1.8.1 Born-Haber cycles

use of Born-Haber cycles

allow lattice enthalpies to be calculated which cannot be measured directly

• we cannot isolate 1 mole of free, oppositely charged gaseous ions

anhydrgrous magnesium chloride can absorb water to form the hydrated salt MgCl₂.4H₂O

MgCl_{2 (s)} + 4 H₂O _(l) → MgCl₂.4H₂O _(s)

why can’t the enthalpy change for this reaction cannot be determined directly by calorimetry?

MgCl₂ is soluble, not possible to prevent some dissolving

upwards arrow on Born-Haber cycles

endothermic reaction

downwards arrow on Born-Haber cycles

exothermic reaction

enthalpy of lattice dissociation

the enthalpy change when 1 mole of a solid ionic lattice dissociates fully into gaseous ions under standard conditions

• endothermic

• upwards arrow on Born-Haber cycle

why is the lattice dissociation enthalpy for sodium oxide greater than that for sodium chloride?

• oxide ions have a higher negative charge and a smaller size so have a higher charge density

• so stronger attraction between oxide ions and sodium ions, so more energy required to overcome force of attraction

enthalpy of lattice formation

the enthalpy change when 1 mole of a solid ionic lattice is formed from its gaseous ions in under standard conditions

• exothermic

• downwards arrow

standard enthalpy of formation

enthalpy change when 1 mole of a substance is formed from its elements with all substances in their standard states and under standard conditions

• usually exothermic

• downwards arrow

atomisation enthalpy

the enthalpy required to form 1 mole of gaseous atoms under standard conditions

• endothermic

• upwards arrow

equation for the reaction that represents the atomisation of

• sodium

• chlorine

Na _(s) → Na _(g)

½ Cl_{2 (g)} → Cl _(g)

ionisation enthalpy

the enthalpy required to remove 1 mole of electrons from 1 mole of gaseous atoms to form 1 mole of gaseous 1+ ions, under standard conditions

• endothermic

• upwards arrow

enthalpy of electron affinity

the enthalpy change when 1 mole of electrons is added to 1 mole of gaseous atoms forming 1 mole of gaseous 1- ions, under standard conditions

• first electron affinity is exothermic, downwards arrow

• second electron affinity is endothermic, upwards arrow

  • negative ion formed from the first electron affinity repels the electron being added

mean bond enthalpy

• the enthalpy required to break 1 mole of a specific covalent bond in a gaseous state under standard conditions

• averaged over a range of different compounds containing that bond

enthalpy of hydration

the enthalpy change when 1 mole of gaseous ions is dissolved in water to form 1 mole of aqueous ions under standard conditions

• usually exothermic

why is the enthalpy of hydration of calcium ions less exothermic than that of magnesium ions?

• Ca²⁺ ions are bigger and have a lower charge density

• weaker electrostatic attraction to δ- O in water molecules

• so less energy is released when attractions form

why is the enthalpy of hydration of fluoride ions more negative than that of chloride ions?

• F^- ions are smaller and have a higher charge density

• stronger electrostatic attraction to δ+ H in water molecules

• so more energy is released from this force of attraction

enthalpy of solution

the enthalpy change when 1 mole of an ionic solid is dissolved to water to infinite dilution so that the ions no longer interact, under standard conditions

why do data books not contain a value for the enthalpy of solution of sodium oxide?

it reacts with water to form a solution of NaOH

why do experimental values for enthalpy of solution differ from data books values?

heat gain from surroundings / incomplete dissolving

how to measure the enthalpy of solution

• use a burette to measure 10-200 cm³ of water into a polystyrene cup

• record initial temperature before adding ionic solid

• measure the mass of the weighing boat and (powdered) ionic solid

• add the solid to the cup

• reweigh the weighing boat and subtract to find the exact mass of solid added

  • do NOT add washings

• record temperature after addition at regular intervals for 10 minutes, until a trend is observed

• plot temperature against time

• extrapolate lines to when the solid was added to

how to measure enthalpy of hydration

• cannot be measured directly as we cannot isolate 1 mole of free, oppositely charged gaseous ions and surround them with water

• calculate using enthalpy of solution and lattice enthalpy

link between enthalpy of hydration and enthalpy of solution, example NaCl

perfect ionic model

all ions are perfect spheres and have no covalent character

what is covalent character?

• partial sharing of electrons in an ionic bond

• due to a cation polarising and distorting the electron cloud of an anion

causes of covalent character in an ionic compound

• smaller cation or higher positive charge

• so cation has a higher charge density

• so cation is more polarising

• so polarises and heavily distorts anion electron cloud

_

• large anion or higher negative charge

• so anion has higher charge density

• so anion is less polarisable

• so electron cloud easily polarised and distored by cation

how does covalent character affect lattice enthalpies?

increased covalent character =

• stronger forces holding the lattice together

• experimental lattice enthalpies from Born-Haber cycles will be more exo / more endo (larger in magntitude) than theorectical value calculated using perfect ionic model

the value for enthalpy of lattice formation obtained by experiment is the same as the value obtained by calculation using the perfect ionic model

what does this indicate?

perfectly / purely ionic bonding