Thermodynamis of electrolyte solutions I

Sähkökemian peruseetKE-31.4100

Tanja Kalliotanja.kallio@aalto.fiC213

CH 2.1-2.3, 2.6

Components and species

Exampleelectrolyte: aqueous acetic acidcomponents: CH3COOH and H2O species: CH3COOH, H2O, CH3COO-, H+,OH-,

component - independent of the other particles in the system neutral particles

species – all the particles in the system neutral and charged particles equilibrium constants electroneutrality

Electrochemical potential

dU = dq + dw

dw can include• volume change - PdV• streching - Fdl• surface tension – gdA• electrical – fdqe

• etc.ii

nTPii aRT

n

G

ij

ln0

,,

VdPTdSVdPPdVdUdHPVUH PdVSdTSdTTdSdUdFTSUF VdPSdTSdTTdSdHdGTSHG

wqU state functions

FzaRTFz iiiiii ln~ 0 f inner or galva potential

outer or voltapotential

surface potential

Conventions and standard states (T = 25oC, p = 1 atm): elements in their stable state of aggregationproton in aqueous solution (all temperatures)electrons in any metal

ions in pure metal

00 H

0;0~~ SHESHE

eeF

zFzz MM

~;00

00 element

Activity of non-electrolytes

S Sanjari, M. Nosrati, A. Haghtalab, Fluid Phase Equilibria 277 (2009) 107

Measuring activity coefficienti) Colligative properties – activity of solvent

i) Freezing point depression (most used)ii) Boiling point elevationiii) Osmotic pressure

ii) Vapour pressure depressioniii) Potentiometric methods

iixii xfRT ln,0

iim

ii myRT ln,0

iicii cRT ln,0

mole fraction (mooliosuusasteikko)

molality (molaalisuusasteikko)

molarity, moleular concentration (molaarisuusasteikko)

*/ln,0 mmyRT iim

ii

*/ln,0 ccRT iic

ii

m* = 1.0 mol/kg ; yi = 1

c* = 1.0 mol/dm3 ; gi = 1

Activity of an electrolyte

aRTaaRT

FzaRTFzaRT

lnln

lnln~~

000

00

ca by definition: u = u+ + u and

/1/1;cc

electroneutrality: u+z+ + uz = 0

electrochemical potential of an electrolyte:

cc

cccca

mean activity coefficient(keskiaktiivisuuskerroin)

Can be measured!

i

ii

i

z

c0ln

thus

and

to estimate activity coefficients for ions it has been agreed that

Osmotic pressure

diluted solution

strong solutionosmotic membrane

p + pp

only solvent, e.g. water, permeates trough the membraneosmotic pressure results from imbalance in chemical potential of the solvent

),(),( 11 ii xpxp

pVxfRTpVxfRT 111111 lnln

in equilibrium

1

1

111

11

1

lnlnx

x

V

RT

xf

xf

V

RTpp

as water is incompressible

kk

kk

kk cRTx

V

RTx

V

RTx

V

RT

1111

1

1lnln

if phase b is pure water

van’t Hoff equation

111 VVV

a

b