Post on 02-Jul-2022
Carlos U. Häubi Segura, PhDdrhaubi@yahoo.com
Physics, Chemistry and Biology of
WATERThe Tenth Annual Water Conference
Bulgaria, October 1-4. 2015
Homeopathy
Memory of water
Messages from water
Bulk water vs.
structured water vs. EZ
Energy from light?
Chronic dehydration
And what about …pH?
“Discovery is seeing what
everybody else has seen, and
thinking what nobody else has
thought.”
Albert Szent-Györgi
Canadian physiologist
University of Manitoba (1943)
MSc in physics and mathematics (1949)
PhD in biophysics (1951)
Emory University , Physiology (1954)
Brown University , Medical science (1965-1983)
Stewart, P.A. (1981). How to Understand Acid-Base. A Quantitative Acid-Base Primer for Biology and Medicine,Elsevier Nordholland, New York
Stewart, P.A. (1983). Modern quantitative acid-base chemistry. Can J Physiol Pharmacol. 61: 1444-1461
Kellum, John A; Elbers, Paul WG, eds. (2009). Stewart's Textbook of Acid-Base. ISBN 978-1-4092-5470-6
.
http://www.acidbase.org/
http://issuu.com/acidbase/docs/htuab
If the data does not fit the theory, it is time to change
the theory
What makes it acid? What makes it alkaline?
What is biologicaly apt pH?Blood?
Cells?
What is an acid diet? What is an alkaline diet?
What are biological limits?
Acids taste sour
acids change blue litmus to red
their aqueous (water) solutions conduct electricity
react with bases to form salts and water as the only products
evolve hydrogen gas (H2) upon reaction with an active metal, such as alkali metals, alkaline earth metals, zinc, iron, aluminum, forming a salt as the only other product
An acid is a substance which forms H+ ions as the only positive ion in aqueous solution
Bases taste bitter
feel slippery or soapy
bases turn red (acidified) litmus back to blue
their aqueous (water) solutions conduct electricity
react with acids to form salts and water as the only products
An alkali is a substance which forms OH- ions as the only negative ion in aqueous solution. A base is an insoluble hydroxide.
Author A theory of Hydrogen A theory of Oxygen
PARACELSUS
(S.XV)Discovers Hydrogen upon
acting on a metalROBERT BOYLE
(1671)(Pointy corpuscules?)
ANTOINE LAVOISIER
(1777)Oxy = acidAll acids contain “O”
HUMPHREY DAVY
(1800)Not all acids contain “O”Hydracids (HCl, HF, HI)“H” = Principle of
acidificationJ.P. DULONG
(1820)Union of an electronegative
compound (Oxygen, halogen) with an electropositivo compound (H) and this can besubstituted by a metal
J.J. BERZELIUS
(1830)Oxides of metaloides
produce acids in waterOxygen = Sauerstoff
(German for “acid substance”)JUSTUS VON LIEBIG
(1838)An acid contains a H-atom
which can be subtituted by a metal
GRAHAM
(1880)Monobasic and polibasic
acids: H is subsituted by a base
Arrhenius (1887)◦ An acid is a substance which forms H+ ions as the only positive ion in
aqueous solution.
◦ An alkali is a substance which forms OH- ions as the only negative ion in aqueous solution. A base is an insoluble hydroxide
Brønsted-Lowry (1923)◦ An acid is a proton donor.
A base is a proton acceptor.
Lewis (1923)
◦ An acid is an electron acceptor,and a base is an electron donor.
◦ This totally removes the concept of hydrogen ions being a pre-requisite for an acid. But like the Brønsted-Lowry definiton above, it still includes every acid and base under the Arrhenius definition, and all those under the Brønsted-Lowry definition.
HCl(g) + NH3(g) ---> NH4Cl(s)
2HCl + MgO ---> MgCl2 + H2O
Zn(OH)2 + 2NaOH(aq) ---> 2Na+(aq) + [Zn(OH)4]2-
(aq)
HCl ---> H+ + Cl-
Water is an acid or a base?
Bicarbonate is a base or an acid?
Where does HCO3- come from?
From NaHCO3
Where does the OH- come from?
From NaOH
H2CO3 is an acid or a conjugated
acid?
Classical theories of acids
◦ Theory of dissociation, Arrhenius-Ostwaldt (1887)
◦ pH scale (pH = -log [H+]), Sørenson (1909)
◦ Henderson-Hasselbalch equation (1916)
◦ Proton donors, Brønsted-Lowry (1923)
◦ Electron donars, Lewis acids (1923)
General definitions of solvents
◦ Effects of solutes on the solvent (Germann, 1925)
◦ Quantitative theory of acids (Stewart,1981)
Concepts of acids in Medicine
◦ Dissociation of strong acids and bases
◦ Partial pressure of CO2 (PCO2)
◦ Buffers
◦ Henderson-Hasselbalch – only one variable
Iatrogenic?
Any new theories?
Old theories are
still actual?
Qualitative or
Quantitative?
Water is really weird...
◦ It forms a permanent dipole
◦ It hydrates other molecules, even other
molecules of water
◦ It forms liquid crystals with moving electric
charges
It dissociates with difficulty (Kd) but re-
associates rapidly (Ka) :
◦ It is the main donador and receptor of hydrogen
ions (= protons: H+) and hydroxile ions (OH-)
◦ Protons (H+) cannot live freely; they associate
and hydrate : H3O+(H2O)n
◦ Water has a high concentration of H2O: 55.5 M
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
H
HOd-d+
HO
H
H3O
+
H3O+
HO
H
H
O
HH
HO
H
O H +
H +104.5°
Protonicjumps
----
One molecule in each 10 million dissociates
spontaneously:
◦ 0.1 ppm , 1/107 , 10-7 (pH=7)
The reaction is the following:
H2O H+ + OH- H+ + H2O H3O+
The proton binds to another molecule of water
O -
H +
H +
O -
H +
H +
O -
H +
H +
O -H + O -
H +
H +
H +
H3O+
H +
O -H + OH-
Theory of dissociation, Arrhenius-Ostwaldt
(1887)
How is this possible?
General definitions of solvents
H3O+
O -
H +
C
H +
H +
H +
CO -
O -
H +
H2OÁcido no-disociado:
No tiene carga
Ácido disociado:
Carga (-) = anión
O -
H +
H +
O -
H +
H +
O -
H +
O -
H +
H +
H +
O - Ac
O -
H +
O -
H +
H +H +
H +
H +H +
Cristal de agua tiene carga
neutra
Matriz de agua:
Donador y receptor
de protones
y iones OH-
Saltos protónicos
Dónde quedó la bolita?
H +O -
H +
H +
Acido orgánico se protoliza:
se forma un anión solvatadoPor cada carga negativa se
genera un protón H+
El protón no tiene vida
libre, se forma el ion
hidrogenion H3O+
The neutral charge
in water is always
maintained
According to Germann (1925)
◦ Cation of water (H3O+): “Lyonium”
◦ Anion of water (OH-): “Lyate”
For a given solvent:
◦ Acid: a substance that increments the concentration of the “Lyonium” ion
and reduces the concentration of the “Lyate” ion
◦ Base: a substance that increases the concentration of the “Lyate” ion and
decreases the concentration of “Lyonium” ion.
In the case of water, acids and bases can be defined as :
◦ Acid: A negative charge that produces a mayor dissociation of water and
an increase in the concentration of protons, [H+]
◦ Base: A positive charge that produces a mayor dissociation of water
molecules and an increase in the concentration of hydroxile ions, [OH-]
Strong Ion Difference
PCO2=
ATOT=
pH
[H+]
[OH-]
[HCO3
-]
[CO3
2-]
[A-][HA]
Variables dependientes
PresiуnParcial deCO2 Total de
anionesdйbiles
SID=
Seis ecuacionessimultбneas
Henderson-HasselbalchpH = pKa + Log [A-]/[HA] ?
Aniones dйbiles
Cationesfuertes
PCO2
Anionesfuertes
Na+
Cl-
K+
Ca2+
Mg2+
OH- H3O
+HCO3
-
CO3
2-
A-
HA
SO4
2-
??
?
?
?
Dissociation of strong acids and bases
Partial pressure of CO2 – PCO2
Dissociation of weak acids
SID – Strong Ion Difference
Partial pressure of CO2 – PCO2
ATOT – Total of weak anions
Three factors that affect pH but could not be reconciled...
now braught together by a quantitative method
Strong Ion Difference:
Na + K + Ca +Mg
-Cl – strong ions
= SID
pCO2:
Protein concentration Atot]
Chemistry laws:
- Mass action:
- Electro-neutrality:
- Dissociation of: water, carbonic acid,
weak acids, weak bases, ammonia, etc.
[H+] [OH-] [HCO3-] [CO3
2-] [A-] [Pi] [VFAs] [Lactates]
Phosphates, ammonia, etc.
Weak acids: VFA Lactate
Stewarts theory is based on the effect of three
basic principles of chemistry, on the balance
of electrical charges in aqueous solutions:
1) Principle of electro-neutrality,
2) Law of Mass Action,
3) Law of Mass Conservation
1) Principle of electro-neutrality
the sum of all positive charged ions must equal the sum of allthe negatively charged ions:
[Na+] + [K+] + [Ca2+] + [Mg2+] + [H+] - [Cl-] –
[Anion-]-[OH-] - [HCO3-] - [CO3
2-] = 0
0
20
40
60
80
100
120
140
160
Cationes Aniones
mm
ol/L
OH-
Pi
Atot
HCO3-
Otros Aniones
Cl-
H+
Ca2+
K+
Na+
2) Law of Mass Action
States that all incompletely dissociated substances reach a dissociation equilibrium:
[A] * [B] = K * [C]
where K is the rate constant for the reaction.
Water has a very small dissociation constant:
KW (KW = 1*10-14)
but a very large association constant:
(1/KW = 1*1014)
3) Law of Mass Conservation
States that the amount of a substance remains constantunless it is added, removed, generated or destroyed:
[HA] + [A-] = [ATOT]
The total of a weak acid (ATOT) is an independent variable
and can be present as a dissociated acid (A-)
or non-dissociated (HA),
both being dependent variables.
The dissociation of water into H+ ions (pH) and OH- and thebehavior of other weak acids (organic acids, carbonates,phosphates and proteins) and bases (ammonia), dependson three independent variables:
1) The Strong Ion Difference (SID)
Na+ + K+ + Ca2+ + Mg2+ - Cl- - SO42-
2) The partial pressure of carbon dioxide (PCO2)
CO2 + H2O H2CO3 H+ + HCO3- 2 H+ + CO3
2-
3) The total amount of weak anions (ATOT)
HAlb + Alb- = AlbTOT
Water is the primary and inexhaustible source and sink for
hydrogen ions.
[H2O]* KW = [H+] * [OH-]
The dissociation constant KW is very small
( 4.3 * 10-16Eq/l at 37 oC).
KW varies with temperature
(e.g., at 25 °C, KW is about 1.8 * 10-16Eq/l)
The approximate value of KW' is:
KW' = 8.754 * 10-10 * e(-1.0^1*10^6) / T^2)
where temperature T is expressed in degrees Kelvin
This can be done with the solution of six simultaneous
equations:
[H+] * [OH-] = KW‘ Equation #0
[H+] * [A-] = KA * [HA] Equation #4
[HA] + [A-] = [ATOT] Equation #5
[H+] * [HCO3-] = KC * PCO2 Equation #8
[H+] * [CO32-] = K3 * [HCO3
-] Equation #9
and finally, to maintain electrical neutrality:
[SID] + [H+] - [HCO3-] - [A-] - [CO3
2-] - [OH-] = 0
Equation #10
This makes the solution for the hydrogen ion concentration[H+] possible with the aid of computers:
[SID] + [H+] - KC * PC / [H+] - KA * [ATOT] / (KA + [H+]) – K3 *
KCPC / [H+]2 - KW' / [H+] = 0
Equation #10
PC = PCO2 mmHg
Constants are:
KW = 4.40*10-14 (Eq/L)
KC = 2.34 * 10-11 (Eq/L)2 mmHg-1
K3 = 6.0*10-11 Eq/L
KA = 1.64*10-7 Eq/L (rest)
KA = 1.98*10-7 Eq/L (exercise)
KC = K * S◦ where K = 7.42*10-7 Eq/L, K is the constante of dissolution;
◦ S = 0.0351 Eq/L mmHg-1 a 37°C y 300 mOsm, S is the constant of Solubility.
The algebra to solve these six simultaneous equations gives
a fourth-order polynomial.
The exact solution for [H+] is:
[H+]4 + ([SID] + KA) x [H+]3 +
(KA x ([SID] – [ATOT]) – K’W – KC x PCO2) x [H+]2
- (KA x (K’W + KC x KCO2) – K3 x KC x PCO2) x [H+] – KA x K3
x KC x PCO2 = 0
There are four possible solutions
PROGRAM STARTS:
◦ TOO_SMALL = 4.4 * 10-14
◦ TOO_BIG = 1.0
◦ CLOSE_ENOUGH = 0.000001
BEGIN:
◦ MY_GUESS = ROOT ( TOO_SMALL * TOO_BIG )
◦ RESULT = F(MY_GUESS)
◦ IF ABS(RESULT) LESS THAN CLOSE_ENOUGH THEN RETURN MY_GUESS
◦ IF RESULT IS POSITIVE THEN
TOO_BIG = MY_GUESS
OTHERWISE
TOO_SMALL = MY_GUESS
GO TO BEGIN
PROGRAM ENDS:
Written by J. van Schalkwyk, 1999, from the website:
http://www.anaesthetist.com/icu/elec/ionz/Stewart.htm
University of South Carolina, School of Medicine
http://ppn.med.sc.edu/watson/Acidbase/Acidbase.htm
No free-living protons (H+):
The acidity of the bicarbonate ion
The volatility of the bicarbonate ions
The effect of acids on EZ-water
Let’s start with this one!
Fig. 5.9 Time course of pH-dye distribution
as current flows between wire electrodes
immersed in a water bath containing pH-
sensitive dye.
Cathode (-):
◦ Purple corresponds to high pH
◦ Attracts cations (+), Produces OH-
Anode (+):
◦ Orange corresponds to low pH
◦ Attracts anions (-), Produces H+, H3O+
low pHhigh pH
Initial state
Fig. 5.5 Addition of microspheres alters water’s pH.
(a) Carboxylate microspheres, 1 μm diameter.
Increasing microsphere concentration changes dye color
toward red, indicating lower pH.
(b) Positively charged amino microspheres change dye
color toward green, indicating higher pH.
Does Stewart help explain EZ
after formation or depletion?
Pollack (2013):
“an H3O+ combining with a
lattice-structural unit (OH-),
which yields two water
molecules (Fig. 6.11). This
erosive action loosens the
EZ’s hexameric structure.”
Sufficiently acidic pH does diminish EZ size.
Salts erode the EZ similarly.
Consider NaCl:
The Cl– component can combine with H3O+ in
the bulk to yield HCl + H2O,
Na+ can invade the negative lattice, and go on to
create NaOH by extracting a lattice OH– unit.
The EZ erodes and adds a water molecule to the
bulk water. Wherever the lattice is open, positive
ions of any sort can enter and cause EZ erosion.
According to Stewart:
• Cl- increases [H+], therefore [H3O+]
• Na+ ion reduces [H+] and increases [OH-]
• Question to Jerry: Effect of NaOH on EZ?
“an H3O+ combining with a lattice-
structural unit (OH-), which yields two
water molecules (Fig. 6.11). This erosive
action loosens the EZ’s hexameric
structure.”
The no free-living existence of protons (H+):
◦ Protons disociate and re-associate from the water
matrix in order to maintain the principle of
electroneutrality
◦ Hydrogen ions H+ have a diameter of 10-15m, therefore
cannot be pumped by membrane proteins
◦ Hydrogen ions H+ are dependent variables
◦ Mitchell’s Chemiosmotic Hypothesis (1961) cannot be
correct (ATP is formed through another mechanism!)
http://bcs.whfreeman.com/thelifewire/content/chp07/f07012.gif
The acidity of the bicarbonate ion
◦ The bicarbonate ion is not a buffer… it cannot
neutralize acidity in a solution
◦ CO2(d)+ H2O H2CO3 H++ HCO3-H++H+ + CO3
2
◦ It’s an anion (HCO3-), a negative charge, pKa 6.1: it’s a
weak acid
◦ What increases pH is the cation (e.g. Na+, K+)
◦ Henderson-Hasselbalch equation is wrong !!
H-H (1916)
◦ pH = pKa + log [A-] /[HA]
◦ It’s a circular relationship:
pH affects the dissociation of carbonic acid into bicarbonate
The dissociation of carbonic acid affects the concentration of bicarbonate and carbonic acid
Anion Gap◦ (Na+ + K+) - (Cl- + HCO3
-) = UA –UC
◦ Value: 10-12 mEq/L
Base Excess◦ Van Slyke equation:
◦ PaCO2 40 mmHg, pH 7.4, 37 °C, full O2 saturation)
◦ Base excess = 0.93 × HCO3− − 24.4 + 14.8 × (pH − 7.4)
◦ SBE = 0.9287 × (HCO3- − 24.4 + 14.83 × ([pH − 7.4]))
pH = 6.1 + log10 [HCO3− ]
0.03 × PaCO2
Winter’s equation:
PCO2 = 1.54 × [HCO3- ] + 8 ± 2
Ole Siggard-Andersen Nomogram
The volatility of bicarbonate ions
◦ Bicarbonate ions are dependent variables, which are formed
or destroyed according to the Henderson reaction:
CO2(d)+ H2O H2CO3 H++ HCO3-H++H+ + CO3
2
◦ Carbonic Anhidrase, a really fast enzyme
◦ There is NO evolutionary advantage of pumping HCO3- ions
from one side of a membrane to the other, because it will be
change to another species of carbonate according to
conditions of the medium
The volatility of bicarbonate ions (continues):
◦ There is no reabsorption of bicarbonate in the kidneys
during urine production
◦ NO interchange of HCO3- ions for Cl- ions during gastric
juice production
◦ NO secretion of HCO3- ions during pancreatic juice
production
◦ NO use of applying bicarbonate in IV-solutions – it’s the
sodium ion (Na+HCO3-)
Lumen Cell Blood
Cl-
No c.a.
c.a. = carbonic anhidrase
met
aboli
zed
Ac- Ac
-
HAc HAc
H+
H++
Na+
CO2
H2O
H2CO
3
HCO3
-
H+
+
+
c.a.CO
2H
2O
H2CO
3
HCO3
-
H+
+
+
Ac-
CO2
H2O
H2CO
3
HCO3
-
H+
+
+
c.a.
A hypothetical model of rumen epithelial ion transport (adapted from Stevens, 1988).
Lumen Cell Blood
No c.a.
met
abol
ized
Ac- Ac
-
HAc HAc
H+
H++
CO2
H2O
H2CO
3
HCO3
-H
+
+
+
Ac-
Strong ions (e.g. NaCl) completely dissociate in water and are hydrated by water molecules releasing
an opposite charged water ion (H30
+ or OH
-) to maintain electroneutrality in the aqueous solution.
Carbon dioxide (CO2) dissolved in water reacts to forms different species of carbonate according to
other variables in the medium.
Weak acids (HAc) dissociate into their anions (Ac-) according to their dissociation constant (Ka).
(H30
+ = H
+); c.a. = carbonic anhidrase.
H2ONa
+
H2OCl
-+ H
++
+ OH-
+
Cl-
Na+
NaCl
CO3
2-H
++
HAc
H2O
OH-
H2O
Pool
H+
H+
H+
H+
KaKa Ka
H2O
OH-
H2O
Pool
H+
H+
H+
OH-
OH-
H+
H+
Cl-
Na+ Na
+
Cl-
H+
+
Fermentation
OH-+
H++
CO2
H2O
H2CO
3
HCO3
-H
+
+
+
c.a.
CO3
2-H
++
CO2
H2O
H2CO
3
HCO3
-H
+
+
+
c.a.
CO3
2-H
++
Definition:
◦ The administration of fluids and electrolytes with the
objective of maintaing or restablishing corporal
homeostasis
Priorities:
◦ To conserve the volume of blood
◦ To conserve osmotic pressure and equilibrate ion
composition in each body compartment
◦ To conserve normal concentration of hydrogen ions (pH) in
each compartment
Author(s), year Research Solution used Observations
Denys, 1667 First blood transfusion From a dog to a human RIP
O’Shaughnessy, 1831 Loss of water, alcali and salts in blood in cases ofcholera
Pérdida de agua, álcali libre, urea en orina, bajo en carbonato de sodio
Not known if it was 0.9 % NaCl
Latta, 1832 Loss of soidum volumein an elderly woman
Use of glass tube intobasilic vein, 3.4 L
“Rapid recovery butdied because treatmentwas not followed”
Stadelman, 1883 Acidosis in diabeticcoma
Alcaline Sol.: Na2CO3: 2-3 %
2 % = 208 mM3 % = 312.5 mM
Ringer, 1882 Frog’s heart can survivein a balanced solution
1 Litre contains: Sodium chlorine (6.5 g), Sodium bicarbonate (0.2 g) Calcium chlorine(0.25 g) y Potassiumchlorine (0.42 g)
NaCl: 111.2 mEq/LNaHCO3: 3.125 mEq/LKCl: 5.63 mEq/LCaCl2: 2.25 mEq/L
Hamburger, 1882 Establishes thephysiological salinesolution
0.9 % NaCl Mistake: 154 mEq/L !NaCl is only 0.6 %Other salts of Na+ 0.3%
Cantani, 1892 Comatose patients Subcutaneoussolutions: Typhic reactions – RIP!
0.4 % NaCl = 68.44 mM0.3 % Na2CO3 = 31.25 mM
Author(s), Year Research Solutions used Observations
Hartwell & Houget, 1912
Perros: estudio sobre muerte de perros con obstrucción intestinal no estrangulada
Gran pérdida de líquidos por vómito excesivo, administración SC con SSF
SSF puede provocar más vómito, por sobrecarga de cloruro
Rowntree, 1922Produce intoxicación por agua experimentalmente
Descripción del trastorno en el ser humano
Dilución de iones puede llevar a la muerte
Mata, 1924Goteo IV, en vez de goteo rectal y epidermoclisis
Cánula de vidrioMayor velocidad de infusión, pero no da tiempo a que el organismo regule
Hartmann, 1935 Lactantes con diarrea severa
Requieren más sodio que cloruroRinger con LactatoIncluye Calcio, potasio
Na+ : 131 mmol/LCl- : 111 mmol/LLac-: 29 mmol/LK+ : 5 mmol/LCa2+: 2 mmol/L
Darrow & Yannet, 1935Movimiento de liquido entre compartimentos, sin radioisotopos
Diagrama Darrow- Yannet
Gamble, 1942Movimiento de liquido entre compartimentos
Gamblegrama Diagrama muy útil
Darrow, 1949Pediatría,Diarrea severa
35 mEq/L de KClSe recomienda en casos de acidosis por pérdida de potasio, pero contiene alto cloruro y lactato
Na+ .: 121 mmol/LCl- : 103 mmol/LLac-: 53 mmol/LK+ : 35 mmol/L
Fogelman & Wilson, 1960Perros, hombresTraumatismo severo
Pérdida de liq. Extracelular, reposición con sal.
Solutions Na+ K+ Ca2+ Cl- Precursors SID pH*
SSF
0.9% NaCl
154 0 0 154 0 0 7.30
Ketone-R 131 5 3 111 +28 ßOH-Butirate
+25.5 7.38
Ringer
DL-Lactate
131 5 3 111 +28DL-Lactate +25.5 7.38
Ringer
L-Lactate
131 5 3 111 +28 L-Lactate +25.5 7.38
Glucosa 5% + 0.9% NaCl
154 0 0 154 + 5 % Glucose
(560 mOsm)
0 7.30
Plasma
Stewart
143 4 3 107
+ 1
+25.1 HCO3- +42 7.42
McSherry 138 12 3 100 +50 Acetate +54.5
+41
7.45
7.42
PlasmaLyteA
140 5 0
Mg2+ 3
98 + 27 Acetate
+ 23 Gluconate
+40 7.40**
*pH: calculated as the result of adding 1 L solution to a patient with 5 L of blood:
pH 7.41 , PaCO2 40mmHg, Albumin 19mEq/L.
** published values
Plasma cationes
Plasma aniones
Intersticial cationes
Intersticial aniones
Intracelular cationes
Intracelular aniones
Proteínas citoesqueleto 0 0 50
Proteínas solubles 16 0 55
Ácidos orgánicos 3 4 3
SO42- 0.5 0.5 10
PO43- 1 1 57
HCO3- 26 30 8
Cl- 102 114 2
Mg2+ 1 0.5 13
Ca2+ 2.5 2.5 1.5
K+ 4 4 160
Na+ 142 144 10
0
20
40
60
80
100
120
140
160
180
200
Ion
co
ncn
etr
ati
on
(m
Mo
l/L
)
Plasma (g/dL)
Urine(g/dL)
Plasma (mmol/L)
Urine(mmol/L)
Diff. Conc.
Reabs. %
Water 90-93 95 52M 53M - 99.1
Protein 7.0-8.5 - 1.3 -
Urea 0.03 2 5 333 X 60 41.4
Uric acid 0.002 0.03 X 15
Glucose 0.1 - 5.5 - 100
Creatinine 0.001 0.1 X 100
Sodium 0.32 0.6 140 188 X 2 99.1
Potasium 0.02 0.15 5 38 X 7
Calcium 0.01 0.015 2.5 3.8 X 1.5 98.8
Magnesium 0.0025 0.01 1 4 X 4
Chlorine 0.37 0.6 105 171 X 2 98.5
Phosphates 0.003 0.12 0.32 12.6 X 40
Sulfates 0.003 0.18 0.31 18.75 X 60 76.5
Ammonia 0.0001 0.05 0.06 29.4 X 500 20.5
Plasma (mmol/L)
Urine
(mmol/L)
Urine+NH4+
(mmol/L)
Sodium 140 188 188
Potasium 5 38 38
Calcium 2.5 3.8 3.8
Magnesium 1 4 4
Chlorine 105 171 171
Phosphatos 1.4 12.6 12.6
Sulfates 0.31 18.75 18.75
Cations +148.5 +234 +234
Anions -106.7 -203 -203
SID’ +41.8 -31 -31
Other Cations 0.06 - 38 (29 NH4+)
SID” +42 -31 +7
pH-calc 7.4 1.4 5.6
Variables Normal ↑Anion- ↓Na+ SO42- ↑PaCO2 ↑PaCO2
↓ ATOT
Na+ 140 140 131 140 140 131 131
K+ 4 4 4 4 4 4 4
Ca2+ 4 4 4 4 4 4 4
Cl- 104 104 110 104 104 104 104
Otros- 6 16 6 6 6 6 6
SO42- 0.6 0.6 0.6 7.0 7.0 7.0 7.0
SID 38 32 23 31 31 22 31
PaCO2 40 40 40 40 50 50 50
Alb- 4.2 4.2 4.2 4.2 4.2 4.2 2.1
Pi- 1.4 1.4 1.4 1.4 1.4 1.4 1.4
HCO3- 24.0 18.5 10.8 17.6 18.1 10.5 23
CO2tot 25.3 19.8 12.0 18.9 19.6 12.0 24.5
BE -0.65 -6.65 -15.65 -7.65 -7.65 -16.65 -1.96
AG 12.0 11.6 10.2 18.4 17.9 16.5 13.0
pH 7.39 7.28 7.04 7.25 7.17 6.93 7.27
Traditional theories of acids Stewart’s theory (1981)
Proton donors
Brønsted-Lowry (1923)
Generalized solvent definitions
(Germann, 1925)
Henderson-Hasselbalch equations (1916)
only one variable
Nomogramas
A system of simultaneous equations with 6
variables
Electroneutral equilibrium of water
Confussion of dependent and independent
variables: H+, HCO3-
Independent variables:
SID, PCO2, ATOT
Dependent variables:
H+, OH-, HCO3- CO3
2-, A- , HA
Anion gap: 10-12 mEq/L Anion gap: 6-8 mEq/L
Applications: Only for small ranges of pH
e.g. Blood pH (7.0-7.8)
Cations: Na+, K+, Ca2+, Mg2+, NH4+
Anions: Cl-, SO42-, PO4
3-, R-COO-
pH PaCO2
Boston School
(Henderson-
Hasselbalch)
Stewart’s
theory
Respiratory
Acidosis
Normal or HCO3-
(compensated)
PaCO2
(dysnea)
Respiratory
Alcalosis
Normal or HCO3-
(small)
PaCO2
(hypervent.)
Metabolic
Acidosis
Anion gap
-Normal:
-Augmented:
Normal or HCO3-
- loss HCO3-
Excr. H+
Prod. HCl
Anions (Lac-)
H+ + HCO3-
They do not
affect!
Cations
Anions
Metabolic
Alcalosis
Normal or
(small)
HCO3-
Anions
Cations
Electrochemical acidosis
Analysis of clinical cases in ICU
Cálculo de pH y otros iones según Stewart
-
10
20
30
40
50
60
70
80
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7
Tiempo (8am a 7am)
Co
nce
ntr
ació
n (
mm
ol/L
)
7.0
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
SIDcambio
PCO2
Atot
pH
H+
OH-
HCO3
CO32-
A-
HA
PO4
Acidez H+ nanoEq/L
pHcalc
pHpaciente
Pacient with HyponatremiaTiempo pH Na+ K+ Ca2+ Mg2+ Cl- SO42-Lactato-PO43- SID pCO2 ATOT pHcalc
1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
4 7.2 131 4 2 1 105 3 1 2 29 40 19 7.209
5 7 124 4 2 1 105 3 1 2 22 40 19 7.009
6 7 124 4 2 1 105 3 1 2 22 40 19 7.009
7 7.05 126 4 2 1 105 3 1 2 24 40 19 7.074
8 7.1 127 4 2 1 105 3 1 2 25 40 19 7.104
9 7.2 131 4 2 1 105 3 1 2 29 40 19 7.209
10 7.3 135 4 2 1 105 3 1 2 33 40 19 7.297
11 7.35 138 4 2 1 105 3 1 2 36 40 19 7.354
12 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
13 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
14 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
15 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
0
20
40
60
80
100
120
140
160
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Na+
K+
Ca2+
Mg2+
Cl-
SO42-
Lactato-
PO43-
SID
pCO2
ATOT
pH
pHcalc
Pacient with lactic acidosisTiempo pH3 Na+ K+ Ca2+ Mg2+ Cl- SO42-Lactato-PO43- SID pCO2 ATOT pHcalc
1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
4 7.2 140 4 2 1 105 3 11 2 28 40 19 7.209
5 7 140 4 2 1 105 3 20 2 19 40 19 7.04
6 7 140 4 2 1 105 3 20 2 19 40 19 7.04
7 7.05 140 4 2 1 105 3 19 2 20 40 19 7.07
8 7.1 140 4 2 1 105 3 18 2 21 40 19 7.103
9 7.2 140 4 2 1 105 3 14 2 25 40 19 7.209
10 7.3 140 4 2 1 105 3 10 2 29 40 19 7.297
11 7.35 140 4 2 1 105 3 7 2 32 40 19 7.354
12 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406
13 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406
14 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406
15 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406
0
20
40
60
80
100
120
140
160
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8Na+
K+
Ca2+
Mg2+
Cl-
SO42-
Lactato-
PO43-
SID
pCO2
ATOT
pH3
pHcalc
Pacient with respiratory acidosis
0
20
40
60
80
100
120
140
160
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8Na+
K+
Ca2+
Mg2+
Cl-
SO42-
Lactato-
PO43-
SID
pCO2
ATOT
pH
pHcalc
Tiempo pH Na+ K+ Ca2+ Mg2+ Cl- SO42-
Lactat
o- PO43- SID pCO2 ATOT pHcalc
1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
4 7.2 140 4 2 1 105 3 1 2 38 64 19 7.201
5 7 140 4 2 1 105 3 1 2 38 106 19 7.001
6 7 140 4 2 1 105 3 1 2 38 106 19 7.001
7 7.05 140 4 2 1 105 3 1 2 38 93 19 7.053
8 7.1 140 4 2 1 105 3 1 2 38 82 19 7.102
9 7.2 140 4 2 1 105 3 1 2 38 64 19 7.201
10 7.3 140 4 2 1 105 3 1 2 38 50 19 7.299
11 7.35 140 4 2 1 105 3 1 2 38 44 19 7.351
12 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
13 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
14 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
15 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389
Stewart, P.A. (1981). How to Understand Acid-Base. A Quantitative Acid-Base
Primer for Biology and Medicine, Elsevier Nordholland, New York.
Stewart, P.A. (1983). Modern quantitative acid-base chemistry. Can J Physiol
Pharmacol. 61: 1444-1461.
Häubi Segura, C.U. (2004). Use of the Rumen Simulation Technique (RUSITEC)
to model clinical and subclinical rumen acidosis in dairy cattle. PhD Thesis,
Department of Agriculture, The University of Reading, Reading, UK.
From the above we know that
[H+] * [OH-] = KW'
To determine the hydrogen ion concentration it is necessary
to know KW', and the other variable, the hydroxyl ion
concentration. In pure water the only ions present are
hydrogen ion and hydroxyl ion, so if the water is to be
electrically neutral, then:
[H+] - [OH-] = 0
The dissociation of water into hydrogen ions responds to
the chemical laws to maintain electro-neutrality. An
excess of other positively charged ions will decrease the
dissociation of water into H+ ions, conversely, an excess
of negatively charged ions increase the dissociation of H+
ions.
With the addition of strong electrolytes to water, such as
NaOH and HCl, which will almost completely dissociate,
there is a mix of water, Na+, Cl-, H+ and OH- ions.
[H+] - [OH-] + [Na+] - [Cl-] = 0 .. Equation #1
If the amount of sodium and chloride ion (or any other
strong ions) in solution is known, it is possible to
determine the hydrogen ion concentration. Only the
difference in ionic concentrations (SID) is of importance,
therefore the above equation can be abbreviated to:
[SID] + [H+] - [OH-] = 0
A weak acid, HA (such as albumin or VFAs) dissociates to form
H+ and A-, as follows:
HA <=> H+ + A-
Previous equations (dissociation of water and the requirement
for electrical neutrality ) are slightly modified to include the
dissociated anion A-, derived from the acid:
[H+] * [OH-] = KW' Equation #0
[H+] + [OH-] + [SID] + [A-] = 0 Equation #1A
The following two equations are based on the dissociation of
the acid, and the necessity for conservation of the total
amount of acid, which is abbreviated to ATOT :
[H+] * [A-] = KA * [HA] Equation #4
[HA] + [A-] = [ATOT] Equation #5
The effect of carbon dioxide on aqueous solutions is
generally expressed by the Henderson-Hasselbalch
equation, but this only represents part of the truth.
Four reactions can happen to CO2 gas when exposed to
water:
1) Dissolution in water,
2) Reaction with water to from carbonic acid,
3) Dissociation to form bicarbonate ion,
4) Second dissociation to form carbonate ions:
CO2(d) + H2O K1 H2CO3 K2 H+ +
HCO3- K3 H+ + H+ + CO3
2-
The two most significant reactions are the formation of
carbonate and bicarbonate, as each has its own equilibrium
constant. These reactions with their equilibrium constants
will have a profound influence on the whole system, but it is
only in the context of the whole system that is possible to
understand the role of carbon dioxide:
1. CO2 can dissolve in water, as expressed by the equation:
CO2(gas) <=> CO2 (dissolved)
The forward reaction depends on partial pressure of CO2,, =
with a rate
Kf * PCO2
The reverse reaction depends on the concentration of dissolved
CO2 with the rate
Kr * [CO2 (dissolved)]
According to Henry´s Law, the dissolution of molecular
carbon dioxide [ CO2(dissolved) ] into the rumen fluid
medium is related to the solubility coefficient for carbon
dioxide (SCO2) and the partial pressure of carbon dioxide
(PCO2) via the formula:
[CO2(dissolved)] = SCO2 * PCO2 Equation #7A
The solubility of CO2 (SCO2) has substituted Kf/Kr .
SCO2 is dependent on temperature, and at 37 °C it is about
3.0 * 10-5 Eq/litre/mmHg.
2. CO2 can react with water to form carbonic acid:
CO2 + H2O H2CO3
Equilibrium is represented by:
[CO2(dissolved)] * [H20] = K * [H2CO3] .. Equation #7B
If [H20] is treated as a constant, it can be rearranged:
[H2CO3] = KH * PCO2
The value of KH at 37 °C is 9 * 10-8 Eq/litre - therefore, the
H2CO3 concentration is far smaller than the amount of
dissolved CO2.
The reaction of CO2 with water is very slow , with a half time
of about 30 seconds, speeded up to microseconds by the
carbonic anhydrase abundantly present in most tissues
but not in the rumen.
3. H2CO3 thus formed can dissociate into bicarbonate and
hydrogen ions:
H2CO3 H+ + HCO3-
Equilibrium is represented by:
[H+] * [HCO3-] = K * [H2CO3]
It follows that:
[H+] * [HCO3-] = KC * PCO2 Equation #8
A physiological value for KC is
2.6 * 10-11 (Eq/l)2/mmHg
4. Once formed, HCO3- can rapidly dissociate:
HCO3- H+ + CO3
2-
Equilibrium is represented by:
[H+] * [CO32-] = K3 * [HCO3
-] Equation #9
A typical value for K3 is 6 * 10-11 Eq/litre.
CO2(d) + H2O K1 H2CO3 Kc H+ + HCO3-
K3 H+ + H+ + CO32-
Stewart’s original theory combined strong ions, carbon
dioxide and a weak acid to model blood plasma and
intracellular fluids.
Blood plasma is rich in weak acids, specially proteins
(albumin) and for the purposes of analysis and simplicity
he regarded them as being all one acid with a single ATOT
and single KA.
Nevertheless it is possible to expand the model with
multiple KA (Figge et al., 1991).
Fencl Model:
pH = f(pH){SID, PCO2, [PiTOT ], [Albumin], [CitrateTOT ]}
The knowledge of the independent variables ( [SID], PCO2,
and ATOT) and the equilibrium constants KW', KA, KC and
K3. allow to calculate any one of eight dependent
variables:
◦ HCO3-
◦ A-
◦ HA
◦ CO2 (dissolved)
◦ CO32-
◦ H2CO3
◦ OH-
◦ H+
Note that dissolved CO2 and H2CO3 are easily determined
from Equations #7A and #7B.