Review Article

International Journal of Chemical & Physical Sciences, 24 May 2021 |
Year : 2021 | Volume: 10 | Issue: 2 | Pages : 10-26

Temperature of Maximum Density of Water - Electrolytes – A Review 

  • 1, LPG Arts and Science College, Shirpur Jain, Tq. Malegaon, Dist. Washim,
  • 2, Vidyabharati Mahavidyalaya, Amravati, IN

Additivity rule is found applicable to the Temperature of Maximum Density (TMD) behavior of strong electrolytes. For the first time a systematic attempt was made to divide Despretz constant Km of an electrolyte into its individual ionic contributions using partial molal expansivity of a proton, E .The large and positive deviations in ionic Km of R4N+ cations proved their well-known structure strengthening ability, corroborating satisfactorily with their structure promoting nature found from measurements of many thermodynamic properties.Despretz rule was found to obey for some amino acids.TMD Study by 1) acoustical technique, 2) Convective flow technique and 3) under pressure is also studied.


Water is known as universally most useful, structurally most complex, and anomalous liquid known to human beings. It plays an important role in life processes and forms an essential constituent of the animal cells & plant tissues. Two lone pairs of electrons on the oxygen atom, causes two bonded hydrogen atoms to give distinctive V-shape with a bond angle of 104.5°. This polarity gives extensive hydrogen bonding between water molecules which is responsible for many anomalous properties of water.

Some important and well-known anomalies of water are remarkably high melting (0 °C) and boiling points (100 °C). An especially important anomalous property of water is a Temperature of Maximum Density (TMD) at 3.98 °C. Thomas Charles Hope1 is the first scientist who recorded the TMD of water in 1805 by measuring convection pattern of water in an assembly of cylinder fitted with two thermometers and a metal basin which is known as Hope’s apparatus. Existence of the TMD of pure water was confirmed through a series of experiments by Hope, which was based on observing a temperature inversion due to natural convection, rather than bulk changes in the volume of the water.

Comparable substances like NH3, CH4, HF & H2S behave differently than water. Water exhibit characteristic properties of an associated liquid more remarkable than hydrides of elements of VIA group. The melting & boiling points of these hydrides decreases with decreasing molecular weights from H2Te, H2Se to H2S in an orderly manner, however, water has remarkably high values indicating a presence of strong force, known as hydrogen bonding. Due to this, water exists as monomers, dimmers, polymers, cage like clusters and many complex structures but cavities in the structure give rise to a lower density.

Conway2 defined the concept of Structure in liquid water in a simple way as follows: Water structure making / breaking ability of the solutes can be defined in terms of the effects on the molecular reorientation time (10-11sec), resulting either from rotational or translational diffusion. If the dissolved solute markedly lengthens this period, it is called as structure maker / promoter. Conversely, if the dissolved solute shortens this period, it is called as structure breaker.

At 3.98oC, water shows a maximum density due to breaking of hydrogen bonded network which allows the loosened water molecules to occupy the voids in the open structure, resulting in the contraction of volume and increase in density. Thus, the TMD is governed by a critical equilibrium between monomers or dimers and hydrogen bonded water molecules. When a solute is dissolved in water, the above equilibrium is disturbed. If a solute enhances hydrogen bonding (e.g. t-BuOH) then TMD increases and if the solute tends to destroy the hydrogen bonding (e.g. most electrolytes) then TMD decreases.

Apparent straight line plot of shift in TMD (Dqobs) versus ‘m’ is called as Despretz rule3, eqn(1).  

                                                   Dqobs  =  m. Km  or       Dqobs  =  x. KD                            … (1)

The constants Km (oC/mol/Kg)4-6 or KD (oC)7 known as Despretz constant are characteristic of the electrolytes. ‘m’ and ‘x’ are the molality and mole fraction of the dissolved solute respectively.

Rosetti8,9 reviewed the early work on shift in TMD of water by the addition of a solute for few simple salts. A considerable portion of this work is due to Despretz3. Most of the earlier work on TMD of aqueous solutions was carried out using density measurement techniques at higher concentration.

Further, Rosetti8,9 tried to correlate the shift in the TMD of water to the lowering of its freezing point due to addition of the same solute, but he failed to formulate any general rule between these two phenomena, as the lowering of the freezing point is related to the osmotic pressure of the solution and thus depends only on the concentration. However, shift in TMD is characteristic of the solute i.e. its interactions with the H-bonding and concentration of solute.

Wright10 studied the lowering of TMD of water for some salts. His findings agreed satisfactorily with the Despretz’s Law. He further, found that highly ionized salts of organic acids behaved in the normal manner like strong electrolytes and mineral acids. Coppet4 & Wright10 measured the shift in TMD only at 2–3 concentrations which were not enough to evaluate Despretz constant reliably. However, the TMD data of later workers for some electrolytes at 6–7 concentrations are reported in the International Critical Tables11 which were used by Pokale12 to calculate Despretz constant graphically using Least square fit method. He observed that Km values for simple electrolytes are always negative. Strong influence of valency and size of the ion is also apparent from this data.

Bernal & Fowler13 demonstrated applicability of additivity principle to the partial molal volumes (V ) of electrolytes at infinite dilution. Wirth14 divided V  of the electrolytes into their ionic components by assuming V  = V , on the consideration that the crystal radii of K+ and F- are nearly identical. This additivity of partial molal volume of electrolytes at infinite dilution in water has also adequately demonstrated by several researchers (Bernal & Fowler13, Horne15, Millero16, Scoot17, Desnoyers et al18, Couture & Laidler19). This additivity rule was found to extend up to moderate concentrations where ion-pairing is not extensive.

Many other electrolytic properties like viscosity B-coefficient, ionic radii, conductance etc. are also found to obey the additivity rule. Kaminsky20 demonstrated the additivity of viscosity B-coefficients for aqueous solutions of electrolytes at various temperatures. He assumed BK+ = BCl- based on the almost identical cation and anion transference number for KCl at all temperatures and calculated ionic B-values for several ions which were in good agreement with those reported by other workers.  

Applicability of the additivity rule to the TMD behavior of strong electrolytes was observed by Wright10 using TMD data of Coppet4, Wada & Miura7, Rosetti8,9. Coppet4, Wada & Miura7, Rosetti8,9 also demonstrated the validity of additivity rule to the TMD behavior of some alkali halides using TMD data reported in literature. (ICT11).


Lilley & Murphy5, derived an eqn. (2) expressing ∂V /∂T in terms of Despretz constant Km as given below:  

 –  ∂V /∂T = Km / 64.1                                      (2)

 Where V  denotes the partial molal volume of electrolyte at infinite dilute.

A good agreement is seen between Km values evaluated from density measurements using eqn. (2) with the Km values obtained from TMD measurement (Wright10 & ICT11). However, the data used for TMD and density measurements are at high concentration which cannot yield reliable values. Hence, Km values reported by them needs to be modified using TMD and density measurements at sufficiently low concentrations, where the Debye – Huckel theory for the ion-water interaction will be valid.


Additivity rule is valid for Temperature of Maximum Density (TMD) of strong electrolytes. Despretz rule for electrolytes at high concentration is inadequate from experimental and theoretical grounds due to ion-ion, ion-solvent, and ion-distant neighbor interactions. Reliable individual ionic Despretz constant Km of electrolytes have been evaluated using partial molal expansivity of a proton, E .

No regular relationship was found between Km with Pauling ionic radii (r) as probably later do not correspond to effective size of the ions in water due to ion-water interactions leading to electrostriction and the change in the structure of water. A much more orderly behavior of Km versus effective ionic radii (r + D) for all the cations and anions including tetra alkyl ammonium cations is remarkable showing two nearly parallel straight lines for cations and anions. The limiting ionic Km values thus seems to be governed by the effective volume of the ions in aqueous solution


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Keywords: TMD, Despretz rule, electrolytes solution, water structure, Hopes appratus

Citation: Dr.Waman Pokale*,awpokale,Dr.Waman Pokale,awpokale ( 2021), Temperature of Maximum Density of Water - Electrolytes – A Review . International Journal of Chemical & Physical Sciences, 10(2): 10-26

Received: 09/05/2021; Accepted: 23/05/2021;
Published: 24/05/2021

Edited by:

Dr.Waman Pokale, , LPG Arts and Science College, Shirpur Jain, Tq. Malegaon, Dist. Washim,

Reviewed by:, , Principal, IN, , Principal, IN

Copyright: Y.

*Correspondence: Dr.Waman Pokale,