Solution for Mastering Chemistry Assign 8

                                      Introduction to Electroplating Learning Goal: To relate current, time, charge, and mass for electroplating calculations. Electroplating is a form of electrolysis in which a metal is deposited on the surface of another metal. To quantify electrolysis, use the following relationships. Electric current is measured in amperes (), which expresses the amount of charge, in coulombs (), that flows per second (): Another unit of charge is the faraday (), which is equal to a mole of electrons and is related to charge in coulombs as follows: Galvanized nails are iron nails that have been plated with zinc to prevent rusting. The relevant reaction is For a large batch of nails, a manufacturer needs to plate a total zinc mass of 4.40  on the surface to get adequate coverage. Introduction to the Nernst Equation Learning Goal: To learn how to use the Nernst equation. The standard reduction potentials listed in any reference table are only valid at standard-state conditions of 25 and 1 . To calculate the cell potential at non-standard-state conditions, one uses the Nernst equation, where is the potential in volts, is the standard potential in volts, is the gas constant, is the temperature in kelvins, is the number of moles of electrons transferred, is the Faraday constant, and is the reaction quotient. Consider the reaction at 61, where 3.30  and 0.210  . Electrolysis of Aqueous Salts Refer to this table of reduction potentials to answer the questions. Electrolytic cells use electricity to cause a nonspontaneous redox reaction to occur. An electrolytic cell is constructed using the following components: a power source, such as a battery, the substance that will undergo electrolysis, and two inert electrodes (usually platinum), which serve as the electrical connection between the power source and the substance undergoing electrolysis. As with any cell, oxidation occurs at the anode and reduction occurs at the cathode. Electrolysis and Current The vapor pressure of water changes with temperature, as shown here. A student designs an ammeter (a device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 3.00 , 14.8  of water-saturated is collected. The temperature and pressure of the system are 25 and 715 . Cell Potential and Free Energy Free-energy change, , is related to cell potential, , by the equation where is the number of moles of electrons transferred and is the Faraday constant. When is measured in volts, must be in joules since . Exercise 18.71: Problems by Topic - Balancing Redox Reactions Calculate and for a redox reaction with  = 1 that has an equilibrium constant of  = 25. Heavy Element Formation Learning Goal: Understand the mechanism through which heavy elements are formed, and balance the equation associated with their formation. A Supernova forms when the gravity of the star is so great that the core of the star can no longer resist the force of gravity and collapses in on itself. As the matter in the star compresses it reaches an unstable state and explodes, blowing most of its matter into space. During the explosion, a great number of neutrons present allow for multiple neutron capture events to take place. This leads to the formation of heavy elements (Z > 58). An example of this type of reaction is the formation of from an nucleus:The neutrons generated in the explosion are taken up by the nucleus to give an unstable intermediate which undergoes radioactive decay to give the more stable . Nuclear Decay Equations Learning Goal: To predict the products of alpha emission, beta emission, positron emission, and electron capture. Radioactivity is the spontaneous emission of radiation from an unstable nucleus. There are four major types of radioactive decay. Alpha () radiation consists of helium nuclei. The helium nucleus is a small particle containing two protons and two neutrons (). Beta () radiation consists of electrons (). Positron emission results from the conversion of a proton in the nucleus to a neutron.The ejected positron () is a particle that has the same mass as an electron but an opposite charge. Electron capture is the capture of an inner shell electron by a proton in the nucleus. The process emits gamma () radiation and results in a proton converting to a neutron. Gamma radiation consists of high-energy electromagnetic radiation. Radioactive Decay Calculations If a substance is radioactive, this means that the nucleus is unstable and will therefore decay by any number of processes (alpha decay, beta decay, etc.). The decay of radioactive elements follows first-order kinetics. Therefore, the rate of decay can be described by the same integrated rate equations and half-life equations that are used to describe the rate of first-order chemical reactions. By manipulation of these equations, we can arrive at the following formula: where is the initial amount or activity, is the amount or activity at time , and is the number of half-lives. The equation relating the number of half-lives to time is where is the length of one half-life. Nuclear Binding Energy Nucleons The term nucleon refers to the particles found in the nucleus of an atom, namely protons and neutrons. A single proton has a mass of 1.007825 . A single neutron has a mass of 1.008665 . Note that amu stands for "atomic mass unit" and is sometimes abbreviated with the symbol .Mass Defect The total mass of the individual nucleons in an atom is always greater than the actual measured mass of the atom. The difference is called the mass defect.Binding Energy The mass defect of an atom corresponds to an amount of energy called the binding energy. Binding energy can be calculated using Einstein's equation, ., where is energy in joules, is mass is kilograms, and is the speed of light, . Predicting Nuclear Stability Predicting nuclear stability is important when determining whether or not a nuclear reaction can take place spontaneously.Use the following set of guidelines to predict the nuclear stability of the elements listed below.1. Stable nuclei have a high neutron-to-proton ratio (greater than 1.25).2. The majority of stable nuclei have even numbers of neutrons and protons.3. Nuclei that have atomic numbers greater than 83 are unstable. Mass-Energy Balance Einstein's famous equation expresses the relationship between energy , in joules, and mass , in kilograms, where  = 3.00×108  is the speed of light. The equation is sometimes expressed as where is the change in energy for a reaction and is the difference in mass between the reactants and products. Measuring Radioactivity Radiation intensity is expressed in different ways, depending on how it is being measured. Mechanical measurements use becquerels () or curies (). Energy absorbed by tissue is expressed in grays () or rads (). Tissue damage is expressed in sieverts () or . These units are related as follows: Radiocarbon Dating All living things contain carbon. Most of this carbon is stable carbon-12. However, a small percentage will be carbon-14, a radioactive isotope of carbon that decays with time. As living things eat and breath, carbon is constantly recycled and therefore the percentage of carbon-14 remains constant. It's not until death that the percentage of carbon-14 will begin to diminish from decay. Because radioactive decay is a first-order process, the integrated rate law for a first-order reaction can be rewritten as where is the time elapsed and is the half-life. The half-life of C-14 is 5730 years.   Study of Plutonium Levels in a Human Population Radiation can be measured according to activity, exposure, or its effect on biological tissue. Units of curies () and disintegrations per second () measure activity. The rad measures exposure, where stands for radiation absorbed dose. The rem measures biological effect, where stands for roentgen equivalent man. RBE is a multiplication factor known as relative biological effectiveness and is approximately 1 for beta and gamma radiation and 10 for alpha radiation. The following conversion factors relate these quantities: Note that the conversion factors between curies and disintegrations per second and between rads and joules per kilogram of tissue are exact (i.e., they contain an infinite number of significant figures). The RBE, however, is approximate and has only one significant figure because it varies with the dose rate, total dose, and type of tissue affected. Tests on human subjects along the East Coast of the United States in 1965 and 1966, following the era of atomic bomb testing, revealed quantities of about 1.11  of plutonium radioactivity (alpha radiation) in a test subject. Exercise 19.57: Problems by Topic - The Kinetics of Radioactive Decay and Radiometric Dating A rock from Australia was found to contain 0.427  of to every 1.00 of . Exercise 19.67: Problems by Topic - Energetics of Nuclear Reactions, Mass Defect, and Nuclear Binding Energy Exercise 19.85: Cumulative Problems Radium-226 (atomic mass = 226.025402 ) decays to radon-224 (a radioactive gas) with a half-life of . Exercise 19.101: Conceptual Problems Identical amounts of two different nuclides, an alpha emitter and a gamma emitter, with roughly equal half-lives are spilled in a building adjacent to your bedroom. Exercise 19.88: Cumulative Problems A typical nuclear reactor produces about 1.0 of power during day.