Energetics II

• lattice enthalpy - the standard enthalpy change when 1 mole of an ionic crystal lattice is formed from its constituent ions in the gaseous state.

  e.g. $Na^+$$\left(g\right)+$$\ Cl^-\left(g\right)\ \rightarrow\ NaCl\ \left(s\right)$
• first ionisation enthalpy - the enthalpy change when 1 mole of electrons is removed from 1 mol of gaseous atoms to form 1 mole of gaseous ions with a single positive charge.

  E.g. $H\left(g\right)\ \rightarrow\ H^+$$\left(g\right)\ +$$\ e^-$
• second ionisation enthalpy - the enthalpy change when 1 mol of electrons is removed from when 1 mole of gaseous ions with a single positive charge to form 1 mole of gaseous ions with a 2+ charge.

  E.g. $Mg^+$$\left(g\right)\ \rightarrow\ Mg^{2+}\left(g\right)\ +$$\ e^-$
• enthalpy of atomisation - the enthalpy change when 1 mole of gaseous atoms is formed from the element in its standard state.

  
  

  (*In a born haber cycle if you were to calculate this value for:

  F2 going to 2F, its value would be multiplied by 2).

  
  

  e.g. $Na\ \left(s\right)\ \rightarrow\ Na\left(g\right)$
• bond dissociation enthalpy - the enthalpy change required to break 1 mole of gaseous covalent bonds into gaseous atoms.

  
  

  (*This value is 2x the value of the enthalpy of atomisation)

  
  

  e.g. $Br_2\left(g\right)\ \rightarrow\ 2\ Br\ \left(g\right)$
• first electron affinity - the enthalpy change when 1 mol of electrons is added to 1 mol of gaseous atoms forms 1 mole of gaseous ions with a 1- charge.

  e.g. $O\ \left(g\right)\ +$$\ e^-\rightarrow\ O^-\left(g\right)$
• second electron affinity - the enthalpy change when 1 mol of electrons is added to 1 mole of gaseous ions with a single negative charge to form 1 mole of gaseous ions with a 2- charge.
• enthalpy of hydration - the enthalpy change when 1 mole of gaseous ions is dissolved in water to form 1 mol of aqueous ions

  e.g. $X^+$$(g)\ +$$\ (aq)\ \rightarrow\ X^{_+}(aq)$

  this process is always exothermic as forces/bonds form between ions and water.
• enthalpy of solution - the standard enthalpy change when 1 mole of an ionic solid dissolves in a large enough amount of water to ensure that the dissolved ions are well separated and don't interact with eachother (a solution of infinite dilution)

  e.g. $NaCl(s)\ +$$\ (aq)\ \rightarrow\ Na^+$$(aq)+$$Cl^-(aq)$
• lattice enthalpy Born-Haber cycle:

  
• the larger the magnitude of the lattice enthalpy, the stronger the attraction between the ions. The more charge dense the cation and the anion, the more attraction between them, and hence the greater the magnitude of the lattice enthalpy. Therefore, lattice enthalpy is directly proportional to $\frac{e^+e^-}{r^+r^-}$
• experimental lattice energies - calculated from born-haber cycles, and are a measure of the ionic bonds with covalent character.

  
  

  Covalent character leads to there being a more exothermic value for lattice energy, as it increases the strength of the bond/attraction due to partial electron sharing.
• theoretical lattice energy - a measure of the ionic bonding only. These are calculated using the following assumptions:

  • ions are perfect spheres
  • ions are point charges (they have no dimensions and hence impossible to be distorted).
• A compound which has a small difference between theoretical and experimental lattice energies is almost purely ionic.

  The bigger the difference between experimental and theoretical lattice enthalpy, the greater the degree of covalent character which is displayed by a compound.
• Factors affecting the amount of covalent character (cations):

  • charge - the higher the charge, the greater the polarisation of the anion, and hence more covalent character.
  • ionic radius - the smaller the ionic radius, the greater the polarisation of the anion, and hence covalent character.

  talking about charge density only IS NOT ENOUGH
• Factors affecting the amount of covalent character (anions):

  • charge - the higher the charge of the anion, the greater its polarisability (ease of distortion) and thus covalent character.
  • ionic radius - the larger the ionic radius, the more polarisable the anion is, and thus the more covalent character it possesses.
• enthalpy of solution Born-Haber cycle

  
• spontaneous process - a reaction that proceeds without a continuous input of energy/any external influence
• In an exothermic reaction (products losing energy), the products are more thermodynamically stable than the reactants. This is the driving force for the reaction, making it spontaneous.

  
  

  A reaction is likely to occur if it leads to a decrease in enthalpy and/or an increase in entropy, such that ΔG is negative.
• in an endothermic reaction (products gaining energy), the products are less thermodynamically stable than the reactants. This means there is no driving force for the reaction.

  Thus, if enthalpy were the only thing to consider, endothermic reactions wouldn't occur. Thus there is another factor — entropy.
• entropy - the measure of disorder (the more disordered the higher entropy)

  
  

  The more degrees of freedom a substance has, the more disordered it is.
• entropy increases as temperature increases as particles have more kinetic energy and are hence more disordered.
• For a perfectly order crystaline solid at 0K, particles are stationary, so entropy is 0 (3rd Law of thermodynamics).

  Thus, for a spontaneous reaction, total entropy must be greater than 0.
• There will be a positive entropy change (more disorder) if:

  • there is a change of state from solid to liquid or liquid to gas.
  • there is an increase in the number of molecules/moles between products and reactants.

  Negative entropy changes will be observed for the reverse.

  The larger the relative formula mass of a gas, the greater its molar entropy.
• the entropy change of the system can be calculated from the following equation:

  
• the entropy change of the surroundings can be calculated from the enthalpy change of the reaction/system, and the temp in Kelvin (the ΔH is normally written in KJmol, so you need to convert to Jmol (this is the unit for ΔS)

  
• total entropy change can be calculated from the following equation:

  
• Gibbs free energy change determines if a reaction is feasible/spontaneous or not:

  • a spontaneous change has a negative value of $\Delta G$
  • a non-spontaneous change has a positive value of $\Delta G$

  $\Delta G$ is calculated from the following reaction:

  
• Gibbs free energy change tells us if a reaction is spontaneous. It tells us nothing about reaction rate however:

  • Gibbs free energy may be negative for a certain process, HOWEVER, the rate may be so slow that the reaction effectively doesn't occur.
• the effect of temperature on Gibbs free energy change is dependent on entropy change and enthalpy change:

  • if $\Delta S$(system) is positive, increasing the temp will make the reaction more likely to have a negative $\Delta G$ (spontaneous)
  • if $\Delta S$(system) is negative, increasing the temp will make the reaction less likely to have a negative $\Delta G$ (non-spontaneous)
• temp can be calculated using the Gibbs free energy change equation:

  
• as a reaction becomes spontaneous when $\Delta G$ = 0, the temperature at which a reaction becomes spontaneous is given by:

  
• the Gibbs free energy change can be calculated from the equilibrium constant for a reversible reaction as well:

  If K>1 (more products than reactants, and hence spontaneous), the forwards reaction will have a negative $\Delta G$

  if K<1 (less products than reactants and hence not spontaneous), the forwards reaction will have a positive $\Delta G$

  
• entropy and changes in state

  
• a positive entropy change from reactants to products means the products are more stable, as the reaction is thermodynamically feasible.

  
  

  A reaction won't occur if the product is less stable.
• enthalpy of hydration diagram:

  
• whether or not a reaction occurs depends on the thermodynamic feasibility calculated using:

  $ΔG\ =$$\ ΔH\ -\ TΔS_{system}$

  • if both $ΔH\ and\ ΔS_{system}$ are negative, a reaction is feasible when $ΔH\ >TΔS_{system}$
  • if both $ΔH\ and\ ΔS_{system\ }$are positive, a reaction is feasible when $TΔS_{system}>ΔH$
  • if $ΔS_{system\ }$is positive and $ΔH\$is negative, the reaction is always feasible.
  • if $ΔH\$is positive and $ΔS_{system\ }$is negative, the reaction is never feasible.

  *The reaction still may not occur due to kinetic factors.