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3. High Temperature Gases

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Terms and Concepts

Dissociation Diatomic element gases Bond energy, dissociation energy (enthalpi) Flood’s dissociation diagram Vaporization, evaporation, boiling, sublimation Heat of evaporation, enthalpy of evaporation

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Bond dissociation enthalpy

Only a limited number of enthalpies of formation have been measured, and there are many reactions for which ∆Ho

f data is not available for one or more reagent.

When this happens, ∆Horxn for the reaction can not be predicted.

The enthalpy of reaction can be estimated using bond-dissociation enthalpies.

By definition, the bond-dissociation enthalpy for an X-Y bond is the enthalpy of the gas-phase reaction in which this bond is broken to give isolated X and Y atoms.

XY(g)↔X(g) + Y(g)

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Bond dissociation enthalpy The bond-dissociation enthalpy for a C-H bond can be calculated by

combining ∆Hof data to give a net equation in which the only thing that

happens is the breaking of C-H bonds in the gas phase.

CH4(g)→ C(s) + 2 H2(g) ∆Ho = 1 mol x 74.81 kJ/mol CH4C(s)→C(g) ∆Ho = 1 mol x 716.68 kJ/mol C2 H2(g)→4 H(g) ∆Ho = 4 mol x 217.65 kJ/mol HCH4(g)→C(g) + 4 H(g) ∆Ho = 1662.09 kJ

If it takes 1662 kJ/mol to break the four moles of C-H bonds in a mole of CH4, the average bond-dissociation enthalpy for a single C-H bond is about 415 kJ/mol.

Bond-dissociation enthalpies are always positive numbers because it takes energy to break a bond.

When a table of bond energies is used to estimate the enthalpy associated with the formation of a bond, the sign becomes negative because energy is released when bonds are formed.

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Reference: Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference DataSeries," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

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Element gases

Many elements form two-atomic molecules; these dissociate:O2 2 ONa2 2 Na (g)

Equilibrium:

(I)

(II)

(III) , degree of dissociation

2

2

Na

NaP p

pK

tottot

ii p

nnp

221

21

NaNa

Na

nn

n

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Degree of dissociation vs Kp

The degree of dissociation in gases is denoted by the symbol α where α refers to the percentage of gas molecules which dissociate.

Various relationships between Kp and α exist depending on the stoichiometry of the equation.

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Degree of dissociation vs Kp: example

N2O4(g)→2NO2(g) When assuming 1 mol N2O4 that

dissociates Left N2O4 will be (1-α), NO2 formed will be

2 α Thus nN2O4=(1- α); nNO2=2 α ntot = nN2O4+nNO2=1- α +2 α =1+ α Kp=(pNO2)2/pN2O4

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Degree of dissociation vs Kp

And rearranging gives

2

22

2

42

22

42

2

14

114

1112

.2

tottottot

ON

NO

ONp ppp

xx

pp

K NO

ptot

p

ptot

p

pptottotpptotp

KpK

KpK

KKppKKpK

44

4441

2

22222

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Degree of dissociation vs Kp

We approximate:

and further:

We can generalize:

Degree of dissociation can be estimated if we know H0298

and specify T and ptot (see Flood’s diagram).

totp

THf ,

0298

molKcal

S

250298

ptot

p

KpK

4

RS

RTHK p

0298

0298ln

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Boiling point

The boiling point of a liquid is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid

A liquid in a vacuum environment has a lower boiling point than when the liquid is at atmospheric pressure.

A liquid in a high pressure environment has a higher boiling point than when the liquid is at atmospheric pressure. In other words, the boiling point of liquids varies with and depends upon the surrounding environmental pressure.

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Heat of vaporisation

The enthalpy of vaporization, (symbol ∆vH), also known as the heat of vaporization or heat of evaporation, is the energyrequired to transform a given quantity of a substance into a gas.

It is often measured at the normal boiling point of a substance; although tabulated values are usually corrected to 298 K,

The heat of vaporization is temperature-dependent, though a constant heat of vaporization can only be assumed for small temperature ranges

The heat of vaporization diminishes with increasing temperature and it vanishes completely at the critical temperature (Tr=1) because above the critical temperature the liquid and vapor phases don't coexist anymore.

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Determining TbVaporization equilibrium: NaCl (s,l) ⇄ NaCl (g)

At ’boiling point’ (TB),pNaCl = 1 atm, thus:

RS

RTH

RTG

NaClp

vvv

eeepK000

0

0

00

00

00

0ln

SHT

STH

RS

RTH

RS

RTHp

v

vB

vB

v

v

B

v

v

B

vNaCl

Clausius Clapeyron

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For ideal gases:

We get:

Boiling point (very) roughly linearly dependant on H0.

HcalmolKT vB

251

molKcal

S

250

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∆vH

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∆vH

Hydrogen bonding gives larges ∆vH Polar substances have higher ∆vH than similar non

polar substances Similar bonding in similar compounds gives similar ∆vH

NH3 lowest ∆vH amonh hydrogen bounded molecules F, Cl, Br, I regular increase in ∆vH Methane, ethane, propane regular increase in ∆vH

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Determining Tb and ∆vH: Neat approach

∆vH can be determined by measuring px at different temperatures. Tb = boiling temp at 1 atm (1bar)

11

ln

11ln

ln

12

2

1

122

1

00

H

TT

ppR

TTRH

pp

RS

RTHp

v

v

vv

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Ex.

A liquid has vapour pressure of 254mmHg at 25°C and 648mmHg at 45°C. What is ∆vH and Tb?

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Heat of sublimation

The heat of sublimation, or enthalpy of sublimation, is defined as the heat required to sublime one mole of the substance at a given combination of temperature and pressure, usually standard temperature and pressure (STP).

The enthalpy of sublimation is the heat of sublimation for vaporizing one mole of the solid substance under three specific conditions: – (1) the pressure remains constant, – (2) the only possible work that occurs is expansion against the

atmosphere (so-called PdV work) and – (3) the temperature remains constant during the process.

A heat of sublimation for a substance is only valid for conversion of the pure solid to the pure gaseous state of the substance.

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Terms and Concepts

Dissociation Diatomic element gases Bond energy, dissociation energy (enthalpi) Flood’s dissociation diagram Vaporization, evaporation, boiling, sublimation Heat of evaporation, enthalpy of evaporation