Significant
results (1979 - 2009
)
(Raji Heyrovska, Ph. D.)
(See list of publications in this webpage for work before 1979)
Contents:
I. Partial dissociation and hydration of Strong electrolytes at all concentrations (Arrhenius, Van't Hoff and Ostwald were right!)
II. Distances of closest approach of ions (evaluated using degrees of dissociation in Bjerrum's equation)
III. Anomalous Stokes ionic radii explained (so-called anomaly disappears on using "local" instead of "bulk' viscosity in the S-E Eqn.)
IV. "Wet-and-measure" polarography (uses small amounts of solution held by surface tension between a silver ring and the glass capillary)
V. Current spike polarography for films and surfaces (tip of the mercury drop contacts the solution at the end of its drop life)
VI. Rest mass based neutron numbers, N(rm) (exact rest masses shows that for A > 108 (Ag), N(rm) = N -1 and for A > 254 (Es), N(rm) = N - 2)
VII. Interpretation of Michelson & Morley's observations (without invoking the contraction of distance hypothesis demanded by the special theory of relativity) (First author: Albert Heyrovsky)
VIII. Mass defect due to neutrinos evaluated from nuclear mass defects (based on the fact that fusion of a proton and a neutron to form a deuteron releases a neutrino, antineutrino pair and causes a definite mass defect attributable to neutrinos)
IX. A new theory of the energy of the hydrogen atom (shows that the Bohr radius is divided into two Golden sections pertaining to the electron and proton. This leads to the assignment of Golden ratio based ionic radii which explain quantitatively the interionic distances in all alkali halides and further, to the additivity of atomic/ionic radii in bond lengths (1999 - 2009))
X. The absolute potentials of the standard hydrogen electrode (and of redox couples of elements have been obtained (2009)).
XII. Women in Science (2002 - 2009)
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Full texts of 14 papers are
available at:
http://arxiv.org/find/all/1/all:+Heyrovska/0/1/0/all/0/1
Abstracts
and full texts (DOI) of 13 articles are at:
------------------------------------------------------------------------------------------------------------------------------
I. Partial dissociation of Strong electrolytes (Arrhenius, Van't Hoff and Ostwald were right!)
Introduction: I got acquainted with the properties of strong electrolytes when I was working for my Ph. D. degree. Ever since, I was wondering why the theory of electrolytes was so complicated. It was based on extensions to higher concentrations of the Debye-Huckel equations, which were valid only for very dilute solutions, and there was no unified interpretation of the thermodynamic properties over the whole concentration range (e.g., see: R. A. Robinson and R. H. Stokes, Electrolyte Solutions, Butterworths, London 1955, 1970).
During the years 1979 - 1984, by a systematic analysis of the existing data on the thermodynamic properties of electrolytes, it became gradually clear to me that the assumption of complete dissociation of strong electrolytes that prevailed from 1923 onwards had to be abandoned in favor of the earlier van't Hoff's factor for non-ideality and its interpretation by Arrhenius through the idea of partial dissociation. On combining the ideas of partial dissociation and hydration (as Arrhenius himself had suggested) as pointed out by Bousefield (1917), I could show unambiguously in 1984, that the thermodynamic properties of electrolytes could be quantitatively explained using simple equations (a century after Arrhenius wrote his dissertation for the Ph. D.!).
Subsequently,
in 1987 I could explain the solution properties quantitatively from
zero upto a higher concentration of about 3.5m by using the degrees
of
dissociation
and hydration numbers obtained from the
equation for the
vapor
pressure. It was published
in a detailed form in: R. Heyrovska, Chapter
A full paper on this was accepted with encouraging remarks in: R. Heyrovska, Journal of Electrochemical Society, 143 (1996) 1789. Thus, since solution properties could now be explained quantitatively using concentrations and volumes of ions and ion pairs and of free water, the arbitrary thermodynamic correction factors like activity and osmotic coefficients, evaluated on the assumption of complete dissociation of electrolytes, finally proved to be unnecessary.
Since
1996, I have extended the above work to all the alkali halides, strong
acids,
bases and many more strong electrolytes. After my talk on the
subject at Harvard University, (my host) Prof. J.N. Butler, Editor
of
"Ionic Equilibrium" (John
Wiley and
Sons, New York, 1998), invited me
to write a
short account in his book which he had almost completed. An invited
full review of my work is in: R.
Heyrovska,
Chemicke Listy, 92 (1998)
In 2003, it was a great honour for me to have been awarded the Invited Plenary Lecturership in the Svante Arrhenius Symposium commemorating the award of the Nobel Prize to him in 1903. The text of this Lecture is in my above webpage and has now been published along with more data in: R. Heyrovska, Electroanalysis, 18 (2006) 351-361.
Further, I have worked out a concise equation of state for solutions of electrolytes, based on hydration and partial dissociation, which incorporates the thermodynamic laws (see: R. Heyrovska, Special Issue of ENTROPY, 6 (2004) 128). This was on the analogous lines of an equation of state that I had developed earlier for gases (presented at a conference on the Second Law of Thermodynamics in San Diego, CA, in 2002) in: R. Heyrovska, AIP Conference Proceedings, 643 (2002) 157.
Outline of the work: The idea of partial dissociation of strong electrolytes in aqueous solutions due to Arrhenius was highly appreciated at a time when solution chemistry was in bad need of it. The use of the conductivity ratio for the degree of dissociation could satisfactorily explain many experimental results for dilute solutions. Since the conductivity ratio became unsatisfactory for higher concentrations, especially for highly dissociated electrolytes like NaCl, Lewis and Randall arbitrarily introduced the "activity coefficients" as empirical non-ideality correction factors for concentrations (in the absence of an exact knowledge of the concentration of the undissociated form). Since the Debye-Huckel theory, which treated non-ideality as due to interionic interactions, was able to account for the dependence of the actvity coefficient (and other properties of electrolyte solutions) on the square root of concentration for dilute solutions, strong electrolytes were "assumed" (erroneously) to be completely dissociated as shown,
NaCl -----> Na+ + Cl- ... (1)
The
DH equations were then gradually extended by the addition of more and
more
parameters for explaining the solution properties over larger ranges of
concentration [and finally upto saturation, e.g., see the Pitzer
equations in: D. G. Archer, J. Phys. Chem.
Ref. Data
28 (1999) 1 and elsewhere].
As these elaborate parametrical equations could not provide a molecular insight into non-ideality, the author undertook a systematic re-investigation of the available thermodynamic data as such and eventually found (by evaluating the degrees of dissociation from vapor pressure or solvent activity data) that strong electrolytes are indeed only partially dissociated in aqueous solutions as originally supposed by Arrhenius a century earlier:
NaCl <=====> Na+ + Cl- ... (2)
(1- a) <=====> a + a; [sum = i = (1+a)]
Thus, a fraction a of one mole of NaCl dissociates into a moles each of Na+ and Cl- ions, amounting to 2a moles of ions, and (1-a) mole remains as neutral NaCl. a is the degree of dissociation at the given concentration of NaCl in the solution. The total number of moles of solute per mole of NaCl (solid) dissolved in the solution is given by the van't Hoff factor, i = (1+a) (which is the non-idealilty factor i in van't Hoff's law for electrolyte solutions).
Thus, with the degrees of dissociation and hydration numbers (both surface and bulk) obtained from the experimental values of solvent activities (aA), many thermodynamic properties could be interpreted quantitatively using simple mathematical relations, valid from zero even up to saturation in many cases. The DH equations were shown to be asymptotic laws for complete dissociation at infinite dilution, and hydration and ion association proved to be the causes of their inapplicabilty to higher concentrations beyond infinite dilution.
"The thermodynamic dissociation constant", K for NaCl(aq) was shown to obey the Guldberg and Waage's Law, defined as,
K = ( ci)2
/cip
= constant (at all concentrations)
where ci = am/Vi is the number of moles of either ion per unit volume of solution occupied by the ions and cip= (1-a)m/Vip is the number of moles of ion pairs per unit volume of the solution occupied by the ion pairs (R. Heyrovska, Chemicke Listy, 92 (1998) 157).
Therefore,
since now we
have the values of the thermodynamic "ionic molality, am"
of an ion at any molality m of the electrolyte, there is no need
for
the
arbitrary correction factors, activity and osmotic
coefficients.
Complete details can be found in the above mentioned text
of the
Invited Plenary Lecture in my webpage and in: R.
Heyrovska,
Electroanalysis, 18 (2006) 351-361.
II. Distances of closest approach of ions (evaluated using degrees od dissociation in Bjerrum's equation)
Bjerrum
thought that in a strong electrolyte like NaCl in aqueous solutions,
ion pairs
are unlikely since the critical distance of approach for ion pair
formation, q ~
(1-a)/c = 2.755 Q(b); Q(b) = f(a)
where Q(b), the Bjerrum's integral is a function of "a". For NaCl(aq), (1/a) changes linearly with 1/m and even at saturation, a < q.
References
(R. Heyrovska): Journal of Molecular Liquids, 81 (1999) 83 (Letter) and
Current
Science, 76 (1999) 179 (full paper).
III. Anomalous Stokes ionic radii explained (so-called anomaly disappears on using "local" instead of "bulk" viscosity in the S-E Eqn)
The Stokes ionic radius, RSi is obtained from the Stokes-Einstein equation (S-E eqn),
Diwo = kT/6phoRSi ... (1)
where ho
is the coefficient of viscosity of the pure solvent (water, w) in the
bulk. The
"anomalous" values of RSi are usually associated with
ionic hydration. It is shown here that the "anomaly" is
due to the
(incorrect) use of ho instead
of hwi,
that of water adjacent to the ions. The modified
S-E
eqn. is thus:
Diwo = kT/6phwi Rwi ... (2)
where RSi = Rwi hwi /ho and Rwi is the radius of a water molecule adjacent to ion i.
Reference (R. Heyrovska): Chemical Physics Letters, 163 (1989) 207.
IV. "Wet-and-measure" polarography (uses small amounts of solution sticking by surface tension between a silver ring and the glass capillary)
This device shows that the volume of solution that sticks by surface tension betwen a silver ring and the end of the glass capillary of the mercury electrode is quite enough for polarogarphy, since it gives the same polarograms as those with mercury electrodes dipping in bigger volumes of solution as in conventional polarography.
Reference (R. Heyrovska): Journal of Electrochemical Society, 139 (1992) L50.
V. Current spike polarography for films and surfaces (tip of the mercury drop contacts the solution at the end its of drop life)
Here, the mercury drop contacts the surface or film of the solution in a silver ring electrode at the end of its drop life and hence a current spike is recorded. This is sensitive to oxygen and can be used as an oxygen sensor, also for measuring the difference between the surface and bulk potentials (c -potential), for fast electron transfer processes and for detecting the polarographic maxima of the 1st and 2nd kinds.
Reference
(R. Heyrovska): Langmuir, 9 (1993) 1962.
VI. Rest mass based neutron numbers, N(rm) (exact rest masses show that for A > 108 (Ag), N(r,m) = N - 1 and for A > 254 (Es), N(r,m) = N - 2)
These
values of N(rm) are based
on the exact rest masses of the electron (me =
0.00054858
u), proton (mp = 1.0072765 u) and neutron (mn =
1.0086649
u). Note that the
conventional neutron numbers (N) are approximate
values since they are based on the approximations me
= 0, mp = mn = 1 u.
Therefore,
N(rm) ~ [A - Z (me+ mp)]/mn ~ N only for atomic masses A < 108, and for A > 108(Ag), N(r,m) = N - 1 and for A > 254 (Es), N(r,m) = N - 2.
References
(R. Heyrovska): Journal of Chemical Education, 69 (1992) 742 (short
paper);
216th Meeting of the American Chemical Society, Boston, Aug. 1998,
short
abstract no. 11.
VII. Interpretation of Michelson & Morley's observations (without invoking the contraction of distance hypothesis demanded by the special theory of relativity) (First author: A. Heyrovsky)
As the interpretations usually involve the "contraction of distance" and dilation of time hypotheses (as per the special theory of relativity), which have NOT been directly experimentally verified, M&M's observations are explained here by a vector addition of the velocity of the Earth with that of light assuming Galilean kinematics, WITHOUT the contraction or dilation hypotheses.
Reference
(A. Heyrovsky and R. Heyrovska): Physics Essays, 7 (1994) 265.
VIII. Mass defect due to neutrinos evaluated from nuclear mass defects (based on the fact that fusion of a proton and a neutron to form a deuteron releases a neutrino, antineutrino pair and causes a definite mass defect attributable to neutrinos)
The idea behind this is that a neutrino, antineutrino pair is released during the synthesis of a deuteron from a neutron and a proton. Therefore, if the neutrinos have mass, the nuclear mass defect, MD = (ZmH+Nmn) - A, where A is the atomic mass of the nuclide X(Z.N) must also contain the mass defect due to neutrinos. Based on this, it is shown here that the mass defect due to neutrinos, MD(n), for any nuclide is a definite fraction of MD:
MD(n)/MD = [Z/(ZmH+Nmn)](mn-mp)2/mn
The values of the mass defect per nucleon due to neutrinos/antineutrinos, MDPN(n) = MD(n)/(Z+N), (which are in the expected eV range!) have been tabulated for the most abundant nuclide of everyone of the 105 elements.
References
(R. Heyrovska): 216th Meeting of the American Chemical Society, Boston,
Aug.
1998, short abstract no. 9. In book form: Arjun Consultancy &
Publishing
Inc., Desktop publisher, Wayne, NJ (USA), 1998. (Full paper)
IX. A new theory of the
energy of the hydrogen atom (shows that the Bohr radius is
divided
into two Golden sections pertaining to the electron and proton.
This
leads to the assignment of Golden
ratio based ionic radii
which explain quantitatively the interionic distances in all alkali
halides and further, to the
additivity of
atomic/ionic radii in
bond lengths (1999 - 2009)).
X. The absolute potentials of the standard hydrogen electrode and of redox couples of elements
136, 141. The absolute potential of the standard hydrogen electrode (which was so far taken arbitrarily as zero) and of redox couples of elements have been obtained from a simple linear correlation of aqueous standard potentials with gaseous ionization potentials.
XI.
Other significant results
(1999 - 2009) (Selected
few only. Reference numbers are as in the List of publications.)
85. Degrees of
dissociation and hydration numbers of monovalent
sulphates including
ammonium
sulfate (1999).
See: http://www.electrochem.org/dl/ma/196/pdfs/2041.PDF
and a Table of data
in:
http://www.jh-inst.cas.cz/~rheyorvs
86, 96.
Thermodynamic significance of transfer
coefficients and E. M. F. of
concentration cells (2000, 2002).
Shows that the
transfer coefficient is not
merely a kinetic parameter, but is basically a thermodynamic parameter
which
influences the kinetics.
90. Aqueous redox
potentials related to ionization potentials and electron
affinities of
elements
by simple linear equations (2000).
Linear relations
have been shown for elements in
many groups in the Periodic Table.
92.
An estimation
of the ionization
potentials of actinides from a simple dependence of
the
aqueous standard potentials on the ionization potentials of elements
including
lanthanides (2000/2001).
Using the linear
relation shown above in Ref. 90, the ionization
potentials for the
actinides (which had not been obtained before due to their instability)
have
been estimated. See also Ref. 136 (2009)
on absolute potentials for newer estimation..
98. A
The new concise
equation of state (with
association/dissociation of molecules) incorporates also heat
capacities,
the thermodynamic laws and entropy. The fundamentals of the 2nd law are
discussed.
The new concise
equation of state (with ion
association and hydration), analogous to that for gases in Ref. 98, incorportaes also heat
capacities,
the thermodynamic
laws and entropy.
106. Hydrogen
as an atomic condenser (2004).
While
working on the ionization potentials, the author arrived at the
conclusion that the ground state Bohr
radius is divided into two Golden sections at the point of electrical
neutrality. The ionizational
potential is
the difference of two terms pertaining to the proton and electron. This
explains why the two oppositely charged particles do not fall into each
other,
and shows that the two terms in
the Rydberg equation for spectra arise
in the
ground state term itself. The energy of hydrogen can thus be
considered
as the electromagnetic energy of the simplest atomic condenser
with the Golden mean capacity. Reference: http://flux.aps.org/meetings/YR04/DAMOP04/baps/abs/S400132.html
110.
The Golden ratio (f), ionic
and atomic radii and bond lengths (2005).
Shows
that since the Bohr radius has
two Golden sections, interatomic distances (between like atoms)
are
divided
into two Golden sections, representing meaningful anionic and cationic
radii. The
latter account for the full (as in alkali halides) and partial ionic
(like hydrogen halides) character of some chemical bonds,
and show
that bond
lengths, in general, are sums of atomic/ionic radii. Tables of ionic
and atomic radii and bond lengths
are provided.
Reference: R. Heyrovska, Special Issue of Molecular
Physics, 103 (2005)
877 - 882. For more publications: see full List of publications.
112.
Fine-structure
constant, anomalous magnetic moment, relativity
factor, the Golden ratio, and the Bohr radius (2005)
Shows
that the ratio of the difference
in g-factors (of the electron and proton) to their sum, is equal to f-3, and that
they are related to the inverse fine-structure constant (137.036) and
the
Golden
section (360/f2 = 137.51).
Sommerfeld's relativity correction factor (for the advance of the
perihelion for hydrogen atom), is also explained.
Reference: http://arxiv.org/ftp/physics/papers/0509/0509207.pdf
(2005)
115. Dependence of
ion-water distances on covalent radii, ionic radii
in water and distances of oxygen and hydrogen of water from ion/water
boundaries (2006).
The
linear dependences give the
aqueous ionic radii of many different elements and lengths of the
hydration bonds,
which are all functions of the Golden ratio. The hydrogen bond with all
the halide
ions is found to be have a constant length and is the sum of the f-based cationic
radius and covalent radius of hydrogen (of water).
Reference: R. Heyrovska, Chem. Phys. Letts., 429 (2006)
600 -
605.; doi:10.1016/j.cplett.2006.08.073
117. Dependence
of the length of the hydrogen bond on the
covalent and cationic radii of hydrogen, and additivity of bonding
distances.
Reference:
R. Heyrovska, Chem. Phys. Letts., 432 (2006) 3498 - 351; doi:10.1016/j.cplett.2006.10.037
XII.
Women in
Science (see full articles in List of Publications)
References
1 - 14 (in
pink):
Publications (2002 - 2009) on suggestions
for
improving the
academic status/situation of Women in Science.
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