.71 Mg2+(aq) + 2e- -> Mg(s) -2.38 positive) in the table. Al3+(aq) + 3e- -> Al(s) -1.66 Example: F2 will oxidize Cl2; 2H2O(l) + 2e- -> H2(g) + 2OH-(aq) -0.83 H+ will oxidize Na(s) Zn2+(aq) + 2e- -> Zn(s) -0.76 Fe2+(aq) + 2e- -> Fe(s) -0.41 Pb2+(aq) + 2e- -> Pb(s) -0.13 – can reduce H+; 2H+(aq) + 2e- -> H2(g) 0.00 Cu2+(aq) + 2e- -> Cu(s) 0.34 can be oxidized by H+ Hg22+(aq) + 2e- -> 2Hg(l) 0.80 + can not reduce H+; Ag+(aq) + e- -> Ag(s) 0.80 can not be oxidize by H+ Br2(l) + 2e- -> 2Br-(aq) 1.07 O2(g) + 4H+(aq) + 4e- -> 2H2O(l) 1.23 Cl2(g) + 2e- -> 2Cl-(aq) 1.36 Species having E°< -0.83V MnO4-(aq) + 8H+(aq) + 5e- -> Mn2+(aq) + 4H2O(l) 1.49 can react with water. F2(g) + 2e- -> 2F-(aq) 2.87  Reactions of metals with acids and water I. Metal + diluted acid The metals is oxidized: M Mn+ + n e Emetal = ? H+ of acid is reduced: 2 H+ + 2 e H2 E = 0.0 V Spontaneous if Emetal < 0.0 V Metal + water The metals is oxidized: M Mn+ + n e Emetal = ? Water is reduced: H2O + 2 e H2 + 2 OH E = -0.83 V Spontaneous if Emetal < -0.83 V  Reactions of metals with acids and water II. Li+(aq) + e- Li(s) -3.04 K+(aq) + e- K(s) -2.92 Metals react Na+(aq) + e- Na(s) -2.71 with diluted Mg2+(aq) + 2e- Mg(s) -2.38 acids and Al3+(aq) + 3e- Al(s) -1.66 water 2H2O(l) + 2e- H2(g) + 2OH-(aq) -0.83 Zn2+(aq) + 2e- Zn(s) -0.76 Fe2+(aq) + 2e- Fe(s) -0.41 Metals react Cd2+(aq) + 2e- Cd(s) -0.40 with diluted Ni2+(aq) + 2e- Ni(s) -0.25 acids Pb2+(aq) + 2e- Pb(s) -0.13 2H+(aq) + 2e- H2(g) 0.00 Cu2+(aq) + 2e- Cu(s) 0.34 Metals react Ag+(aq) + e- Ag(s) 0.80 with cc. Hg2+(aq) + 2e- Hg(l) 0.86 oxidizing Au3+(aq) + 3e- Au(s) 1.50 acids  Reactions of metals with acids and water III. Metals with water: Sodium reacts readily: 2 Na + 2 H2O → 2 NaOH + H2 Aluminum reacts only after removal of the protecting oxide layer from its surface: 2 Al + 6 H2O → 2 Al (OH)3 + 3 H2  Metals with diluted acids: Zinc reacts readily: Zn + 2 HNO3 → Zn(NO3)2 + H2  Iron reacts readily: (no simple steel containers for diluted acids!) Fe + 2 HCl → FeCl2 + H2  Electropositive metals react only with concentrated, oxidizing acids: Cu + 2 H2SO4 → CuSO4 + SO2  + 2 H2O Ag + 2 HNO3 → AgNO3 + NO2  + H2O  Some other redox reactions Metals + metal ions: a) Cu2+ + Zn Cu + Zn2+ Spontaneous, because E(Cu2+/Cu) = 0.34 V and E(Zn2+/Zn) = –0.76V, so copper must be the oxidizing agent (copper is being reduced) and zinc must be the reducing agent (zinc must be oxidized.) b) Cu + Zn2+ no reaction Halogens + halide ions: a) Cl2 + 2 Br– 2 Cl– + Br2 Spontaneous, because E(Cl–/Cl2/Pt) = 1.36 V and E( Br–/Br2/Pt) = 1.07 V, so chlorine must be the oxidizing agent (chlorine is being reduced) and bromine must be the reducing agent (bromine must be oxidized.) b) Cl– + Br2 no reaction  Thermodynamics of redox reactions maximum electrical work attainable by a voltaic cell G = wmax wmax = ‒nFEcell G = ‒n F Ecell G° = ‒n F E°cell G: free energy n = number of electrons transferred in balanced redox reaction F = Faraday constant = 96,485 Coulombs/mole (charge of a mole of electrons) in spontaneous reactions Ecell > 0, G < 0 in equilibrium Ecell = 0, G = 0 in nonspontaneous reaction Ecell < 0, G > 0 Cellpotential at non-standard state G = G° + RTlnQ ‒nFEcell = ‒nFE°cell + RTlnQ Ecell = E°cell – (RT/nF) lnQ [product] [red] Q= [reactant] = [ox] reaction quotient E = potential under the nonstandard conditions E° = standard potential R = gas constant, 8.314 J/mol.K T = absolute temperature n = number of moles of electrons transferred F = Faraday, 96,485 J/V.mol e-  Nernst equation Electrodepotential at non-standard state RT [product] E = E° – ln [reactant] nF 0.0592 [oxidized] E = E° + log [reduced] n reduction Zn2+(aq) + 2e— Zn(s) 0.0592 E = –0.76 + n log [Zn2+aq]  Nernst equation Ecell = EMF = Ecathode – Eanode 0.0592 Ecath = E°cath + n log [ioncathode] 0.0592 Eanode = E°anode + n log [ionanode] Determination of equlibrium constant from EMF Ecell = 0, G = 0 nFE°cell = RTlnK nFE°cell lnK = RT Concentration cell  Determination of pH Pt(s) | H2 (1 atm)| H+ (test) || H+ (1M) | H2 (1 atm) | Pt(s) ½ H2  H+ + e— Ecell = 0 – (RT/nF) log[H+] = 0.0592 pH Ecell pH = 0.0592 Glass electrode Si Si O O Si Si + H3O+ O O H3O Si Si + O O H3O Si Si H3O+ O H3O+ O Si Si H3O+ partially populates both the inner and outer SiO2 surfaces of the glass membrane. The concentration difference results in a potential across the glass membrane. A special glass is used: 22% Na2O, 6% CaO, 72% SiO2 Combined glass electrode  Redox reactions in living cells Oxidation–reduction reactions exist in all living cells and are critical for cell homeostasis and signaling, including energy metabolism, gene expression, cell cycle regulation, immune response, cell growth, and cell apoptosis. These reactions are especially crucial in energy metabolism processes such as photosynthesis and cellular respiration. In photosynthesis, carbon dioxide and water are converted to glucose using the energy of the Sun. 6CO2+6H2O+photons→C6H12O6+6O2 carbon dioxide is reduced to glucose, and water is oxidized to oxygen gas  Cellular metabolism Cellular respiration is a set of metabolic reactions and processes that take place in the cells of organisms to convert biochemical energy from nutrients into adenosine triphosphate (ATP), and then release waste products. The overall reaction occurs in a series of biochemical steps, most of which are redox reactions themselves. Nutrients that are commonly used by animal and plant cells in respiration include sugar, amino acids and fatty acids, and the most common oxidizing agent (electron acceptor) is molecular oxygen (O2). C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l) + energy In this equation, 24 electrons move from the carbon atoms in the sugar to the oxygen atoms, releasing energy to drive even more redox reactions along the way.  Biological oxidation Most biological oxidation reactions (such as those found in glycolysis, Szent-Györgyi‒Krebs cycle, and fatty acid oxidation) do not use O2 as the immediate oxidizing agent. Rather they use nicotinamide adenine dinucleotide (NAD+) or flavin adenine dinucleotide (FAD) as oxidizing agents, which get reduced. Enzymes that catalyse these processes are dehydrogenases, oxygeneses, hydroxylases etc. Oxidation can occur by: addition of oxygen (less common) removal of hydrogen (common) removal of electron (most common)  Standard redox-potentials in living systems (E°’) Redox reaction E°’(V) Acetate  acetaldehyde – 0.60 NAD+  NADH – 0.32 Glutation ox  Glutation red – 0.23 Pyruvate  lactate – 0.19 Fumarate  succcinate + 0.03 Dehydroascorbic acid  + 0.08 Ascorbic acid Cytochrom C ox  red + 0.25 ½ O2  H2O + 0.82 E°’: standard electrodepotential at pH=7, temperature 298K  Redox reactions in living systems NAD+ + H+ + 2e-  NADH E°= –0,32V Piruvate + 2H+ + 2e-  lactate E°= –0,19V (Electrons will always flow to the half-cell with the higher reduction potential.) reduction Piruvate + NADH + H+  lactate + NAD+ oxidation E°’ = –0.19 – (–0.32) = 0.13V (NAD: nicotinamide adenine dinucleotide  Electrochemical cells Voltaic cell electrolytic cell Zn(s) Zn2+(aq) + 2e— Cu2+(aq) + 2e— Cu(s) Zn2+(aq) + 2e— Zn(s) Cu(s) Cu2+(aq) + 2e— anode: oxidation cathode: reduction cathode: reduction anode: oxidation negative pole positive pole negative pole positive pole G < 0 Ecell > 0 G > 0 Ecell < 0  Thank you very much for your attention! Please stay a few more minutes and answer the questions. Reaction kinetics Prof. Tamas Janaky  Thermodynamics Thermodynamics is the study of what provides the driving force of chemical reactions. Why do reactions occur in a spontaneous direction from reactants to products? What is the energy requirement of a given reaction? Is a reaction product-favored or reactant-favored? Reactions that have a strong driving force can be either fast or slow! C diamond  O2g  CO2g  G298 o  396 kJ very slow H + aq  + OHaq  H2Ol  G - o 298 = -79 kJ very fast  Fast and slow reactions reaction in airbag after collision rusting of iron 4Fe + 3O2 + 6H2O → Fe2O3 x H2O Overview  Chemical Kinetics Chemical Kinetics is the study of the relative rates of chemical reactions. Kinetics studies how fast reactions occur and the conditions that effect the rates of reactions. Kinetics also attempts to understand the behavior of reactions at a molecular level—how does the reaction mechanism relate to the macroscopically observed reaction rate behavior. Rate The concept of rate is a familiar one. When we travel in a car, we often talk about the rate of distance traveled or speed.  position x2 - x1 km mi Speed = = t2 - t1 ( hr )  time  something Rate of Something =  time  Rates of Chemical Reactions What is changing in a chemical reaction? A  B The extent of reaction can be measured by monitoring the quantity of product (B) formed or reactant (A) consumed => moles. More often, reactions are done at constant volume and the quantity of reactant or product is represented as concentration. The reaction rate is the increase in molar concentration of product of a reaction per unit time or the decrease in molar concentration of reactant per unit time. reaction rate =  concentration =  [B] = ̶  [A]  time  time  time The unit of reaction rate is moles per liter per second, mol/(L ∙ s).  Concentration [A] [B] Time  Expression of reaction rate Average rates are taken over long intervals [A] Concentration rate = t [A] t Time  Expression of reaction rate Instantaneous rates are determined by finding the slope of a line tangent to the curve at any given point because the rate can change over time. Concentration d[A] dt [A] [A] t t Time If the time interval is very short, the equation gives the instantaneous rate—that is, the rate at a particular instant of time.  Production of ammonia N2 + 3H2 2NH3 Concentration [H2] [NH3] [N2] Time  Reaction rates and stochiometry A + 3B 2C In order to avoid ambiguity when expressing the rate in terms of different components, it is customary to divide each change in concentration by the appropriate coefficient:  [A] 1  [B] 1  [C] rate = ̶ = ̶ = t 3 t 2 t  Reaction rate in a stochiometrically complicated reaction aA + bB cC + dD divide each change in concentration by the appropriate coefficient 1  [A] 1  [B] 1  [C] 1  [D] rate = ̶ = ̶ = = a t b t c t d t  Factors affecting reaction rate The nature of reactants Concentration of reactants Temperature Catalysts Surface area of a solid reactant or catalyst  The nature of the reactants Ions in solution tend to react very quickly. Covalent molecules tend to react more slowly. Large covalent molecules tend to react more slowly than small covalent molecules. Molecules with strong covalent bonds tend to react more slowly than those with weak bonds.  Effect of concentration on rate How does the rate of a chemical reaction depend upon the reactant concentrations? 2 N2O5 (g) 4 NO2 (g) + O2 (g) In decomposition of N2O5, the rate depends upon [N2O5]. Rate  [N2O5] Rate = k [N2O5], where k is a constant. The relationship between reactant concentration and reaction rate is called the rate equation or rate law.  Rate Law Rate law: equation which describes the rate of the reaction as a function of he concentrations of the reactants. Rate law is an experimentally determined characteristic of the reactions. Differential Rate Law: expresses how rate depends on concentration. Integrated Rate Law: expresses how concentration depends on time.  Differential rate law reaction rate  k x concentration k: rate constant (depends on temperature, but independent of the concentration) A product(s) v = k [A] aA + bB cC + dD v=k x [A] [B]y v: reaction rate x and y: exponents, reaction order  Reaction order The reaction order is the exponent to which the concentration of a species is raised, and it indicates to what extent the concentration of a species affects the rate of a reaction. Differential rate law v = k [A]x [B]y x is the order with respect to species A y is the order with respect to species B x + y is the overall order of reaction  Reaction order Chemical equation Rate law aA + bB cC + dD v = k [A]x [B]y a, b, c, d: stoichiometric coefficients x, y: exponents, reaction order x and y cannot be determined from a balanced chemical equation: the exponents are not the same as the stoichiometric coefficients! The exponents must be determined experimentally! x and y are usually positive integers, but can be 0, negative or fraction. Sum of exponents (x + y) = overall order of the reaction  Examples A zeroth order reaction: 2 NH3 (g) → N2 (g) + 3 H2 (g) (1130K, Pt catalyst ) v=k A first order reaction: 2 N2O5 (g) → 4 NO2 (g) + O2 (g) v = k [N2O5] Radioactive decay A second order reaction: 2 NO2 (g) → 2 NO (g) + O2 (g) v = k [NO2]2  Integrated Rate Law Concentration-Time Relationships Is there a mathematical relationship between concentration and time? – Can we derive an equation from the rate law that will tell us a) the concentration at any time after the start of a reaction, or b) how long it takes to reach a certain concentration? Yes! We get these equations by integrating the rate law derived experimentally. rate = k [A]x [B]y f([A],[B]) = f (k, t) Graphical Interpretation of Rate Law for First-order Reaction ln[ A]t  k t  ln[ A]0 y = mx + b  Half-life of First-order Reactions Half-life (t1/2) : Time needed for the amount of reactant to decrease by half. At t1/2, [A]t = ½[A]0. 0.693 t½ = ln 2 = k k At 1st order reaction t1/2 is constant, independent of reactant concentration.  Half-life of Second-Order reactions Half-life (t1/2) : Time needed for the amount of reactant to decrease by half. At t1/2, [A]t = ½[A]0. t½ = 1 k[A]0 At 2nd order reactions the half-life depends on concentration. Summary of Rate Law to One-Component First-Order Second-Order Zeroth-Order Differential k[A] k[A]2 k rate law Half-Life ln(2)/k 1/k[A0] [A0]/2k  Reaction rate depends on temperature Increasing the temperature usually has a dramatic effect on reaction rates (by increasing the rate constant). Chemists use a “rule of thumb” that a 10°C rise in temperature doubles the rate of a reaction. The dependence of reaction rate on concentration and temperature can be explained by the Collision Theory and Activated-complex Theory.  Molecular View of Reaction Rates Collision theory: chemical reactions occur as a result of collisions between reacting molecules. Rate of reaction is proportional to the number of effective collisions. Factors affecting reaction rate: frequency of collisions energy of collisions orientation of reactants during collision COLLISION THEORY OF CHEMICAL KINETICS Frequency of collisions  temperature  concentration (homogeneous reactions)  surface area (heterogeneous reactions) < increase temperature  molecules move A+B→C faster and therefore collide more frequently, increase concentration  increase the rate = k[A] [B] frequency of collision, increase the rate of reaction  Collision Theory In a chemical reaction molecules collide and bonds may break and form. In order to react the colliding molecules must have a total kinetic energy equal to or greater than the activation energy (Ea), which is the minimum energy required to initiate the chemical reaction. transition state E < Ea potential energy Ea reactant product E E > Ea reaction progress  Kinenetic energy (KE) – Activation energy (Ea) Maxwell-Boltzmann distribution of kinetic energy relative number of molecules At higher temperature more molecules have appropriate energy. At higher temperature more collisions lead to reaction. kinetic energy The fraction of molecular collisions having energy greater than the activation energy changes rapidly in most reactions with even small temperature changes.  Collision Theory In order to react the colliding molecules must have the proper orientation. If the orientation of the colliding molecules is wrong, no reaction occurs. If properly oriented molecules come together, reaction may occur. independent of temperature changes  Transition-State Theory Transition-state theory explains the reaction resulting from the collision of two molecules in terms of an activated complex. An activated complex (transition state) is an unstable grouping of atoms that can break up to form products. activated complex  Potential energy diagrams for reactions The activation energy (Ea) is the potential energy barrier that must be surmounted before reactants can be converted to products (the energy required to go from reactants to transition state). Exothermic Reaction Endothermic Reaction products reactants net released net absorbed energy energy products reactants Total energy = potential energy + kinetic energy  Temperature and Rate The Arrhenius Equation Ea/RT k=Ae k: rate constant A: frequency factor Ea: activation energy R: gas constant T: temperature Reactions with high activation energy have small rate constant and small activation energies have large rate constant.  Reaction Mechanisms In most cases, an overall balanced equation does not tell us much about how the reaction takes place, what happens at molecular level. It may be the sum of several elementary steps, instead of a single step. Reaction mechanism - sequence of molecular events, or elementary reaction steps, that defines the pathway from reactants to products. Overall Reaction: A → Z Reaction Mechanism: A → B→ C→ D→ Z  Reaction Mechanisms An elementary step describes the results of a collision occuring at the molecular level, how individual atoms or molecules change. It generally involves the forming or breaking of 1 or 2 bonds. An overall reaction describes the reaction stoichiometry of the balanced chemical equation. It may be the result of many bonds breaking and forming. The mechanism of a chemical reaction can not be determined directly from the balanced equation.  Reaction mechanism 2NO(g) + O2(g)  2NO2(g) But N2O2 is detected. How? In fact Elementary step: NO+NON2O2 Elementary step: N2O2+O22 NO2 Overall reaction: 2 NO+O2+N2O22 NO2+N2O2 N2O2 : intermediate The elementary steps must sum up properly to give correct stoichiometry for the overall chemical reaction.  Molecularity Elementary reactions are classified according to their molecularity the number of molecules (or atoms) on the reactant side of the chemical equation for an elementary step. A unimolecular reaction occurs when a molecule rearranges itself to produce one or more products. Examples: radioactive decay, in which particles are emitted from an atom, cis-trans isomerization, thermal decomposition, ring opening, and racemization...  Molecularity Bimolecular reaction: involves the collision of two particles Termolecular reaction: requires the collision of three particles at the same place and time. This is very uncommon because all three reactants must simultaneously collide with each other, with sufficient energy and correct orientation.  Rate Laws & Elementary Steps aA + bB cC + dD v = k [A]x [B]y The rate law for an overall reaction must be determined experimentally. Knowing the elementary steps enables us to deduce the rate law. The reaction order for each reactant in an elementary reaction is equal to its stoichiometric coefficient in the chemical reaction for that step. NO+NON2O2 2nd order 2NO(g) + O2(g)  2NO2(g) N2O2+O22NO2 2nd order The rate law for elementary step follows from its molecularity - a unimolecular reaction is always first order - a bimolecular reaction is always second order - a termolecular reaction is always third order  Rate Determining Steps Some reactions have a mechanism in which one of the elementary steps is much slower than the others. Such a slow elementary step is called the rate determining step, since it acts as the bottleneck for the overall reaction. The overall rate law is then simply the rate law for the rate determining step.  Rate determining step NO2(g) + CO(g) NO(g) + CO2(g) Overall Elementary steps (slow) k1 k2 >> k1 (fast) k2 Overall rate law: Rate = k [NO2]2 Overall rate is determined by k1 Types of reactions with several elementary steps Consecutive reactions Equilibrium reactions Parallel or simultaneous reactions Chain reactions  Consecutive reactions series of 1st order irreversible reactions k1 k2 A B C reactant intermediate product [A]: [A]0 → 0 [B]: 0 → max →0 [C]: 0 → [A]0 [C] [A] B transiently exists [B]  Consecutive reaction NO2(g) + CO(g) NO(g) + CO2(g) Overall Elementary steps (slow) k1 intermediate k2 >> k1 (fast) k2 intermediate Overall rate law: Rate = k [NO2]2 Overall rate is determined by k1  Steady-state k1 k2 A B C Steady-state: at an appropriate k1/k2 ratio the concentration of the intermediate (B) remains constant for a while. If k2>>k1 If k2