TOPIC 15

TOPIC 15

ENERGETICS/THERMOCHEMISTRY

15.1

ENERGY CYCLES

By: Merinda Sautel Alameda Int’l Jr/Sr High School Lakewood, CO [email protected]

ESSENTIAL IDEA

The concept of the energy change in a single step reaction being

equivalent to the summation of smaller steps can be applied to changes involving ionic compounds.

NATURE OF SCIENCE (3.2)

Making quantitative measurements with

replicates to ensure reliability – energy cycles allow for the calculation of values that cannot be

determined directly.

INTERNATIONAL- MINDEDNESS

The importance of being able to obtain measurements of something which

cannot be measured directly is significant everywhere. Borehole

temperatures, snow cover depth, glacier recession, rates of evaporation and

precipitation cycles are among some indirect indicators of global warming.

Why is it important for countries to collaborate to combat global problems

like global warming?

UNDERSTANDING/KEY IDEA 15.1.A

Representative equations

(e.g. M

→ M

) can be used for enthalpy/energy of

hydration, ionization,

atomization, electron affinity, lattice, covalent bond and

solution.

GUIDANCE

The following

enthalpy/energy terms should be covered: ionization,

atomization, electron affinity, lattice, covalent bond,

hydration and solution.

• The lattice enthalpy (ΔH

) is defined as the change in enthalpy that occurs when one

mole of a solid ionic compound is separated into its gaseous ions under standard

conditions.

• Electron affinity (ΔH

) is the enthalpy change when one mole of gaseous atoms attracts one mole of electrons.

• Enthalpy change of atomization (ΔH

)

is the heat change when one mole of gaseous atoms are formed from the element in its

standard state.

• The bond enthalpy for a covalent bond (E) or (ΔH

) is defined as the energy needed to break one mole of bonds in gaseous

molecules under standard conditions.

• Ionization energy (ΔH

) is the energy

required to remove a mole of electrons from

a mole of gaseous atoms to form a mole of

cations in the gaseous state.

• ΔH

M

→ M

• E = bond enthalpy

• ΔH

M

→ M

+ e

• ΔH

X

+ e

→ M

• ΔH

MX

→ M

+ X

• ΔH

MX

→ M

+ X

• ΔH

M

→ M

APPLICATION/SKILLS

Be able to construct Born-

Haber cycles for group 1 and

2 oxides and chlorides.

APPLICATION/SKILLS

Be able to calculate enthalpy

changes from Born-Haber or

dissolution energy cycles.

Born-Haber Cycle

• This is an energy cycle based on Hess’s Law.

• This is used because lattice energies cannot be determined directly.

• The formation of an ionic compound from its elements takes place in a

number of steps.

Formation of NaCl

Na

+ ½ Cl

→ NaCl

ΔH

˚ = -411 kJ/mol

• Step 1: Atomize sodium ΔH_atom˚ = +107

• Step 2: Form one chlorine gas ½E(Cl-Cl) = ½(+243) break the Cl₂ bond

½ Cl2(g) → Cl(g) E is bond enthalpy given in table

• Step 3: Remove one e- from the ΔH_i˚= +496 gaseous sodium atom

Na(g) → Na+(g) + e-

• Step 4: One e- is added to the ΔHe˚= -349

• gaseous chlorine atom Cl(g) + e^- → Cl_-(g)

• Step 5: The gaseous ions form ΔH_lat˚ = ?

• one mole of solid NaCl.

• Na+(g) + Cl^- (g)→ NaCl (s)

• ΔHf˚ (NaCl)= ΔHatom˚+½E(Cl-Cl) + ΔHi˚(Na) + ΔHe˚(Cl) - ΔHlat˚(NaCl)

• -411 = 107 + ½ (243) + 496 + (-349) - ΔH_lat˚(NaCl)

• ΔHlat˚(NaCl) = +786.5kJ/mol

ΔH_atom˚ = +107

Na_(g) +½Cl_2(g) ½E(Cl-Cl) = ½(+243) Na_{(g) +} Cl_(g)

ΔH_i˚(Na)= +496

ΔH_f˚ (NaCl)= -411 kJ/mol From Table 10 NaCl_(s)

Na⁺_(g) + e- +Cl^-_(g)

ΔH_e˚(Cl)= -349 Na⁺_(g) + Cl^- _(g)

ΔH_lat˚(NaCl) = ?

OXYGEN EXCEPTION

• Note that when oxygen is used in an ionic

compound that there is a different treatment for (ΔH

)

• If your cation is a 2+ ion, you will be using 2

ionization energies. The 2

ionization energy will have to be given to you in the problem. The 1

can be found in the data booklet.

• Oxygen will have an exothermic 1

(ΔH

) and an endothermic 2

(ΔH

)

• The 2^nd is endothermic because you are trying to add an electron to a negatively charged species and you have to overcome the neg-neg repulsions.

APPLICATION/SKILLS

Be able to relate size and

charge of ions to lattice and

hydration enthalpies.

• Two things affect lattice enthalpy:

• The higher the charge – the stronger the lattice enthalpy.

• The smaller the ion – the stronger the

lattice enthalpy.

UNDERSTANDING/KEY IDEA 15.1.B

Enthalpy of solution,

hydration enthalpy and

lattice enthalpy are related in

an energy cycle.

• The enthalpy change of solution (ΔH

) is

defined as the change in enthalpy that occurs when one mole of a solute is dissolved in a

solvent to form aqueous ions in an infinitely dilute solution under standard conditions.

•

Dissolving an ionic cmpd to make aq ions.

• The enthalpy change of hydration (ΔH

) is defined as the change in enthalpy that occurs when one mole of gaseous ions is dissolved to form an infinitely dilute solution of one mole of aqueous ions under standard conditions.

•

Refers to the individual ions

INFINITELY DILUTE SOLUTIONS

• The interaction between the solute and the solvent water molecules depends upon the concentration of the solution.

• The enthalpy of solution strictly refers to the ideal situation of infinite dilution.

• To obtain this value, measure the enthalpy

changes for solutions with increasing volumes

of water until a limit is reached.

SOLUTIONS

• Ionic compounds are crystal lattices.

• They readily dissolve in water.

• The ions are strongly attracted to the polar water molecule.

• The partial positive charge on the

hydrogen attracts the negative ions.

• The partial negative charge on the

oxygen in the water molecule attracts the positive ions.

• Ions separated from a crystal lattice in this manner become surrounded by

water molecules and are said to be hydrated.

• The strength of interaction between the polar water molecules and the

separated ions is given by the

hydration enthalpy.

• The enthalpy of hydration of individual ions cannot be measured directly

because both types of ions are present and the contribution of each ion cannot be disentangled.

• The problem is resolved by measuring the enthalpy of hydration of the H

ion and then combining this value with the hydration enthalpy of different

compounds to obtain values for

individual ions.

• Remember the enthalpy of hydration of an ion is the enthalpy change that occurs when one mole of gaseous

ions is dissolved to form an infinitely dilute solution of one mole of

aqueous ions.

• There is a force of attraction between the ions and the polar water

molecules so the process is

exothermic and the value for ΔH

is

negative.

• The ΔH

becomes less exothermic as ionic radius increases (down a group).

• The force of attraction is less as the distance between the water molecule and the ions increases.

• The ΔH

becomes more exothermic across a period

because charges increase and size

decreases.

APPLICATION/SKILLS

Be able to construct energy

cycles from hydration, lattice and solution enthalpy. For

example dissolution of solid

NaOH or NH

Cl in water.

GUIDANCE

Values for lattice enthalpies (section 18), enthalpies of

aqueous solutions (section 19), and enthalpies of

hydration (section 20) are

given in the data booklet.

EXAMPLE PROBLEM

• Use an energy cycle to calculate the enthalpy of solution of NaCl from

data sections 18 and 20 in the IB data booklet.

• Compare your value with the value in section 19 of the data booklet and

comment on the disagreement

between the 2 values.

The enthalpy of solution is solved by adding the lattice enthalpy of the ionic solid (section 18) and the separate

hydration enthalpies of the ions (found in section 20 of the IB data booklet).

ΔHsolº = ΔHlatº(NaCl) + ΔHhydº(Na⁺) + ΔHhydº (Cl^-) = +790 – 424 – 359 kJ/mol

= +7 kJ/mol

The value obtained in section 19 is +3.88 kJ/mol.

The % inaccuracy = (7-3.88)/3.88 x 100 = 80%

The disagreement between the two values illustrates a

general problem when a small numerical value is calculated from the difference of two large numerical values.

Citations

International Baccalaureate Organization. Chemistry Guide, First assessment 2016. Updated 2015.

Brown, Catrin, and Mike Ford. Higher Level Chemistry. 2nd ed. N.p.: Pearson Baccalaureate, 2014. Print.

ISBN 978 1 447 95975 5 eBook 978 1 447 95976 2

Most of the information found in this power point comes directly from this textbook.

The power point has been made to directly complement the Higher Level Chemistry textbook by Brown and Ford and is used for direct instructional purposes only.