Chemistry For Engineering Students - Chapter 13 - Electrochemistry PDF

Larry Brown Tom Holme Chapter 13 Electrochemistry Jacqueline Bennett SUNY Oneonta www.cengage.com/chemistry/brown Chapter Objectives Describe at least three types of corrosion and identify chemical reactions responsible for c...

Larry Brown Tom Holme Chapter 13 Electrochemistry Jacqueline Bennett SUNY Oneonta www.cengage.com/chemistry/brown Chapter Objectives Describe at least three types of corrosion and identify chemical reactions responsible for corrosion. Define oxidation and reduction. Write and balance half-reactions for simple redox processes. Describe the differences between galvanic and electrolytic cells. Use standard reduction potentials to calculate cell potentials under both standard and nonstandard conditions. 2 Chapter Objectives Use standard reduction potentials to predict the spontaneous direction of a redox reaction. Calculate the amount of metal plated, the amount of current needed, or the time required for an electrolysis process. Distinguish between primary and secondary batteries. Describe the chemistry of some common battery types and explain why each type of battery is suitable for a particular application. Describe at least three common techniques for preventing corrosion. 3 Corrosion Corrosion is the degradation of metals by chemical reactions with the environment. Uniform corrosion occurs evenly over a large portion of the surface area of a metal. Galvanic corrosion occurs when two different metals contact each other in the presence of an appropriate electrolyte. Crevice corrosion occurs when two pieces of metal touch each other, leaving a small gap or crevice between the metals. 4 Corrosion Different metals corrode differently. Aluminum has a greater tendency to corrode than iron, but corrosion of aluminum is not problematic compared to iron. The aluminum oxide corrosion product forms a protective layer on the surface of aluminum metal. The iron oxide corrosion product flakes off the surface of iron, exposing fresh iron to corrosion. 5 Corrosion Corrosion occurs in a variety of forms. The chain shows uniform corrosion. The grill cover shows crevice corrosion where the handle is attached. 6 Oxidation-Reduction Reactions and Galvanic Cells Special conditions must be present before iron reacts with oxygen to form iron(III) oxide. Rust formation is a slow process, so the basics of electrochemistry must be investigated using more easily observed reactions. Reactions that transfer electrons between reactants are known as oxidation-reduction or redox reactions. Oxidation is the loss of electrons from some chemical species. Reduction is the gain of electrons to some chemical species. 7 Oxidation-Reduction and Half-Reactions For an oxidation-reduction reaction to occur, one reactant must be oxidized and one reactant must be reduced. Oxidation cannot occur without reduction. When copper wire is placed in a silver nitrate solution, a redox reaction occurs. A reaction is observed to occur because the solution changes color and crystals form on the surface of the copper wire. 8 Oxidation-Reduction and Half-Reactions When a clean copper wire is placed into a colorless solution of silver nitrate, it is quickly apparent that a chemical reaction occurs: silver metal forms on the copper wire the solution turns blue. 9 Oxidation-Reduction and Half-Reactions The solution’s blue color is indicative of Cu2+ ions in solution. Cu2+ is formed when a copper atom loses two electrons. The copper metal is oxidized. ® Cu 2+ (aq) + 2e - Cu(s) ¾¾ The crystals forming on the surface of the copper wire are silver metal. Silver is formed when a silver cation gains an electron. The silver cation is reduced. - Ag (aq) + 1e ¾¾ + ® Ag(s) 10 Oxidation-Reduction and Half-Reactions For the reaction between silver cation and copper metal, two half-reactions are written. One for the oxidation of copper and one for the reduction of silver. Neither half-reaction can occur without the other. The half-reactions as written indicate that Ag+ only accepts one electron whereas Cu loses two electrons. The electron transfer must balance, so the reduction half- reaction is multiplied by 2. ® Cu 2+ (aq) + 2e - Cu(s) ¾¾ 2Ag + (aq) + 2e - ¾¾ ® 2Ag(s) 11 Oxidation-Reduction and Half-Reactions Add the two half-reactions together, the electrons cancel out, leaving the net ionic equation for the redox reaction. ® Cu 2+ (aq) + 2e - Cu(s) ¾¾ 2Ag + (aq) + 2e - ¾¾ ® 2Ag(s) Cu(s) + 2Ag + (aq) ¾¾ ® Cu 2+ (aq) + 2Ag(s) 12 Oxidation-Reduction and Half-Reactions The species undergoing oxidation is referred to as a reducing agent. The Cu was oxidized and is the reducing agent. The Cu facilitated the reduction of Ag+ by losing electrons. The species undergoing reduction is referred to as an oxidizing agent. The Ag+ was reduced and is the oxidizing agent. The Ag+ facilitated the oxidation of Cu by gaining electrons. 13 Building a Galvanic Cell A galvanic cell is any electrochemical cell in which a spontaneous chemical reaction can be used to generate an electric current. The name electrochemistry comes from the observation of electric currents in galvanic cells. To harness electricity from a galvanic cell, each half-reaction is prepared separately in half-cells. Cu metal immersed in Cu2+ solution is one half-cell. Ag metal immersed in Ag+ solution is the second half-cell. 14 Building a Galvanic Cell A salt bridge is crucial to a galvanic cell. The salt bridge allows ions to flow between each half-cell, completing the circuit. 15 Building a Galvanic Cell Current flows by the migration of ions in solution. To transfer current between the half-cells, a salt bridge is used. The salt bridge contains a strong electrolyte that allows either cations or anions to migrate into the solution where they are needed to maintain charge neutrality. A metal wire cannot transport ions and cannot be used. 16 Building a Galvanic Cell For a salt bridge composed of NH4Cl: NH4+ will flow into the Ag+ beaker to offset the removal of Ag+ from solution. Cl– will flow into the Cu2+ beaker to offset the production of Cu2+ in solution. The circuit is completed by connecting wires to each metal strip. A voltage potential of 0.46 V will be measured for the described cell. 17 Terminology for Galvanic Cells Electrodes are the electrically conducting sites at which either oxidation or reduction occurs. The electrode where oxidation occurs is the anode. The electrode where reduction occurs is the cathode. Cell notation - a shorthand notation for the specific chemistry of an electrochemical cell. Cell notation lists the metals and ions involved in the reaction. A vertical line, |, denotes a phase boundary. A double vertical line, ||, denotes a salt bridge. The anode is written on the left, the cathode on the right. 18 Terminology for Galvanic Cells General form of cell notation anode | anode electrolyte || cathode electrolyte | cathode For the previous example of copper and silver Cu(s) | Cu2+ (aq) (1 M) || Ag+ (aq) (1 M) | Ag The electrolyte concentration is also given. An electrochemical cell is at its standard state when the electrolyte concentrations are 1 M. For half-cells that generate or consume a gas, a partial pressure of 1 atm is required for the standard state. 19 Atomic Perspective on Galvanic Cells Before half-cells are connected by a salt bridge, a small build up of charge occurs for each half-cell at the interface between the electrode and the electrolyte. At the anode, some oxidation occurs and cations dissolve into solution, leaving a negative charge on the anode. At the cathode, some reduction occurs and cations are removed from solution, leaving a positive charge on the cathode. 20 Atomic Perspective on Galvanic Cells An equilibrium can be described for each half-cell, the half- reaction equilibrium. Not an oxidation-reduction equilibrium. The build up of charge on the electrode means there is potential for electrical work. This potential is the cell potential, or electromotive force (EMF). EMF is related to the maximum work obtainable from an electrochemical cell. wmax = qE q is the charge, E is the cell potential. 21 Atomic Perspective on Galvanic Cells Without a salt bridge to close the circuit, local charges build up around both electrodes. Neither electrode reaction can proceed to any significant extent, so no cell voltage can be measured. 22 Galvanic Corrosion and Uniform Corrosion Metals in contact with a solution establish an oxidation half- reaction equilibrium. If the solution contains a substance that can undergo reduction, a redox reaction may occur. For two metals in contact, such as a tin-plated steel can, exposure to air and moisture results in rapid corrosion. The half-reaction equilibrium for the tin facilitates the process by which iron is oxidized. This is an example of galvanic corrosion. 23 Galvanic Corrosion and Uniform Corrosion A “tin can” is usually tin-plated steel. If the tin coating is scratched to expose the underlying steel, iron in the steel will corrode rapidly. 24 Galvanic Corrosion and Uniform Corrosion Metal not in contact with another metal can also corrode. A nonmetal is involved in the second half-cell. For the corrosion of iron, iron is one half-cell and oxygen dissolved in water is the second half-cell. The electrode for the oxygen half-cell is the iron itself. Dissolved salts facilitate the corrosion reaction. This is an example of uniform corrosion. 25 Galvanic Corrosion and Uniform Corrosion Iron is oxidized, and oxygen from the air is reduced. Water is needed for ion mobility between the anodic and cathodic regions, and the presence of ionic salts speeds the reaction considerably. 26 Cell Potentials The relative corrosivities of various plated steels can be expressed as cell potential. A voltmeter measures the size of the electrical potential and also its polarity - the locations of the negative charge (negative pole) and the positive charge (positive pole). An electric potential has a fixed polarity and voltage. Reversing the poles of a battery with respect to a voltmeter changes the sign on the measured voltage but does not influence the electrochemical reaction in the battery. 27 Measuring Cell Potential When a voltmeter is connected to the previously described copper/silver cell, a potential of 0.462 V is measured. Connecting the copper half-cell to a reducing iron(III)/iron(II) half-cell, a cell potential of 0.434 V is measured. Connecting the iron(III)/iron(II) half-cell to the silver half-cell results in a cell potential of 0.028. For the three cell potentials measured, the fact that 0.462 V = 0.434 V + 0.028 V suggests two things: The behavior of cell potentials is akin to state functions. If a specific standard electrode is chosen, comparison to all other electrodes will result in a practical system for determining cell potential. 28 Measuring Cell Potential Measurement of standard cell voltages for various combinations of the same half-reactions suggests that a characteristic potential can be associated with a particular half-reaction. 29 Measuring Cell Potential The standard hydrogen electrode (SHE) is the choice for the standard component in cell potential measurements. The cell is constructed of a platinum wire or foil as the electrode. The electrode is immersed in a 1 M HCl solution through which H2 gas with a pressure of 1 atm is bubbled. The SHE has been chosen as the reference point for the scale of standard reduction potentials, and assigned a potential of exactly zero volts. 30 Measuring Cell Potential For the Standard Hydrogen Electrode + The half-reaction for the SHE is: 2H (aq) + 2e ® H 2 (g) – The half-cell notation is: Pt(s) | H2(g, 1 atm) | H+ (1 M). The half-cell is assigned a potential of exactly zero volts. The cell potential is attributed to the other half-reaction. 31 Measuring Cell Potential For some galvanic cells, the SHE acts as the anode and for other galvanic cells, the SHE acts as the cathode. The anode is the site of oxidation, releasing electrons and creating a negatively charged electrode. If the anode is connected to the positive terminal of the voltmeter, a negative potential is measured. The cathode is the side of reduction, consuming electrons and creating a positively charged electrode. If the cathode is connected to the positive terminal of the voltmeter, a positive potential is measured. 32 Measuring Cell Potential When the SHE is always connected to the positive terminal, the sign of the potential tells us the direction of the redox reaction. When the potential is negative, the SHE is the anode, and H2 is oxidized to H+(aq). When the potential is positive, the SHE is the cathode, and H+(aq) is reduced to H2. 33 Measuring Cell Potential Just like a commercial battery, a galvanic cell has a fixed polarity. Electrons flow through the external circuit from the anode to the cathode. Reversing the leads of the voltmeter changes the sign of the reading, but does not influence the flow of current. 34 Standard Reduction Potentials To compare the oxidation-reduction trends of species used in electrochemistry, all half-cell potentials are written as reductions. A table of standard reduction potentials lists the potential of any half-reaction when connected to a SHE. All materials are 1 M for aqueous species and 1 atm partial pressure for gases. 35 Standard Reduction Potentials Standard reduction potentials for several half-reactions involved in the cells discussed in the text. 36 Standard Reduction Potentials Although the half-reactions are listed as reductions in the table, one half-reaction in any electrochemical cell must be an oxidation and, therefore, reversed from what appears in the table. The cell potential sign must be changed when writing the half-reaction as an oxidation. Some half-reactions have positive potentials, whereas others have negative potentials. 37 Standard Reduction Potentials All potentials are measured with a SHE connected to the positive terminal. If the voltage is positive, the SHE is the anode, the oxidation site. A positive standard reduction potential means the half- reaction proceeds as written (reduction occurs). If the voltage is negative, the SHE is the cathode, the reduction site. A negative standard reduction potential means the half- reaction proceeds as an oxidation. 38 Standard Reduction Potentials The tendency for the chemicals involved in a half-reaction to be an oxidation or reduction depends on the value of the reduction potential. A large, positive value for the standard reduction potential implies the substance is reduced readily and a good oxidizing agent. A large, negative value for the standard reduction potential implies the substance is oxidized readily and a good reducing agent. 39 Standard Reduction Potentials For a galvanic cell, the half-reaction with the more positive reduction potential will be the cathode. The half-reaction with the more negative reduction potential will be the anode. The standard reduction potential for any pair of half-reactions, E°cell, is calculated from the standard reduction potentials for the cathode and anode. Ecell = Ered - Eox E°red is the standard reduction potential for the cathode and E°ox is the standard reduction potential for the anode. 40 Standard Reduction Potentials For standard reduction potentials arranged horizontally, the anode and cathode for a galvanic cell can easily be determined. The reduction potential furthest to the left is the anode. 41 Example Problem 13.1 Using standard reduction potentials, identify the anode and the cathode and determine the cell potential for a galvanic cell composed of copper and iron. Assume standard conditions. Confirm that the potential of the following galvanic cell is 0.462 V: 2+ + Cu(s) | Cu (1 M) || Ag (1 M) | Ag(s) 42 Nonstandard Conditions The cell potential at nonstandard conditions is calculated using the Nernst equation. RT E=E - lnQ nF Q is the reaction quotient, F is the Faraday constant, and n is the number of electrons transferred in the reaction. F = 96,485 J V-1 mol-1 or 96,485 C mol-1 43 Example Problem 13.2 Assume that you have a cell that has an iron(II) concentration of 0.015 M and an H+ concentration of 1.0 × 10-3 M. The cell temperature is 38°C, and the pressure of hydrogen gas is maintained at 0.04 atm. What would the cell potential be under these conditions? 44 Cell Potentials and Free Energy Corrosion is a spontaneous process and has a negative Gibbs free energy change. The Gibbs free energy change for an electrochemical reaction can be calculated from the standard reduction potential. DG = -nFE n is the number of electrons transferred and F is Faraday’s constant. The minus sign in required because a galvanic cell has a positive cell potential, spontaneously generates electrical work, and thus must have a negative ΔG value. 45 Example Problem 13.3 Suppose that we wish to study the possible galvanic corrosion between zinc and chromium, so we set up the following cell: Cr(s) | Cr 2+ (aq) || Zn2+ (aq) | Zn(s) What is the chemical reaction that takes place and what is the standard free energy change for that reaction? 46 Equilibrium Constants The cell potential can be used to calculate the equilibrium constant for an electrochemical reaction. RT E = ln K nF n is the number of electrons transferred, R is the universal gas law constant, and F is Faraday’s constant. 47 Equilibrium Constants The relationship between the cell potential and the equilibrium constant can be re-written in terms of the common (base 10) log. 2.303RT E = log K nF The equation can be simplified for reaction carried out at standard temperature, 25°C (298 K). 0.0592 V E = log K n 48 Equilibrium Constants The equilibrium constant increases as the cell potential and number of electrons transferred increases. The different lines correspond to reactions involving 1, 2, or 3 electrons transferred. 49 Batteries A battery is a cell or series of cells that generate an electrical current. Batteries are the means by which we harness the electrical work of a galvanic cell and use it productively. 50 Primary Cells Single-use batteries that cannot be recharged are primary cells, or primary batteries. The most prevalent type of primary cell is the alkaline battery. An alkaline battery has a zinc electrode at which oxidation occurs. - - Zn(s) + 2OH (aq) ¾¾ ® Zn(OH)2 (s) + 2e The cathode is derived from manganese(IV) oxide. 2MnO2 (s) + H 2O( ) + 2e - ¾¾ ® Mn2O3 (s) + 2OH- (aq) 51 Primary Cells Zn(s) + 2 MnO2 (s) + H 2O( ) ¾¾ ® Zn(OH)2 (s) + Mn2O3 (s) The chemistry of an alkaline dry cell battery. The net reaction is shown above. The alkaline battery is termed a dry cell because the KOH electrolyte is in the form of a paste or gel. 52 Primary Cells Lithium batteries are small and long lasting. They are used for medical devices like pacemakers. Lithium is the anode. ® Li+ + e- Li(s) ¾¾ Manganese(IV) oxide is the cathode as in the alkaline battery, but in this case the MnO2 reacts with lithium ions. MnO2 (s) + Li+ + e - ¾¾ ® LiMnO2 (s) The lithium battery provides a stable current and electrical potential for long periods. 53 Primary Cells Zinc-air batteries are also primary cells. Zinc is the anode. Zn(s) + 2OH- (aq) ¾¾ ® Zn(OH)2 (s) + 2e - Oxygen reacts at the cathode. 1 O2 (g) + H 2O( ) + 4e - ¾¾ ® 2OH - (aq) 2 In a zinc-air battery, one of the reactants is oxygen from the surrounding air. As a result, these batteries can offer a very attractive energy density. 54 Secondary Cells Rechargeable batteries are secondary cell or secondary batteries. Nickel-metal-hydride batteries are an example of secondary cells. The anode reaction is - - ® M + H2O( ) + e MH(s) + OH (aq) ¾¾ The complex cathode reaction can be represented as NiO(OH)(s) + H2O( ) + e- ¾¾ ® Ni(OH)2 (s) + OH- (aq) 55 Secondary Cells Nickel-metal-hydride batteries have become popular as rechargeable cells. 56 Secondary Cells The lead-acid storage battery found in cars is a secondary cell. The anode for a lead-acid battery is lead metal. Pb(s) + HSO-4 (aq) ¾¾ ® PbSO4 (s) + H+ (aq) + 2e - The cathode for a lead-acid battery is lead oxide. PbO2 (s) + 3H + (aq) + HSO-4 (aq) + 2e - ¾¾ ® PbSO4 (s) + 2H 2O( ) The lead-acid storage battery consists of Pb anodes alternating with PbO2 cathodes, all immersed in sulfuric acid. 57 Secondary Cells Comparison of battery characteristics 58 Fuel Cells A fuel cell is a voltaic cell in which the reactants can be supplied continuously and the products of the cell reaction are continuously removed. Most common type is based on the reaction of hydrogen and oxygen to produce water. 2H2 + O2 ® 2H2O Oxygen is reduced at the cathode. + - O2 + 4H + 4e ® 2H2O Hydrogen is oxidized at the anode. + - H2 ® 2H + 2e 59 Limitations of Batteries Corrosion is a major cause for the loss of performance in batteries. Protective plating of materials used in batteries is an attempt to limit the performance-diminishing effects of corrosion on batteries. 60 Electrolysis Electrolysis is the process of passing an electric current through an ionic solution or molten salt to produce a chemical reaction. Electrolytic cells are divided into two categories based on the nature of the electrodes used. Passive electrolysis: the electrodes are chemically inert materials that simply provide a path for electrons. Active electrolysis: the electrodes are part of the electrolytic reaction. 61 Electrolysis and Polarity Electrolysis changes the polarity of the electrodes in a system. For reduction, electrons are forced to the cathode. The cathode becomes the negative electrode. For oxidation, electrons are pulled from the anode. The anode becomes the positive electrode. In electrolysis, an external source of current drives a redox reaction that would otherwise not be spontaneous. The flow of ions through the solution completes the circuit. 62 Passive Electrolysis in Refining Aluminum Electrolysis provides the means to overcome the nonspontaneous reaction to separate aluminum from its oxide. The Hall-Heroult refining process uses carbon electrodes as inert sites for passive electrolysis. The Hall-Heroult process involves the electrolytic refining of aluminum from Al2O3 to produce aluminum metal and oxygen gas. 63 Active Electrolysis and Electroplating The process of depositing a thin coat of metal on another metal by using electrolysis is electroplating. In some cases, the thin coating is cosmetic, or to provide some vital functionality for the coated piece, such as corrosion resistance or desirable conductive properties. Silver is plated onto electrical devices because silver is a good conductor and resistant to corrosion. The solution from which silver is plated contains CN–(aq) ions, which form a complex with Ag+. The need for uniform coatings makes this an important step. 64 Active Electrolysis and Electroplating The object being electroplated is the cathode. Anode Ag(s) + 2CN - (aq) ¾¾ ® Ag(CN)-2 (aq) + e- Cathode Ag(CN)-2 (aq) + e - ¾¾ ® Ag(s) + 2CN - (aq) Opposite reactions at the anode and cathode are common for electroplating operations. Silver is transferred from the anode to the cathode, coating the cathode in a thin layer of silver. The zero cell potential is not critical since an external current drives electrolysis. 65 Active Electrolysis and Electroplating Barrel plating is often used to apply coatings to small parts. 66 Electrolysis and Stoichiometry For electroplating, it can be vitally important to use carefully controlled amounts of materials. Controlling the flow of electrons (current) in an electroplating operation provides a method to accurately limit the amount of material deposited. Electroplating is often used to prevent galvanic corrosion in an electrical apparatus in places where different metals come into contact with one another. 67 Current and Charge When current is measured in an electric circuit, the observation is the flow of charge for a period of time. The unit of current, the ampere (A), is defined as one coulomb per second: 1 A = 1 C s-1. If a known current flows through a circuit for a known time, the charge can be easily calculated. Charge = current ´ time Q= I ´t 68 Current and Charge Using Faraday’s constant, F = 96,485 C mol-1 and the calculated charge, the number of moles of electrons that pass through the circuit can be calculated. If the number of electrons required to reduce each metal cation is known, the number of moles of material plated can be calculated. Electricity use is often measured in terms of power. The SI unit for power is the watt (1 watt = 1 J s-1) Electrical utilities normally determine consumption in kilowatt- hours, kWh (1 kWh = 3.60 × 106 J) 69 Example Problem 13.4 In a process called flash electroplating, a current of 2.50 x 103 A passes through an electrolytic cell for 5.00 minutes. How many moles of electrons are driven through the cell? 70 Example Problem 13.5 Suppose that a batch of parts is plated with copper in an electrolytic bath running at 0.15 V and 15.0 A for exactly 2 hours. What is the energy cost of this process if the electric utility charges the company $0.0500 per kWh? 71 Calculations Using Masses of Substances in Electrolysis A knowledge of current, how long the current flows, stoichiometry, and the number of electrons required to reduce a metal cation are used to answer the following questions. How much material is plated given a specific current for an allotted time or electrical energy expenditure? How long must a given current to pass through the cell to yield a desired mass of plated material? 72 Example Problem 13.6 An electrolysis cell that deposits gold (from Au+(aq)) operates for 15.0 minutes at a current of 2.30 A. What mass of gold is deposited? 73 Example Problem 13.7 Suppose that you have a part that requires tin coating. You’ve calculated that you need to deposit 3.60 g of tin to achieve an adequate coating. If your electrolysis cell (using Sn2+) runs at 2.00 A, how long must you operate the cell to obtain the desired coating? 74 Batteries in Engineering Design Lithium-ion batteries have recently come under scrutiny because of a high-profile fire during the first commercial flight of the Boeing Dreamliner 787 75 Batteries in Engineering Design What factors led to the Dreamliner’s Problems? The Dreamliner requires higher levels of electrical power than conventional aircraft due in large part to replacing the traditional hydraulic system for controlling the flight of the plane with an all-electronic alternative. Increased fuel efficiency was a major goal, so it was important to minimize weight. Lithium-ion batteries have high energy capacity and low weight. 76 Batteries in Engineering Design Schematic of lithium-ion battery 77 Batteries in Engineering Design The anode is a form of graphite into which lithium atoms have been incorporated, or “intercalated.” The cathode is cobalt oxide that also has lithium incorporated into it. Because the electrodes both consist of solids with lithium embedded in them, it is difficult to write a simple chemical equation for the cell reaction.The chemistry is summarized reasonably by the following reactions: Anode: LinC6 ® nLi+ + ne – + 6C Cathode: Li1-nCoO2 + nLi+ + ne _ ® LiCoO 2 78 Batteries in Engineering Design Two reasons energy density is high: Li+/Li has one of the largest standard reduction potentials Both lithium and carbon are relatively light High temperatures cause lithium-ion batteries to degrade fairly quickly, so engineering designs that use them generally must account for this. 79 Larry Brown Tom Holme Chapter 14 Nuclear Chemistry Jacqueline Bennett SUNY Oneonta www.cengage.com/chemistry/brown Chapter Objectives Describe cosmic rays and some of the ways they influence Earth and its atmosphere. Write, balance, and interpret equations for simple nuclear reactions. Define and distinguish among various modes of nuclear decay, including alpha decay, beta decay, positron emission, and electron capture. Interpret the kinetics of radioactive decay using first-order rate equations. 2 Chapter Objectives Use the chart of the nuclides to understand and explain how radioactive decay processes increase nuclear stability. Use Einstein’s equation to calculate the binding energies of nuclei and the energy changes of nuclear reactions. Describe nuclear fission and fusion, and explain how both processes can be highly exothermic. Discuss the potential of both fission and fusion as energy sources, and identify the pros and cons of the two technologies. 3 Chapter Objectives Explain how penetrating power and ionizing power combine to determine the effect of radiation on materials, including living tissues. Describe how radioisotopes can be used in medical imaging techniques to monitor organ function. 4 Cosmic Rays and Carbon Dating Cosmic Rays - subatomic particles traveling at high speeds that constantly bombard Earth. Majority are atomic nuclei. 87% hydrogen nuclei. 12% helium nuclei. The rest are heavier nuclei. Can originate outside the solar system. 5 Cosmic Rays and Carbon Dating Cosmic rays originate from solar flares on the sun, which can accelerate highly charged cations until they approach the speed of light. Distribution of atomic nuclei reflect composition of the sun. Hydrogen and helium are the most prevalent. Carbon, nitrogen, oxygen, neon, magnesium, silicon, and iron are also present. 6 Cosmic Rays and Carbon Dating The energies of cosmic rays are much higher than in other areas of chemistry. Chemical energies measured in kJ/mol. Cosmic ray energies measured in electron volts (eV) 1 eV = 96.5853 kJ mol-1 Cosmic rays are in the MeV or GeV range. Upon entering the atmosphere, cosmic rays start to collide with gas molecules and induce nuclear reactions. Formation of radioactive 14C is an example. 7 Cosmic Rays and Carbon Dating When a free neutron is absorbed by a nitrogen nucleus, a proton is emitted and 14C is produced. Terrestrial carbon is 98.9% 12C and 1.11% 13C. Both are stable. 14Cis unstable and undergoes spontaneous radioactive decay. Particles are ejected and a nitrogen atom is formed. 8 Radioactive Decay Nuclear reactions are written in a format similar to chemical reactions. Reactants and products are atoms or subatomic particles instead of molecules. Nuclide symbols (E) are written to represent the composition of a nuclide. mass number A atomic number E or E Z These symbols can be used to represent atoms, ions, and nuclei. 9 Radioactive Decay Nuclide symbols for subatomic particles: Neutron, 01 n 1 Proton, p1 Electron, -10 e Atomic number = charge on the nucleus. Nuclear reactions are written using nuclide symbols. 14 7 N + n ¾ 1 0 ¾® C + p 14 6 1 1 Nuclear reactions are balanced when the sums of the mass numbers and atomic numbers for both sides of the equation are equal. 10 Radioactive Decay Soon after uranium was discovered to be radioactive, Ernest Rutherford demonstrated two distinct types of radiation. One type was stopped by thin pieces of aluminum, alpha rays. The second type passed through the aluminum, beta rays. 11 Radioactive Decay In magnetic fields alpha and beta rays are deflected, indicating they carry charge. Alpha and beta rays were deflected in opposite directions, indicating they held opposite charges. One type of particle was deflected more than the other indicating their mass to charge ratios were different. A third type of radiation, gamma rays, was revealed and which passed through the magnetic field undeflected. 12 Radioactive Decay A thin sheet of aluminum blocks alpha rays but not beta rays. In a magnetic field, beta and alpha particles are deflected in different directions, while gamma rays are undeflected. 13 Radioactive Decay Alpha particles, α, are the more massive and positively charged particles. 4 Alpha particles are helium nuclei, 2 He Beta particles, b - or -10 b , are lighter and negatively charged. Beta particles are electrons, -10 e , emitted from the nucleus. Gamma rays, γ, are the particles unaffected by the magnetic field. Gamma rays are high-energy photons of electromagnetic radiation emitted by the nucleus. 0 0 g 14 Alpha Decay During alpha decay, an alpha particle is emitted from the nucleus. The mass number decreases by 4. The atomic number decreases by 2. 238 92 U ¾ ¾® 234 Th + He 90 4 2 The reactant nucleus is the parent. The product nucleus is the daughter. 15 Example Problem 14.1 Complete the equations for each of the following nuclear decay processes. 210 84 Po ¾¾ ® 206 82 Pb + ? 230 90 ® ? + 24 He Th ¾¾ 16 Beta Decay During beta decay, a beta particle and an antineutrino, n , are emitted from the nucleus. A neutron decays into a proton, a beta particle, and an antineutrino. The proton remains in the nucleus. 1 0 ® p+ b +n n ¾¾ 1 1 0 -1 The atomic number increases by 1. 14 6 ¾® N + b + n C ¾ 14 7 0 -1 17 Example Problem 14.2 Complete the equations for each of the following beta decay reactions using the beta nuclide symbol to represent the beta particle. 234 90 Th ¾¾ ® 234 91 Pa + ? 234 91 ®? + Pa ¾¾ 0 -1b +n 18 Gamma Decay Gamma decay is the emission of high-energy photons and tends to accompany other types of decay. Protons and neutrons occupy energy levels within a nucleus analogous to energy levels for electrons. When alpha and beta particles leave the nucleus, the nucleus is left in an excited state. The nucleus returns to the ground state by emitting a gamma ray. 19 Gamma Decay The energy level spacing in the nucleus is very large. The emitted gamma rays have high energies. Wavelength ~10-12 m and frequency ~3 × 1020 s-1. Gamma ray energies are on the order of 108 kJ/mol, several orders of magnitude larger than ordinary chemical reaction energies. Gamma decay does not change the atomic number or mass number of a nucleus, and generally accompanies beta decay. 14 6 ¾® N + b + n + g C ¾ 14 7 0 -1 0 0 20 Electron Capture and Positron Emission In electron capture, the nucleus captures an electron, converting a proton to a neutron and decreases the nuclear charge by one. The reverse of beta emission. 1 1 p + b ¾ 0 -1 ¾® n 1 0 Positron decay occurs when a proton decays into a neutron, positron, and a neutrino, v. A positron, 1 b , is a positively charged electron. 0 The nuclear charge decreases by one. 1 1 ® 01 n + 10 b + n p ¾¾ 21 Positron Emission A positron and an electron form a matter- antimatter pair. Matter-antimatter pairs are identical in mass and spin, but opposite in charge. When a positron and electron collide, they are annihilated and their mass converted into energy. Positron - electron collisions produce two 511-keV gamma-ray photons, traveling in opposite directions. 22 Example Problem 14.3 Complete the following equations with the correct particles and identify the mode of decay. 15 8 O ¾¾ ® 15 7 N + ? 40 19 ®? + K ¾¾ 0 -1 b + n 40 19 K + ? ¾¾ ® 40 18 Ar + n 23 Kinetics of Radioactive Decay The activity of a sample of N nuclei is the rate of disintegration of the sample, given by ΔN/Δt. The SI unit of nuclear activity is the becquerel (Bq), defined as one nuclear disintegration per second (dps). The curie (Ci) is an older and larger unit defined as the number of disintegrations per second in 1 gram of radium- 226. 1 Ci = 3.7 × 1010 Bq 24 Kinetics of Radioactive Decay For radioactive decay, the activity of a sample decreases exponentially with time. The activity is proportional to the number of nuclei present, N. N also decreases exponentially. - kt N = N0 e N0 is the initial number of nuclei and k is the decay constant. Radioactive decay follows first order kinetics. 25 Kinetics of Radioactive Decay The half-life, t1/2, is the time required for half the sample to disintegrate. 0.693 t1/2 = k Radioactive decay always follows first-order kinetics. The half-life is constant for any given isotope. 26 Example Problem 14.4 The half-life of carbon-14, used in radiocarbon dating, is 5730 years. What is the decay constant for carbon-14? 27 Radiocarbon Dating 14C is continually formed through the interaction of cosmic rays with the atmosphere. The 14C is incorporated into living plants and animals and the 14C/12C ratio remains constant over time. When a plant or animal dies, 14C is no longer incorporated and its activity decreases with time. An artifact’s age is determined by measuring its 14C/12C ratio and then comparing it to the 14C/12C ratio of living organisms. 28 Radiocarbon Dating First order kinetics equations are used to determine the age of the artifact. Dendrochronology, which is based on counting growth rings in long-lived trees, has been used to calibrate carbon dating. Ages are determined to within ±40 to 100 years. Objects less than 60,000 years old can be carbon dated. 29 Example Problem 14.5 A piece of cloth is discovered in a burial pit in the southwestern United States. A tiny sample of the cloth is burned to form CO2, which is then analyzed. The 14C/12C ratio is 0.250 times the ratio in today’s atmosphere. How old is the cloth? 30 Radiocarbon Dating Half-lives of some radioactive isotopes. Long lived isotopes, such as uranium, can be used to date minerals and geological formations. 31 Nuclear Stability The Chart of the Nuclides is a plot of the number of protons versus the number of neutrons for all known, stable nuclei. The chart is used in a manner similar to the periodic table, to look for patterns and trends to explain nuclear stability. Virtually all stable nuclides are found in the central region in the chart of the nuclides, in a region called the band of stability. The nuclides outside the band of stability are in the region referred to as the sea of instability. 32 Nuclear Stability The chart of the nuclides is a plot of atomic number (Z) versus neutron number (N) for all known nuclides. All stable isotopes lie in the region shown with blue dots. 33 Nuclear Stability For low atomic numbers, the band of stability is found along a line with Z and N approximately equal. Above around Z = 20, the band of stability deviates from straight line behavior. A nucleus with more protons appears to require additional neutrons to maintain stability. Above Z > 83, no number of neutrons can stabilize the nucleus and its large collection of protons. 34 Nuclear Stability Isotopes below or to the the right of the band of stability tend to have more neutrons than necessary and emit beta particles to gain stability. Beta decay converts a neutron to a proton. Isotopes above or to the left of the band of stability have more protons than necessary and undergo positron emission or electron capture. Positron emission and electron capture convert a proton to a neutron. 35 Nuclear Stability The band of stability ends with Z = 83. Beyond Z = 83, all nuclei are unstable and decay to reach a stable nucleus. Heavier nuclei tend to emit alpha particles, decaying successively, often with beta particles emitted, until a stable nucleus is formed. Alpha decay is a quick way to lower proton and neutron numbers. A decay series is the series of radioactive decays a nucleus undergoes to reach a stable isotope. 36 Nuclear Stability The decay series starting with 238U involves a series of alpha and beta emissions before it eventually produces a stable 206Pb product. 37 Nuclear Stability The nucleons (protons and neutrons) are held together by the strong nuclear force. The strong nuclear force acts through the very short distances between nucleons and overcomes the coulombic repulsion between protons in the nucleus. The strong nuclear force acts between protons and neutrons. Neutrons help hold the nucleus together. Neutrons may “dilute” protons in the nucleus, keeping the protons farther apart to minimize coulombic repulsion. These two neutron functions may help explain the need for a larger ratio of neutrons to protons in heavier nuclei. 38 Energetics of Nuclear Reactions Binding energy is the energy released when a nucleus is formed from a collection of free nucleons. Binding energy is also the energy required to take apart a nucleus. The greater the binding energy, the more stable the nucleus. 39 Binding Energy A helium-4 atom is composed of 2 protons and 2 neutrons. Each proton has a mass of 1.007825 u. Each neutron has a mass of 1.008665 u. The sum of 2 protons and 2 neutrons is 4.032980 u. The experimentally observed mass of helium-4 is 4.002603 u. The difference between calculated mass and measured mass is the mass defect, Δm. Δm = 0.030377 u for helium-4. The missing mass is converted to binding energy, Eb, according to Einstein’s equation, E = mc2. Eb = 4.5335 × 10-12 J or 2.7301 × 109 kJ mol-1. 40 Binding Energy The binding energy per nucleon plotted as a function of mass number for elements hydrogen through uranium. The curve reaches a maximum at 56Fe. 41 Magic Numbers and Nuclear Shells Of the more than 260 stable nuclei, most have even numbers of both protons and neutrons. Only a handful, such as 14N, have odd numbers of both. The rest have either even numbers of protons and odd numbers of neutrons or vice versa. 42 Magic Numbers and Nuclear Shells Isotopes with atomic numbers, Z, or neutron numbers, N, of 2, 8, 20, 28, 50, 82, 126, or 184 show special stability. These values are referred to as magic numbers. Any isotope in which Z or N is a magic number can be expected to be especially stable. If both Z and N are magic number values, the effect is greater and the nucleus is said to be “doubly magic.” 43 Transmutation, Fission, and Fusion There are three categories of nuclear reactions. Transmutation, where one nucleus changes into another, either by natural decay or in response to some outside intervention. Fission, a heavy nucleus splits into lighter nuclei. Fusion, light nuclei merge into a heavier nucleus. 44 Transmutation 10B reacts via neutron capture to produce 11B*, an unstable intermediate nucleus called the compound nucleus, which decays almost instantly like an activated complex in a chemical reaction. The compound nucleus decays almost instantly, emitting particles and energy to produce a stable nucleus. 10 5 B + n ¾ 1 0 ¾® B ¾ ¾® Li + He 11 5 * 7 3 4 2 45 Fission Nuclei that undergo fission are fissionable or fissile. Some fission reactions are spontaneous. Others are induced by neutron bombardment, which can also increase the rate of a spontaneous fission process. During an induced fission reaction, a neutron is absorbed by a large fissile nucleus, producing a compound nucleus that separates into two smaller parts, emitting neutrons in the process. 235 92 U + 01 n ¾¾ ® 236 92 U* 236 92 U* ¾¾ ® 141 56 Ba + 92 36 Kr + 3 01 n 46 Fission The neutrons produced during fission can induce further fission via a process called a chain reaction. Chain reactions occur when there are sufficient fissile atoms to ensure the produced neutrons can induce fission before escaping the sample. Critical mass - the amount of material required to sustain a chain reaction. Controlled fission can be used to generate electricity. 47 Fission Bombarding enriched uranium with neutrons induces the fission of 235U, and each decay produces additional neutrons for further induced fission. 48 Fission Fission and fusion both lead to more stable nuclei. Light nuclei undergo fusion to produce a heavier product. Heavier nuclei undergo fission to produce lighter nuclei. 49 Example Problem 14.6 Calculate the energy released by a nucleus of uranium-235 if it splits into a barium-141 nucleus and a krypton-92 nucleus according to the equation shown below. 235 92 U+ n ® 1 0 236 92 U ® * 141 56 Ba + 92 36 1 Kr + 3 n 0 50 Nuclear Reactors 235U is the fissionable material found in commercial nuclear reactors. Only 0.72% of naturally occurring U is fissile 235U. Uranium is enriched to increase the percentage 235U before it can be used as fuel. Enriching uranium separates 235U from 238U. 238U makes up more than 99% of naturally occurring uranium. Weapons-grade uranium is typically >90% 235U. Nuclear reactors contain 3-5% 235U. 51 Nuclear Reactors The uranium oxide fuel is embedded into fuel rods and placed in a water-covered reactor core. The water cools the fuel rods and moderates the reactor, slowing down fast neutrons. The water carries heat released to the steam turbine. Steam turns the turbine, which generates electricity. The chain reaction is initiated by a source of neutrons. The chain reaction is regulated via control rods. The control rods are inserted between the fuel rods to slow or stop the chain reaction. Control rods are composed of cadmium or boron and regulate the chain reaction by absorbing extra neutrons to maintain a steady rate of fission. 52 Nuclear Reactors The general design used in all U.S. nuclear power plants. 53 Nuclear Waste Several of the fission products in a nuclear reactor are radioactive. The radioactive products are concentrated in the used or “spent” fuel rods. The fuel rods are referred to as high-level nuclear waste. The half-lives of several of the products are very long, requiring special storage or disposal. Spent fuel rods can be reprocessed into new fuel rods. Reprocessing is not carried out in the United States due to regulatory concerns and nuclear nonproliferation treaties. All high-level waste is currently stored on-site at the reactor. On-site storage is not a long term solution. 54 Nuclear Waste Yucca Mountain, in southwest Nevada, was proposed as the site for an extensive feasibility study for long term storage of high-level waste because it fulfills several general engineering considerations. Yucca Mountain is extremely remote, the climate is dry, and the water level is about 1000 feet below the potential burial vault. The storage facility must be remain intact for thousands of years. The construction materials will need to withstand the effects of high levels of radiation. 55 Fusion In the sun, four hydrogen nuclei combine to form a helium nucleus, releasing energy in the process. The reaction of 4 protons is a stepwise process, too slow to be used in a nuclear reactor. ® 42 He + 2 10 b + 2n + energy 4 11 H ¾¾ The two heavier isotopes of hydrogen, deuterium (2H) and tritium (3H) can be fused to produce helium The reaction produces more energy per nucleus than fission. 2 1 H + H ¾ 3 1 ¾® He + n 4 2 1 0 56 Fusion Deuterium is naturally occurring; it makes up 0.015% of all hydrogen atoms. The available supply of deuterium is practically unlimited. Tritium can be produced from 6Li. 6 3 Li + n ¾ 1 0 ¾® He + H 4 2 3 1 Fusion does not produce high-level radioactive waste. Energetic neutrons can induce nuclear reactions in reactor materials, producing some level of radioactivity. Risk minimized by careful choices of engineering materials. 57 Fusion During fusion, the repulsion of positively charged nuclei must be overcome. Fusion reactions initiated at temperatures on the order of 106 K. High temperature required to force nuclei close enough to overcome coulombic repulsion. The first application of fusion was the hydrogen bomb. A fission bomb initiated the fusion reaction. Controlled fusion must use a nondestructive means of initiation. As an energy source, fusion must release more energy than it requires as input. 58 Fusion The fusion reaction must be confined somehow. Solid reactor materials would melt at the high initiation temperatures. Two promising means for solving the confinement problem. Magnetic confinement: The high-energy plasma produced at 106 K is controlled in a magnetic field. Inertial confinement: A pellet of fuel is dropped into a reaction chamber and imploded by high-energy lasers. So far, more energy is required to produce fusion than is released. 59 Interaction of Radiation and Matter There are three factors governing the effects of radiation on matter. The amount of radiation to which matter is exposed. Penetrating power of the radiation. Ionizing power of the radiation. If radiation energy is greater than typical ionization energies for atoms and molecules, the radiation could induce ionization in material encountered. 60 Ionizing and Penetrating Power of Radiation Radiation is classified as either ionizing or nonionizing. The distinction is based on the energy carried by a photon or particle. Nonionizing radiation includes visible light, radio waves and microwaves. Photon energies are less than typical ionization energies. Ionizing radiation includes alpha and beta particles, X-rays, and gamma rays. Photon energies are greater than typical ionization energies. 61 Ionizing and Penetrating Power of Radiation Ionization radiation can cause significant damage to any material encountered, including living tissue, by free radical formation. Ionizing radiation ejects electrons from atoms and molecules it encounters. Free radicals scavenge electrons from other molecules, causing damage to tissue. Through free radical formation, ionizing radiation can lead directly to cell death. Penetrating power must be taken into account when examining the impact of radiation on matter. Penetrating power is how far a particle penetrates into a material before its energy is absorbed or dissipated. 62 Ionizing and Penetrating Power of Radiation Alpha particles have greater ionizing power. The relatively large size and charge of alpha particles prevent alpha particles from penetrating deeply into matter. The dissipated energy can cause surface burns on the skin, but do no serious harm because alpha particles can not reach internal organs. Alpha particles produced inside the body cause much greater damage because energy is deposited in the internal organs. This is how radon gas causes serious tissue damage. 63 Ionizing and Penetrating Power of Radiation Beta particles have lower energy than alpha particles. Due to their smaller size/charge, most beta particles can pass several centimeters into the body. Due to its penetrating power, beta radiation is often more dangerous than that from alpha particles. Gamma particles can pass entirely though the body, depositing energy in the vital organs, causing damage. 64 Ionizing and Penetrating Power of Radiation The possible health hazards from exposure to ionizing radiation depend on the penetrating power of the radiation. 65 Ionizing and Penetrating Power of Radiation Ionizing and penetrating power must be considered when designing space-bound electronic devices. Computer chips and other solid-state devices rely on carefully controlled distributions of electrons and holes in semiconductor materials. Production of ions by ionizing radiation can cause catastrophic failure of electronic devices. The single event effect results when a single ionizing particle can produce large numbers of ions. Electronics in satellites are packaged in “hardened” materials to protect against cosmic rays. 66 Methods of Detecting Radiation To assess radiation doses, the type and amount of radiation must be measured. The first measurements used a zinc sulfide phosphor, which produced tiny flashes of light when struck by radiation and the light flashes were counted manually. A scintillation counter uses a fluorescent screen to detect radiation, but the resulting photon strikes a phosphor that releases an electron instead of light flashes. A photomultiplier tube amplifies the electronic signal, producing a current pulse registered electronically. 67 Methods of Detecting Radiation The Geiger counter is a portable detector used to measure radioactivity. A glass tube containing a gas at low pressure (0.1 atm) is coated on the inside with a metal that acts as a cathode. An anode wire runs down the center of the tube. A high voltage is applied across the electrodes. Alpha and beta particles enter though a window and ionize the gas atoms. Electrons released by the gas atoms are attracted to the anode, and ionize more gas as they travel to the anode, releasing more electrons. When the avalanche of electrons reaches the anode, a current pulse is recorded. 68 Methods of Detecting Radiation In a Geiger-Mueller tube, radiation passes through a thin window into a gas-filled tube, producing ions in the gas. The resulting ions are attracted to oppositely charged electrodes, producing a pulse of electric current. 69 Methods of Detecting Radiation A film-badge dosimeter monitors the radiation exposure for people who work with radioactive isotopes. Radiation darkens photographic plates. The darkened badge and a record of exposure provides a warning mechanism if safety levels are exceeded. All measurement methods must take background radiation into account when making measurements. Cosmic rays and natural radioactive isotopes in soil, air, and water are sources of background radiation. Background radiation must be subtracted from measurements of radioactive sources. 70 Measuring Radiation Dose The interplay between ionizing power and penetrating power results in a number of different ways to express radiation dose. The quality factor, Q, is used to calculate the equivalent dose and is also known as the relative biological effectiveness (RBE). The value of Q varies from a value of one for high-energy photons to about 20 for alpha particles. 71 Measuring Radiation Dose Definitions and units used to quantify exposure to radiation. 72 Modern Medical Imaging Methods Modern imaging methods include the use of radioisotopes to obtain images of specific organs and elaborate techniques such as positron emission tomography (PET). During an X-ray, X-ray radiation passes through the body and a photographic image is produced based on the amount of radiation absorbed. Bone absorbs X-rays more strongly than organs or other tissues, and is an excellent orthopedic diagnostic tool. X-rays can also be used to examine the structure of some organs, such as a chest X-ray to examine the lungs or heart. 73 Modern Medical Imaging Methods The function of organs can be examined by selectively introducing small amounts of an appropriate radioisotope into the target organ. Radiation from the isotope is monitored to produce a detailed image of the organ. Structure, as well as function, can be revealed. The radioactive isotopes are introduced into target organs by taking advantage of biochemistry. Certain atoms and compounds are taken up specifically by particular organs. The thyroid gland uses iodine to produce thyroid hormone. Radioactive 131I is introduced and carried to the thyroid via natural biochemical pathways. 74 Modern Medical Imaging Methods In the thyroid, the 131I undergoes beta decay. Detection of the gamma particles produces an image of the thyroid gland. The procedure is extremely safe because the radiation dose is fairly small and the half-life of the isotopes is not too long. PET images are based on isotopes that emit positrons. Neutron-deficient isotopes tend to emit positrons. Available positron emitters are 11C, 18F, 13N, and 15O. These elements are found in common organic molecules, allowing for easy incorporation into appropriate biological molecules. 75 Modern Medical Imaging Methods Each decay of the radioisotope releases a positron. Positrons have extremely short lifetimes in the body. Positrons travel no more than a couple of millimeters before encountering an electron. The positron and electron undergo matter-antimatter annihilation. The positron-electron annihilation produces two gamma rays 180 degrees apart. Detectors register the gamma rays, and computers map out the path taken by the tagged compounds. The result is a map of a slice through the body. 76 Modern Medical Imaging Methods Positron emission tomography (PET) produces high-quality images of the brain and other organs. 77