2.14 The net potential energy between two adja- cent ions, EN, may be represented by the sum of Equations 2.8 and 2.9; that is, A B EN = (2.11)
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- A gold nucleus is located at the origin of coordinates, andan electron is brought to a position 2 Å from the origin inthe 1y direction.(a) Calculate the force on the gold nucleus exerted by theelectron giving its components Fx and Fy.(b) Calculate the potential energy of the gold nucleus andthe electron.At large interatomic separations, an alkali halide molecule MX has a lower energy as two neutral atoms, M+X ; at short separations, the ionic form (M+)(X) has a lower energy. At a certain distance, Rc , the energies of the two forms become equal, and it is near this distance that the electron will jump from the metal to the halogen atom during a collision. Because the forces between neutral atoms are weak at large distances, a reasonably good approximation can be made by ignoring any variation in potential V(R) for the neutral atoms between Rc and R= . For the ions in this distance range, Rc is dominated by their Coulomb attraction. (a) Express Rc for the first ionization energy of the metal M and the electron affinity of the halogen X. (b) Calculate Rc for LiF, KBr, and NaCl using data fromAppendix F.To ionize Mg to Mg2+ costs two times as much energy as to form Mg+. The formation of O2- is endothermic rather than exothermic as for O-. Nevertheless, magnesium oxide is always formulated as Mg2+ O2- rather than Mg+O-a) Give theoretical reason for formulation of Mg2+O2-b) What simple experiment could be done to predict that magnesium oxide wasnot Mg+O- ?
- In a lithium-ionbattery that is discharging to power a device, for every Li+that inserts into the lithium cobalt oxide electrode, a Co4+ion must be reduced to a Co3+ ion to balance charge. Usingthe CRC Handbook of Chemistry and Physics or other standardreference, find the ionic radii of Li+, Co3+, and Co4+. Orderthese ions from smallest to largest.Two particles with charges ?1q1 and ?2q2 are separated by distance ?.d. Arrange these scenarios according to the magnitude of the electrostatic (coulombic) potential energy. Ignore sign.Which group in the periodic table has elements with high (en-dothermic) IE₁ and very negative (exothermic) first electronaffinities (EA₁)? Give the charge on the ions these atoms form
- (a) Which ion is smaller, Co3+ or Co4+? (b) In a lithium-ionbattery that is discharging to power a device, for every Li+that inserts into the lithium cobalt oxide electrode, a Co4+ion must be reduced to a Co3+ ion to balance charge. Using the CRC Handbook of Chemistry and Physics or other standardreference, find the ionic radii of Li+, Co3+, and Co4+. Orderthese ions from smallest to largest. (c) Will the lithium cobaltoxide cathode expand or contract as lithium ions areinserted? (d) Lithium is not nearly as abundant as sodium.If sodium ion batteries were developed that function in thesame manner as lithium ion batteries, do you think “sodiumcobalt oxide” would still work as the electrode material?Explain. (e) If you don’t think cobalt would work as the redox-active partner ion in the sodium version of the electrode,suggest an alternative metal ion and explain your reasoning.(a) Calculate the energy in joules of a 3.23 g object moving at a speed of 713 m/s.Ek = J(b) Determine how much greater the electrostatic energy is between charges of +2 and −2 than it is between charges of +1 and −1 (assume that the distance between the charges is the same in each case).1.5 times2.0 times2.5 times3.0 times3.5 times4.0 times4.5 times5.0 times1) How much energy (in MJ) is required to ionize 21.14 moles of hydrogen atoms?
- In a typical fireworks device, the heat of the reaction betweena strong oxidizing agent, such as KClO₄, and an organic com-pound excites certain salts, which emit specific colors. Stron-tium salts have an intense emission at 641 nm, and barium saltshave one at 493 nm. (a) What colors do these emissions pro-duce? (b) What is the energy (in kJ) of these emissions for 5.00 g each of the chloride salts of Sr and Ba? (Assume that allthe heat released is converted to light emitted.)In the chemical process called electron transfer, an electron istransferred from one atom or molecule to another. A simpleelectron transfer reaction isA(g) + A(g)---->A+(g) + A-(g) In terms of the ionization energy and electron affinity ofatom A, what is the energy change for this reaction? For arepresentative nonmetal such as chlorine, is this process exothermic?For a representative metal such as sodium, is thisprocess exothermic?The first ionization enthalpy for Li is 520 kJ mol^-1. This value corresponds to complete removal of the electron from the nucleus and is achieved when n = infinity. From this value, calculate the effective charge felt by the 2s electron of Li. Why is this less than the actual charge of +3?