Lattice Enthalpy

5 Key excerpts on "Lattice Enthalpy"

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  Chemistry: Atoms First

  • William R. Robinson, Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  Multiple bonds are stronger than single bonds between the same atoms. The enthalpy of a reaction can be estimated based on the energy input required to break bonds and the energy released when new bonds are formed. For ionic bonds, the lattice energy is the energy required to separate one mole of a compound into its gas phase ions. Lattice energy increases for ions with higher charges and shorter distances between ions. Lattice energies are often calculated using the Born-Haber cycle, a thermochemical cycle including all of the energetic steps involved in converting elements into an ionic compound. Exercises 9.1 Energy Basics 1. A burning match and a bonfire may have the same temperature, yet you would not sit around a burning match on a fall evening to stay warm. Why not? 2. Prepare a table identifying several energy transitions that take place during the typical operation of an automobile. 3. Explain the difference between heat capacity and specific heat of a substance. 4. Calculate the heat capacity, in joules and in calories per degree, of the following: (a) 28.4 g of water (b) 1.00 oz of lead Chapter 9 | Thermochemistry 507 5. Calculate the heat capacity, in joules and in calories per degree, of the following: (a) 45.8 g of nitrogen gas (b) 1.00 pound of aluminum metal 6. How much heat, in joules and in calories, must be added to a 75.0–g iron block with a specific heat of 0.449 J/g °C to increase its temperature from 25 °C to its melting temperature of 1535 °C? 7. How much heat, in joules and in calories, is required to heat a 28.4-g (1-oz) ice cube from −23.0 °C to −1.0 °C? 8. How much would the temperature of 275 g of water increase if 36.5 kJ of heat were added? 9. If 14.5 kJ of heat were added to 485 g of liquid water, how much would its temperature increase? 10. A piece of unknown substance weighs 44.7 g and requires 2110 J to increase its temperature from 23.2 °C to 89.6 °C.

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  Phases of Matter and their Transitions

  Concepts and Principles for Chemists, Physicists, Engineers, and Materials Scientists

  • Gijsbertus de With(Author)
  • 2023(Publication Date)
  • Wiley-VCH

    (Publisher)

  The enthalpy H is described as a function of the surface tension  , which on its turn depends on the electron density. Upon alloying the electron density adjusts itself, resulting in an ΔH responsible for stability of alloys. In the embedded atom method [86], the energy is given as a sum of pair potentials, typically Morse potentials (r ij ) with parameters p 1 , p 2 , and p 3 , plus an embedding function with as arguments the total electronic charge density q j at the atomic sites. The q j s are obtained from the sum of the q ij s, described by r ij −6 Σ i p i exp(−p i r ij ). A cutoff distance for the q j s and for (r ij ) is used, which is also adjusted for smoothness at cutoff. The embedding parameters are determined by fitting to various experimental data, such as the sublimation energy, lattice constants, and vacancy formation energy. Both models provide useful predictions in the absence of experimental data. 10.7 Lattice Dynamics So far, in sketching the structure and bonding of crystalline solids we used a static image, taking only into account the potential energy of molecules. However, molecules vibrate around their equilibrium positions, and we must include their kinetic energy as well. We focus here on some basic aspects of the coupled dynamics of atoms in crystals, usually denoted as lattice dynamics to estimate the thermal expansivity , the heat capacity C, and the bulk modulus K [7–9, 87, 88]. To describe waves in a lattice, we need again wave vectors, here labeled q, and the periodic boundary conditions.

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  Foundations of Chemistry

  An Introductory Course for Science Students

  • Philippa B. Cranwell, Elizabeth M. Page(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  • When substances react, the bonds between the atoms must be broken. This process is endothermic. 198 Energy, enthalpy, and entropy • When products are formed, new bonds are made, and this process is exothermic. • The bond energy, E (X ─ X), is a measure of the energy required to break a specific type of chemical bond, i.e. X ─ X. • The Born – Haber cycle is an application of Hess ’ s law to the formation of an ionic lattice and allows us to calculate the Lattice Enthalpy for an ionic solid. • Entropy ( S ) is a measure of disorder or randomness in a system. It is related to the distribution of energy in a system. The greater the amount of energy and the larger the number of species, the greater the entropy. • When a system becomes more disordered, it becomes more energetically stable. • The second law of thermodynamics states that the total entropy of the uni-verse increases in a spontaneous process. • The total entropy change in a reaction is given by: Δ S ϴ total = Δ S ϴ system + Δ S ϴ surroundings . • The entropy change in a system is given by: Δ S ϴ system = S ϴ products − S ϴ reactants . • The entropy change of the surroundings is given by: Δ S ϴ surroundings = − Δ H ϴ /T • The Gibbs free energy change for a reaction is related to the enthalpy change by the equation Δ G ϴ = Δ H ϴ − T Δ S ϴ . A spontaneous reaction is one that is likely to happen and has a negative value of Δ G . End-of-chapter questions 1 Calculate the standard enthalpy of hydrogenation of cyclohexene (C 6 H 10 (l)) to cyclohexane(l) (C 6 H 12 (l)) given that the standard enthalpies of combus-tion of the two compounds are − 3752 kJ mol − 1 (cyclohexene) and − 3953 kJ mol − 1 (cyclohexane) and the standard enthalpy of combustion of hydro-gen is − 286 kJ mol − 1 . 2 Copper(I) oxide and copper(II) oxide can both be used in the ceramics indus-try to give blue, green, or red tints to glasses and enamels. The table lists some values for enthalpies of formation of some copper compounds.

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  Materials Science for Engineers

  • J.C. Anderson, Keith D. Leaver, Rees D. Rawlings, Patrick S. Leevers(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  Thus the lattice can no longer be regarded as rigid, for as a pair of atoms move apart, another may insert itself 7.15 MELTING 141 142 THERMAL PROPERTIES: KINETIC THEORY, PHONONS AND PHASE CHANGES between them, destroying the basic structure of the unit cell. Such a structure must be liquid-like, for the mean atomic separation will still be close to that of the solid, but rigidity is totally lost. It is instructive to note that melting a crystal is not a gradual process, as might be expected from the previous paragraph. A crystalline solid does not become progressively less rigid as the temperature rises until complete fluidity exists: in fact the transition occurs abruptly at a well-defined temperature. This is because the liquid state has quite a distinct structure, and therefore has quite a different specific heat from the solid. As the temperature is raised through the melting point, the stability of the liquid structure first becomes equal to and then greater than the stability of the solid state, exactly as for two solid structures. The transition is therefore abrupt, and there are no stable intermediate states between the solid and liquid phases. In contrast, an amorphous solid such as glass undergoes no structural change, and melting is not abrupt, but involves a gradual fall in viscosity as the temperature rises. 7.16 Thermodynamics In this chapter, the thermal behaviour of solids has been discussed in relation to their structure, with the emphasis on the use of atomic models to explain various phenomena. This is not the only way of treating ther-mal properties; historically, the measurement of heat and work and the changes they effect in matter came first, and the subject of thermodynamics was then built up to coordinate all the observed phenomena. Its basic tenets are that heat and work are interchangeable and that energy cannot be created or destroyed.

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  Introduction to the Physics and Chemistry of Materials

  • Robert J. Naumann(Author)
  • 2008(Publication Date)
  • CRC Press

    (Publisher)

  17 Thermal Properties of Solids Now that we know something about how the molecules in a solid vibrate, we are in a position to connect these vibrations to the thermal properties such as heat capacity, thermal conduction, and thermal expansion. 17.1 Lattice Heat Capacity The measurement of heat capacity of solids has been of great theoretical as well as practical interest because the departure of the observed heat capacity from the predictions based on classical concepts was one of the early hints that something was quite wrong with the classical models and that new models based on quantum concepts were necessary to understand what was going on. 17.1.1 Classical Approach Let us use our statistical approach to obtain the average energy of a molecule of a classical monatomic gas using Maxwell – Boltzmann (M B) statistics. The average energy per mol-ecule is given by E h i ¼ ð 1 0 EN ( E )d E N ¼ ð 1 0 EN ( E )d E ð 1 0 N ( E )d E : (17 : 1) For M B statistics, N ( E ) ¼ A e E = kT g ( E )d E and for a three-dimensional (3-D) system, recall that g ( E )d E ¼ CE 1 = 2 d E where C is a constant. Putting this in the above, E h i ¼ ð 1 0 E 3 = 2 e E = kT d E ð 1 0 E 1 = 2 e E = kT d E ¼ 1 2 m ð 1 0 p 4 e p 2 = 2 mkT d p ð 1 0 p 2 e p 2 = 2 mkT d p : (17 : 2) The kinetic energy of a molecule with a momentum component p is p 2 = 2 m and d E ¼ p d p = m . Carrying out the integration, E h i ¼ 1 2 m 3 = 8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32 p ( mkT ) 5 q 1 = 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 8 p ( mkT ) 3 q ¼ 3 2 kT : (17 : 3) 321 Now consider a 1-D gas con fi ned to a tube of length, L . In this case the volume in phase space, D x D p x ¼ h . The number of states between p x and p x þ D p x is given by L D p x = h or g ( E )d E ¼ m 1 = 2 L d E h (2 E ) 1 = 2 : (17 : 4) It is useful to remember that a distribution function such as g ( E )d E is the number of states between E and E þ d E .

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