Colligative concentration,
electrolytes - Osmosis
Water conversion and movement through interfaces
Latin colligatus meaning bound together,
Greek Osmos meaning water squeeze through membrane,
Oxidation, reduction, Nernst’s
potential and membrane potential
Electron oxidation-reduction balancing and formation inerface potentials
Latin oxidation meaning add oxygen,
Latin reduction meaning oxygen reduce,
Latin potencia meaning might and force is electrochemistry power in volts
Water evaporation-condensation Roul's I law
H2Oliquid
inter face
evapo ration
H2Ogas
conde nsation
(a) p ̊
>
p
p°- p H O
2
p°
=
p°
pH2O (b)
Relative vapor depression Δp/p ̊ is
equal to non electrolyte solute x
mol fraction Nx concentration
p
p°
H2O water
nH2O
number of moles
solute x
water soluble
compounds nx
number of moles
= Nx=
nx
nH O + n x
2
Water evaporation-condensation Roul's I law
Relative vapor depression Δp/p ̊ is equal to non electrolyte solute x mol fraction Nx
concentration
C6H12O6 1 M water solution of glucose mol fraction concentration is
p
p°
nC6H12 O6
= NxC6H12O6= n
C6H12 O6 + n H2 O
One liter contains glucose nC6H12O6= 1 mol.
Molar mass is MC6H12O6=6C+12H+6O=6*12+12*1+6*16=180 g•mol-1.
If density ρ = 1.0 g•cm-3 mass of water mH2O=1000g – 180g=820g .
Molar mass MH2O=2H+O=2*1+16=18 g•mol-1.
mH O
2
Water Number of moles nH2O= M
H O
2
820g
=
1 =45.5(5) mol .
18g  mol
Solute x glucose mol fraction NxC6H12O6 concentration is
1mol
nC6H12 O6
NxC6H12O6= n
= 45.5mol  1mol =0.0215
C6H12 O6 + n H2 O
Phase diagram water evaporationcondensation
0°
100 °
Freezing point depression II Roul’s law states: Δtfreezing= i KcrCm
non-electrolyte (where i = 1)
solution concentration Cm shows
mole number of solute
present in 1000 grams of solution.
Kcr =1.86 is the
cryoscopy constant of the water
(Greek kryos means freezing)
0°
Cryoscopy constant of water 1.86 shows the freezing point depression in a 1 molal
non-electrolyte solution (where i = 1)
which freezes at temperature –1,86°C less zero 0 ̊ C.
180 grams of glucose dissoluted in water 820 grams has freezing point –1,86 ̊ C
Boiling point raise II Roul’s law states: Δtboiling= i Keb Cm
non-electrolyte (where i = 1)
solution concentration Cm shows
mole number of solute
present in 1000 grams of solution.
Keb =0.52 is the
100 °
ebullioscopy constant of the water
(Greek ebulios means boiling)
Ebullioscopy constant of water 0.52 shows the boiling point raise in a 1 molal non
electrolyte solution (where i = 1)
which boils at temperature 100,52 ̊ C over 100 ̊ C.
180 grams of glucose dissoluted in water 820 grams has boiling point 100,52 ̊ C
ISOTONIC COEFFICIENT
1st page :http://aris.gusc.lv/BioThermodynamics/ColigativeProperties.doc
Isotonic coefficient i (or Vant Hoff’s coefficient) is the proportionality factor
between the total concentration in to water dissolved solute molecules and
concentration of water dissolved particles.
Cparticles= i*Ctotal
Swante Arrenius, Wilhelms Ostwalds in Riga during year 1886.
recovering acid, base and salt propereties in
dissociation degree α principles
for strong (α =>1) and weak (α =>0) electrolytes:
C diss
α=
; Cdiss= α * Ctotal .
Ctotal
where α is dissociation degree ,
Ctotal is total concentration of molecules and
Cdiss is dissociated molecule concentration .
i = 1 + α (m–1) ,
where m is the number of formed ions:
dissociation
formed ions
number
=>
Fe3+ + Cl–+ Cl–+ Cl– (1 + 1+ 1+ 1) = 4 = m ions
So isotonic coefficient calculates as :
electrolyte
FeCl3
Cl
3+
Fe Cl
Cl
dissociation
3+
Fe
+ Cl + Cl + Cl
Water solubility ELECTROLYTES DISSOCIATION THERMODINAMICS strong, weak electrolytes
2nd page : http://aris.gusc.lv/BioThermodynamics/ColigativeProperties.doc
Na
Na
+
Cl
+
Na
+
Cl
Na
Cl
Na
+
+
Cl
+
Cl
Na
+
Cl
Na+Cl- Arrenius dissociation theory state sodium chloride in lattice node
points has sodium cations Na+ and chloride anions Cl- surrounded by
opposite charged counter ions with coordination number 6. In water
solution coordinated by six water molecules, water oxygen as electron
pair donor to sodium Na+ electron acceptor empty orbitals.
crystalline
+
Na
Cl
Cl
+
Na
Na
+
Cl
Na
Na
+
Cl
Na
Cl
Cl
+
Na
+
Na
Cl
+
Na+Cl-
H
H
+12H2O =>
[6H2O:=>□Na+]aqua+(Cl-
+6H2O)aqua
O
H
H
+
:O
O
Na
H
H
+
H
OH
H
H
:O
H
H
O
HH
OH H
Cl
O
H
O
H
Dissociation degree α=1, if Na+Cl- dispersed in ions.
H
:O
H
O
H H
Electrolyte solution in water
H
can be treated as a sum of two processes :
1) the separation crystalline Na+Cl- into positive cations Na+ and negative Cl- anions
2) the hydration of ions [6H2O:=>□Na+]aqua un (Cl- +6H2O)aqua coordinated. with six 6H2O
O
H
Overall dissociation process free energy change ΔGr is: ΔGr = ΔHr– TΔSr exoergic,
ΔGr = 3.82•1000 - 298.15•56.312 = -12969 J/mol= -12.969 kJ/mol ;
ΔHr= -240.1-167.2+411.12= +3.82 kJ/mol endothermic heat content change ;
ΔSdispersion=-ΔHr/T=-1000•3.82/298.15=-12.812 J/(mol•K); ΔShydration=59+56.5-(72)=43.5 J/(mol•K);
total entropy change in dissociation process ΔStotal= ΔSdispersion+ ΔShydration=-12.812+43.5=30.688 J/(mol•K)
Strong electrolytes ΔGr<0 negative exoergic are water soluble salt, bases and strong acids.
Weak electrolytes ΔGr>0 positive endoergic are water insoluble salts, bases but weak acids are
water soluble.
Strong electrolyte stoichiometry of dissociation
I = μ = 1/2 Σ Cizi2
μ, I ionic strength is total electrolyte ions stoichiometric concentration
sum half calculated of Ci times ion charge zi exponent zi2
Na+Cl- measured values of α are smaller than 1 - they often are around α = 0.8-0.9.
For medical application of 0.305 M isotonic solution osmo molar concentration
is necessary to keep constant 0.305 M.
Total ionic strength I = μ = 1/2 Σ Cizi2 of salts in to solution should be evaluated
by real α=0.8-0.9 for maintenance constant osmo molar concentration 0.305 M.
For 0.01 M solution of Na2SO4 evaluated ionic strength I = μ = 1/2 Σ Cizi2 calculated
from electrolyte dissociation stoichiometry Na2SO4 => 2 Na+ + SO42- are 3 ions
m=2 + 1=3.
Stoichiometry, molarity of total ions concentration :
[Na+]= 2•0.01 M= 0.02 M, [SO42-] = 0.01 M .
Electrolyte Na2SO4 ionic strength is sum: 2•0.01 M + 0.01 M=0.03 M as
μ = ½(12•0.02+22•0.01)= = ½(1•0.02+4•0.01)= ½ (0.02+0.04) = ½ (0.06) = 0.03 M
total ions stoichiometry molarity concentration sum 0.03 M (2+1=3; 2Na++1SO42- ).
Water osmosis against osmo molar concentration gradient across
aquaporine penetrate membrane iΔCosm= iCM_right - iCM_left
Osmosis organise through an Aquaporins across cell membranes
the osmotic pressure against concentration gradients of colligative properties:
π= iΔCMRT (kPa) ,
where R=8,3144 J/(mol•K) universal gas constant,
T temperature in Kelvin’s degree (K) T=t ̊+273.15 (if t=0 ̊ than T=0 ̊+273.15=273.15 K).
Na+Cl- =Na++Cl- electrolyte dissociation α =1 double pressure on cell membrane, as
i=1+α(m–1)=1+1(2-1)=2; π= iΔCM RT = 2ΔCM RT .
Osmosis is water flow right side against concentration gradient 0<Cosm. Because
Na+Cl- ions close flow of water to left side and make osmo molar concentration
Cright- Cleft = Cosm- 0 = ΔCosm = iΔCM :
membrane
left side zero O O
H
Cleft=0
O
H
aquaporines
+
Na O O
+
O
membrane Cl
right side of membrane
Cright=Cosm=iCM :
<= pressure π= iΔCosm RT , (kPa)
H
<= pressure on cell membrane
H
8th and 9th page: http://aris.gusc.lv/BioThermodynamics/ColigativeProperties.doc
Hypertonic, isotonic, hypotonic H2O, O2aqua osmosis - movement
against osmo molar concentration gradient across cell membranes
Human blood osmo molar concentration sum of all solutes:
Cosm = i1•C1 + i2•C2 + i3•C3 + .... = Σ ik•Ck = 0,305 M,
Glucose, salts, amino acids, proteins, bicarbonate etc.
Hypertonic solution
CHyperton >= 0,4 M ;
Isotonic medium
Cblood= 0.305 M
Hypotonic medium distilled water 0 M
or at least osmo molar concentration
CHypoton<=0,2 M.
Hypertonic salt solutions to apply for
Hypotonic medium the flow of water is
purulent wounds, because pumps out
greater towards the cell (as the
water with toxic compounds and
concentration of solutes in the cell is higher
stimulates blood circulation.
than outside), the cell puffs up until its
membrane is broken.
Note:
Transfer water molecule through membrane aquaporin tunnel in erythrocytes
with rate 3•109 sec-1 in both directions transfer 3000 oxygen molecules in second.
8th and 9th page: http://aris.gusc.lv/BioThermodynamics/ColigativeProperties.doc
Osmosis H2O, O2aqua movement against osmo molar concentration gradient into
erythrocyte and alveolar epithelial surface through membrane aquaporins
Human blood osmo molar concentration sum of all solutes:
Cosm = i1•C1 + i2•C2 + i3•C3 + .... = Σ ik•Ck = 0,305 M,
Glucose, salts, amino acids, proteins, bicarbonate etc.
O O membrane
O O
<=alveolar epithelial surface right
Cosm= 0.305 M aquaporines
H
O
H
H
H
OH
+
O
H C O
O
+
proton
channels
+
H
bicarbonate
channels
H CO 3
membrane
H
O Cosm_right = 0.2 M
H
gas
H
O C O
O
+HH
C O + O O O gas
O
H
H H
H
H
∆Cosm=0.105 M
∆Cosm=0.305–0.2=0.105 M
as Cosm_right=0,2 M;
Osmosis is water and oxygen flow left side against gradient of concentration 0.2 M to
Cosm=0.305 M because water and oxygen flow to right side closed by made left side
osmo molar Cleft-Cright=Cosm-Cosm_right=∆Cosm concentration difference 0.105 M.
Venous deoxy HbT shuttle adsorbs four oxygen 4O2 molecules this way acidify
water medium with 4H+ due to increased H+ , HCO3- 459*6•10–5 M=0,0275 M=[HCO3-]
amounts, which shifts H+ +HCO3-+ Q↔H2O +CO2gas via membrane channels
equilibrium to right. So pH=7,36 remains constant, as bicarbonate ions and hydrogen
ions remove CO2 right side through respiration.
8th and 9th page: http://aris.gusc.lv/BioThermodynamics/ColigativeProperties.doc
Biological Human liquid measurement
(consider blood, sweat, saliva, tear, urine,
etc.).
Cosm = i1•C1 + i2•C2 + i3•C3 + .... = Σ ik•Ck,
Cosm =
t frezing
K cr
=
0.567
=0,305 M
1.86
Isotonic osmo molar blood concentration
Oxidation – Reduction half reaction (RED-OX system) in Table
Half reaction shows two states of compound at equilibrium
by gaining electrons for oxidized changes to reduced form and
loosing electrons for reduced changing to oxidized form.
Half reactions are present in standard potential tables for all known
studied and complete redox systems.
Five columns refers to: 1. Chemical element symbol of responsible atom;
2. oxidized form;
3. number of loosing electrons reduced form and gaining electrons to oxidized form;
4. reduced form;
5. standard potential E ̊ in volts.
Element
Oxidized form
Number of
electrons e-
H
O
2H+
O2(g) + 4H+
H2O2+ 2H+
O2(g) + 2H+
MnO4– + 8H+
MnO4– + 2H2O
MnO4–
Fe3+
2
4
2
2
5
3
1
1
Mn (H+)
(H2O)
(OH-)
Fe
Reduced form
H2
2H2O
2H2O
H2O2
Mn2+ + 4H2O
MnO2↓+ 4OH–
MnO42–
Fe2+
Standard
potential
E̊,V
+0,00
+1,22
+1,78
+0,68
+1,51
+0,60
+0,56
+0,77
6h page: http://aris.gusc.lv/BioThermodynamics/OxRedBiologicalW.doc
Potential E of half reaction by Nernst's’ equation and standard potential E ̊
A conversion between Ox and Red forms in red-ox half reaction can be
in the most general way expressed as free electrons transfer reaction:
free electrons
a Ox + b
+ n e-  c Red + b/2 H2O
oxidized form
reduced form
H+
and the corresponding Nernst's’ equation is:
0.0591
 [Ox ]a [H  ]b 

E=E̊+
•log 
c


n
 [Re d]

Water concentration [H2O]b/2 included in standard potential value E ̊ as logarithm:


0.0591
1

 Because water concentration [H2O] = 55.3 M
E ̊ = Eo +
•log 
b/2 
is constant.
n
 [ H 2 O]

Standard potential value E ̊ is equal to potential E ̊ =E constantly if prepared
solution concentrations of oxidized and reduced ratio is one:
[Ox]a • [H+]b = [Red]c ;
as log(1) is zero
[Ox ]a [H  ]b
[Re d]c
=1;
0.0591
E=E̊+
•log(1) = E ̊ + 0 = E ̊ = E
n
2nd page: http://aris.gusc.lv/BioThermodynamics/ElektrodsAM.doc
Potential of MnO4-/ Mn2+ redox system E
A conversion is expressed between MnO4- + 8H+ and Mn2+ forms of half reaction as:
MnO4- + 5 e- + 8 H+  Mn2+ + 4 H2O
and the corresponding Nernst's’ equation with standard potential E ̊ = 1.51 V is:
 [MnO 4 ][H  ]8 
 [MnO 4 ][H  ]8 
0.0591
0
.
0591
= 1.51 V+

E=E̊+
•log 
•log 
2
2


5
5
 [Mn ] 
 [Mn ] 
Acid concentration increases 10 times increases [H+]8 = 100000000 = 108 times as
hydrogen concentration [H+]8 = 18 =1
times 10 grater 108 =100000000 increase potential + 0.09456 V :
E=E ̊+0.01182•log(10 8) =1.51V+0.01182•8 V=1.51 V+0.09456 V
For electrochemistry acidose oxidation power increase evaluated by potential
as well cams of Latin term potencia means might and force.
Potential E increases: 1) if acidose increase hydrogen ion concentration [H+];
2) if oxidized form concentration increase of [MnO4-];
3) if reduced form concentration decrease of [Mn2+].
Type of electrodes:
present free electrons Type
I,
present free electrons Type
II
present free electrons Red-Ox
absent free electrons
electrode
Membrane electrode.
Nernst’s metallic electrode potential expression formation
Nernst’s awarded Nobel Prize 1920
Free Gibbs energy change product energy
G2 minus initial metal free energy G1
ΔG ̊ = G2 - G1
0.0591
 [Ox ] 
E=E̊+
•lg 
 [Re d ] 
n


free electrons in metal n e-
half reaction Red  Oxn+ + n e- ;
in metal free electrons n e- surface concentration [e-]n is constant included in
standart potential E ̊ constant
[Ox ]  [e  ] n
Keq =
[Re d ]
Electric charge work equal to electrochemical
conversion work from Me
W = qE = nFE = - ΔG ̊ = Wwork = nFE = RTlnKeq
2nd page: http://aris.gusc.lv/BioThermodynamics/ElektrodsAM.doc
Metal/its soluble salt I type electrode Main reference hydrogen electrode
Half reaction of hydrogen saturated platinum:
(Pt)H  H++ e- ; equilibrium constant K = [H+]
Nernst’s equation
EH2 = E ̊H2 + 0.0591•log [H+] = -0.0591•pH
A hydrogen electrode consists of a platinum sheet,
immersed into a solution, containing H+ ions (for example,
H2SO4 solution) and gaseous hydrogen, permanently
bubbling through the solution saturated platinum sheet. If
acid concentration make 1 M hydrogen ion solution pH=0.
EH2 = -0.0591•pH = -0.0591 •0= 0
Hydrogen potential scale origin reference is zero hydrogen electrode [H+] =1 M
0.00 V
E,V
E = -0.0591*pH
Present in standard potential tables for all half reactions given values
refers to hydrogen standard potential zero.
That is general reference for electrochemical potentials in volts
by couple of electrodes measurement devices (potentiometers, voltmeters)
3rd page: http://aris.gusc.lv/BioThermodynamics/Electrode.doc
Metal/insoluble salt/ion II-type electrode
Silver /silver chloride/chloride ion II-type electrode consists
of silver metal, AgCl precipitate insoluble salt and
K+Cl- solution, containing the counter-ions Cl- of
AgCl insoluble salt half reaction is:
AgCl +e-  Ag++ ClNernst’s equation
Eag/AgCl = E ̊AgCl - 0.0591•log [Cl-]
The main application of II-type electrodes is their use as reference electrodes,
Because potential value depends only on chloride ion concentration.
Chloride concentration is precise controlled technology for instruments use.
4th and 5th page: http://aris.gusc.lv/BioThermodynamics/Electrode.doc
Electric potential in volt measurement by couple of electrodes
Electric Motion Force
http://aris.gusc.lv/BioThermodynamics/ElektrodsAM.doc
EMF
V
V
-
+
+
+
+
+
+
+
+
+
+
+
Voltmeter with minus "-" and
plus "+" clamps measures
difference of potentials
J=0
EMF = EI - EII , called
+
e-
+
e-
MeII
+
MeI
Electric Motion Force
EMF .
Between two MeI (Indicator) and MeII (Standard)
on electric circuit linked electrodes
can be expressed MeI Indicator EI as sum :
EI = EMF + EII
Indicator electrode having EI –has reactivity with solution - electrode of investigations,
Standard reference electrode having EII =constant has no reactivity with environment into solution.
Membrane potentials for hydrogen ions H+ protons concentration
gradient in mitochondria pH=7.36 and extra mitochondria space pH=5
http://aris.gusc.lv/BioThermodynamics/MembraneElektrodsAM.doc
mitochondria membrane
extra
+
+
H
H
H +mitochondria
channels H
space
pH=7.36
+
+
+
H
H
H
pH=5
+
membrane H
Wwork=qE=nFE=ΔGr=RTlnKeq;
n charge of ion;
Keq =
RT  [H  ]extra_mito chondria 
Emembrane =
*ln  [ H  ]

mitochondr
ia


nF
H
+
+
[ H  ]extra_mito chondria
[ H  ]mitochondr ia

 [H ]extra_mito chondria 
0,06154

=
*log 


1
 [H ]mitochondr ia 
2,3·8.3144(J / mol / K )·310.15K
ln(10)·R·T
P=
=
=0.06154 V
96485
C
F
EH+
 10  pH
mitochondr ia
=Plg  extra
 10  pH
mitochondr ia





= 0.06154V*lg
 10 5

  7.36
 10



=


0.06154V*log(102.36) = 0,14523V
Membrane potentials for ions HCO3- concentration gradient
in mitochondria [HCO3-Mitochon]=0.0338919 M and cytosol [HCO3-cytosol]= 0.0154 M
O
membrane
C O
Mitochondria O
H
O
O
C
O
H
O
C O
H CO
3
channels
H CO
3
membrane
H
cytosol
O
O
O
C
O
H
[ HCO 3-] cytosol
Emembrane = 0.06154/(-1)*log(
[ HC O 3-] mitochondria )
P=
ln(10)·R·T
F
J
)·310.15K
mol  K
=0.06154 V
96485C
ln(10)·8.3144(
=
[ HCO 3-] cytosol
0.0154 ) = 0,0210821 V
EHCO3-Mitochon,=-Plg(
)=
-0,06154V*log(
[ HC O 3-] mitochondria
0.0338919
 1 


Kin=  [H  ] 
in 

Glass membrane electrode
Kout= [H+out]
↓↓↓↓↓↓↓↓↓
H+in+SiO−3 − SiO2..HSiO3−SiO2..////SiO2////..SiO2−SiO3H...SiO2−SiO−3+H+out
Inner concentration
is constant [H+in]=const
 [ H  out ] 
Kmembrane=Kin*Kout=   
 [ H in ] 
 [ H  out ] 
Emembrane=0.0591/(+1)*log   ;
 [ H in ] 


 1 
Emembrane= 0.0591*log    +0.0591*log([H+out]) ;
 [ H in ] 
 1 
[H+in]=const ; Econst= 0.0591*log    ;
 [ H in ] 
Emembrane= Econst +0.0591*log([H+out]) ;
as pH= -log([H+out])
Eglass= Econst -0.0591*pH .
Glass electrode potential is
proportional to pH of solution.
8th and 9th page: http://aris.gusc.lv/BioThermodynamics/Electrode.doc