Solution for Mastering Chemistry Assign 7

                              Isomers and Enantiomers Learning Goal: To identify coordination (ionization), linkage, and stereoisomers. Isomers are compounds that have the same formula but different arrangement of their constituent atoms. Isomers can be divided into two general classes: constitutional isomers, in which the connections between atoms differ, and stereoisomers, in which the connections between atoms are the same but there is a different spatial arrangement of the constituent atoms. There are two types of constitutional isomers: coordination isomers (also called ionization isomers), which produce different complex ions in solution, and linkage isomers, which differ in the metal-to-ligand linkage. The former can be viewed as containing different complex salt ions. There are also two types of stereoisomers: diastereomers (geometric isomers), which are non-mirror-image isomers, and enantiomers, which are mirror-image isomers. Diastereomers (cis and trans) have the same connections between atoms but differ in the spatial arrangement of the atoms. Enantiomers are mirror images of each other and cannot be superimposed even if rotated in space. Naming Coordination Compounds A coordination complex (or coordination compound) consists of a central metal ion surrounded by ions or neutral molecules called ligands. The name of the complex specifies the number and types of ligands, as well as the name and oxidation number of the metal. Here are some common ligands and their names: Examples To get an idea of how coordination complexes are named, consider the following examples: diamminediaquaplatinum(II), tetrachloroplatinate(II), potassium tetrachloroplatinate(II), and bis(ethylenediamine)platinum(II). Notice that "platinum" becomes "platinate" only if the complex has an overall negative charge. Similarly, copper, gold, and iron become cuprate, aurate, and ferrate, respectively, in complex anions. Also note that for the ethylenediamine ligand, , the prefixes bis, tris, and tetrakis are used instead of di, tri, and tetra. Metal Complexes Learning Goal: To learn about metal complexes and their geometries and to predict something about their stabilities. Metal complexes consist of a central metal ion bonded to one or more ligands. Metal complexes can be positive, neutral, or negative. Electrically charged metal complexes are called complex ions. A compound consisting of a metal complex is called a coordination compound. The coordination number of a compound is the number of metal-ligand bonds (often equal to the number of ligands). Visualizing Complexes The energies of the d orbitals in the metal of a complex ion depend on the relative orientation of the d orbital to the negative charge of the ligands. In other words, different geometries result in different splitting patterns. When the ligand and its negative charge are aligned with a d orbital, that d orbital has a higher energy than another d orbital whose orientation is at an angle or is less direct. The higher energy d orbitals in the splitting pattern will be the ones with lobes closer to the negative charge of the ligand; those with lower energy will be the ones with lobes further away from the ligand charge. Isomers of complex ions Isomers have the same molecular formula but different arrangements of the component atoms in space. Complex ions exhibits three common types of isomerism: Coordination-sphere isomers differ in the ligands that are directly bonded to metal as opposed to those outside the coordination sphere in the solid lattice. Geometric isomers have the same chemical bonds but different spatial arrangements of the atoms. Optical isomers (enantiomers) are mirror images that cannot be superimposed on each other. Exercise 24.22: Problems by Topic - Coordination Compounds Exercise 24.25: Problems by Topic - Coordination Compounds Write the correct formula for the following compounds. Exercise 24.33: Problems by Topic - Structure and Isomerism Will the following complexes exhibit geometric isomerism? A Molecular View of Thermodynamics Learning Goal: To use molecular-level diagrams to predict the signs of thermodynamic properties. The equations and relate entropy change, , enthalpy change, , free energy change, , and the equilibrium constant, , for a given reaction at a given temperature. Free Energy and the Reaction Quotient Learning Goal: To understand how free energy relates to equilibrium under standard and nonstandard conditions. The drive toward equilibrium is what makes a reaction spontaneous. This drive is quantified by , a state function known as free energy. A negative value of indicates a spontaneous reaction. Standard free energies of formation, , can be used to calculate the standard free energy of reaction, , for any given chemical equation. Standard free energy is related to the equilibrium constant by the equation , where is the Kelvin temperature and is the gas constant equal to 8.314 . Standard thermodynamic conditions are 1 and 298 . Free energy is related to the reaction quotient by the equation , where is the Kelvin temperature and is the gas constant equal to 8.314 . Nitrosyl chloride formation Chlorine gas, , reacts with nitric oxide, , to form nitrosyl chloride, , via the reaction The thermodynamic data for the reactants and products in the reaction are given in the following table: The diagram below serves as a pictorial depiction of the relationship between the free energy and standard free energy in the equation . Point A is at standard conditions, which means all reagents have a partial pressure of 1 , as shown in the equation below point A. Points B and C are at nonstandard conditions. Point X indicates the point at which equilibrium lies. The axis labeled refers to the reaction quotient. The actual value of at the point of equilibrium is , which is the equilibrium constant at 298 . Standard Free Energy of Formation The standard free energy of formation, , of a substance is the free energy change for the formation of one mole of the substance from the component elements in their standard states. These values are applicable at 25 and are found in thermodynamic tables. The value of for a substance gives a measure of the thermodynamic stability with respect to the component elements. Negative values for a formation reaction indicate thermodynamic stability of the product. In other words, the compound formed does not spontaneously decompose back into the component elements. Positive values for a formation reaction indicate thermodynamic instability of the product. Thus, the compound will spontaneously decompose, though the rate may be slow. The sign of can be used to predict the feasibility of synthesizing a substance from its component elements. The standard free energy change for a reaction, , is a state function and can be calculated from the standard free energies of formation as follows: Coupled Reactions In nature, one common strategy to make thermodynamically unfavorable reactions proceed is to couple them chemically to reactions that are thermodynamically favorable. As long as the overall reaction is thermodynamically favorable, even the unfavorable reaction will proceed. Enthalpy, Entropy, and Spontaneity The spontaneity of a reaction depends both on the enthalpy change, , and entropy change, . Reactions that release energy produce more stable products, and the universe tends toward disorder. Thus, an exothermic reaction with a positive entropy change will always be spontaneous. Mathematically, this relationship can be represented as where is the change in Gibbs free energy and is the Kelvin temperature. If is negative, then the reaction is spontaneous. If is positive, then the reaction is nonspontaneous as written but spontaneous in the reverse direction. Gibbs Free Energy and Equilibrium The reaction is the basis of a suggested method for removal of from power-plant stack gases. The values below may be helpful when answering questions about the process. Exercise 17.76: Problems by Topic - Free Energy Changes, Nonstandard Conditions, and the Equilibrium Constant Consider the following reaction: The data in the table show the equilibrium constant for this reaction measured at several different temperatures. Exercise 17.38: Problems by Topic - Entropy, the Second Law of Thermodynamics, and the Direction of Spontaneous Change Given the values of , , and below, determine . Exercise 17.86: Cumulative Problems The standard free energy change for the hydrolysis of is -30.5 . In a particular cell, the concentrations of , , and are 3.3×10?3 , 1.2×10?3 , and 4.9×10?3 , respectively.