Properties of Water

When looking at the periodic table, the closest related compounds to water (H₂O) would be H₂S (same group 6A element, just below Oxygen), or maybe H₃N (i.e. NH₃, or ammonia) or HF (hydrofluoric acid).

• However, water is a lot different than these other compounds, in particular, its melting point and boiling point are "abnormally" high
• These properties of water indicate that the intermolecular (non-covalent) attractive forces between water molecules must be unusually strong (because the above mentioned phase transitions are based on thermal motions overwhelming the attractive forces)
• Hydrogen-bonds are the principle non-covalent attractive force between neighboring water molecules, and are responsible for the unusual physical properties of water. For this reason, it is important to understand the nature of hydrogen bonding, particularly between water molecules

Molecular Structure

• Hybrid orbitals, valence electron geometry and molecular geometry:

• Dipole: Oxygen is more electronegative than hydrogen, therefore, the oxygen-hydrogen bonds are polar. Due to the bent geometry, the overall molecule has a dipole.

• Molecular dimensions
• The O-H bond length is ~ 1.0Å (0.1nm)
• The van der Waals distance for hydrogen is ~1.2Å
• The van der Waals distance for oxygen is ~1.4Å

• However, in simple calculations water is often represented as a sphere with a radius of 1.4Å. This is because the oxygen will withdraw the electron cloud from the hydrogen, and thus, the van der Waals distance of hydrogen is reduced.

Water Structure

Water has a "structure" which is a consequence of the molecular geometry and the hydrogen-bonding potential of the water molecule

• Each water molecule can participate in up to four hydrogen bonding interactions:
• The two hydrogens are potential "donors" in a hydrogen bond interaction
• The two oxygen lone pairs are each potential "acceptors" in a hydrogen bond interaction
• Each H-bond is about 23kJ/mol in strength

In liquid water the hydrogen bond network between adjacent water molecules is in constant flux

• Being a liquid, neighbor molecules move around and H-bonds are constantly breaking and new ones reforming
• The average lifespan of a single H-bond in water is about 10ps
• However, an extensive H-bond network always connects all water molecules in a sample
• The combination of so many H-bonds between the water molecules results in the unusually high boiling point and melting point of water

The distance between Oxygen atoms in a typical H-bond between water molecules is about 2.8Å (0.28nm)

• The O-H covalent bond length is ~1.0Å. Therefore the H-bond distance between the donor H and the acceptor O is typically 1.8Å, but can vary from 1.6Å to 2.4Å.
• The typical distance of 2.8Å between O atoms in adjacent water molecules explains why a 1.4Å radius sphere model for waters can be useful
• The orientation is important; the O-H bond vector points directly at the acceptor lone pair, and vice versa

Ice Structure

• Cooling reduces thermal energy and you can get a phase transition to a solid form of water (i.e. "ice")
• A regular (crystalline) H-bond lattice forms (as opposed to the transient nature in the liquid form). This regular lattice is actually less-densely packed than the liquid form. Thus, ice floats in liquid water.
• The lattice is a regular arrangement based on the near-tetrahedral geometry of the Oxygen
• Six molecules can form a closed H-bond ring in ice, resulting in hexagonal appearance of snowflakes
• Water molecules in ice have low entropy

Water is a strongly polar substance. Based on the energetics of "like dissolving like" water is an excellent solvent of other polar and charged molecules and ions, and is a poor solvent for non-polar (e.g. aliphatic and aromatic) compounds

• Water molecules will separate, surround and disperse a polar solute
• Water molecules surrounding a polar or charged solute will orient according to H-bonding or electrostatic principles of dipole-dipole interactions (i.e. oppositely charged ends of dipoles will orient towards each other)
• The water molecules surrounding a solute are referred to as the "hydration or solvation shell" of waters

The ability of water molecules to surround and separate oppositely charged ion pairs in a solution is referred to as the dielectric constant of water.

• The dielectric of a substance is inversely related to the force experienced between opposite charged groups that are separated by the substance

F = e1*e2/Dr²

• What this equation says is that if a substance can prevent opposite charges from attracting each other (i.e. ions in water are "shielded" by the solvation shell from other ions) then it has a high dielectric (i.e. Attractive force between ions is small)
• Water has a dielectric of 78.5, and Hexane has a dielectric of 1.9 (will not shield charged ions from each other)

Water cannot hydrogen bond with non-polar molecules (aliphatic, aromatic hydrocarbons)

• Although C and H have slightly different electronegativities, C-H bonds are essentially non-polar and do not result in a meaningful dipole
• Water will form an ice-like lattice arrangement ("clathrate") around non-polar solutes in solution. Such water molecules will not orient a hydrogen or lone-pair of electrons towards the non-polar group. Thus, three legs of the tetrahedral Oxygen in a water molecule will "sit" on the top of the non-polar group and an ice-like cage of ordered water molecules will surround the non-polar solute

• This arrangements of water molecules is entropically costly.
• Therefore, the entropic cost will be minimized if the non-polar solute adopts a shape with the smallest surface area (i.e. a sphere). This is why oil forms a drop in water and not another shape.
• Removing non-polar groups from aqueous solution frees up water molecules in the clathrate, increases entropy, and is a lower free energy condition (i.e. spontaneous). Thus, individual oil drops in an aqueous environment will coalesce into a single large spherical drop (i.e. the "hydrophobic effect").

Amphiphilic/amphipathic molecules

• Amphipathic and amphipathic molecules possess both polar and nonpolar groups
• "amphi" means both, "pathos" means passion, "philos" means loving (its all Greek to me...)

Such molecules have both a polar region and a non-polar region

• In aqueous solution they have the ability to self organize according to the hydrophobic effect, i.e. they will assemble to as to remove the non-polar group from solution

Ionization of Water

Here are the main points:

• Oxygen has a greater electronegativity than hydrogen and occasionally a water molecule will ionize to form a hydroxide ion (OH^-) and a proton (H⁺)

H₂O(aq) à OH^-(aq) + H⁺(aq)

• Due to the extensive hydrogen bonding network in water, the proton is immediately transferred to another water to form a hydronium ion (H₃O⁺)

2H₂O(aq) à OH^-(aq) + H₃O⁺(aq)

• The H₃O⁺ ion can transfer a proton to another adjacent H-bonded water, resulting in rapid "proton jumping" through the water environment
• In pure water at 25°C, [OH^-(aq)] = [H₃O⁺(aq)] = 1 x 10^-7M

K_eq = [H⁺(aq)]*[OH^-(aq)] / [H₂O]

K_eq = 1 x 10^-7 * 1 x 10^-7 / [H₂O]

• Concentration of water is 55.5M (i.e. 1000g/L and 18g/mole), so

K_eq = 1 x 10^-7 * 1 x 10^-7 / 55.5

• The concentration of water, compared to the amount that would realistically ionize is essentially constant at 55.5M, therefore, we can combine with K_eq to make a new constant K_w (the "ion product of water")

K_w = K_eq * 55.5 = 1 x 10^-7 * 1 x 10^-7 = 1 x 10^-14

pH

pH = -log₁₀ [H⁺]

or

10^-pH = [H⁺]

• Stomach acid: [H⁺] = 6.31 x 10^-2M
• pH = 1.2
• Blood: pH = 7.4
• [H⁺] = 3.98 x 10^-8M

pK_w = pH + pOH = 14

pH = 14 - pOH

• "Neutral" pH: there is no excess of H⁺ over OH^- (they are equal in concentration), and pH = pOH. Therefore,
at neutral pH, pH = pOH = 7.0
• Acidic pH < 7.0
• Basic pH > 7.0

Strong electrolytes, like NaCl (an ionic compound), HCl (a strong acid) or NaOH (a strong base) dissociate completely in solution.

• In the case of HCl, the pH of a solution of HCl is found simply by knowing the concentration of HCl (since it dissociates completely). For example, a 0.05M solution of HCl will dissociate to produce 0.05M of H⁺ ion (and an equal concentration of Cl^- ion). Therefore, the pH will be 1.30

• Weak electrolytes only partially dissociate in solution
• Their dissociation is described by a characteristic "ionization constant" (Ka for acids, Kb for bases)
• Here is an example using acetic acid (CH₃COOH)

CH₃COOH(aq) ó CH₃COO^-(aq) + H⁺(aq)

Ka = [H⁺(aq)]*[CH₃COO^-(aq)] / [CH₃COOH(aq)]

Ka = 1.74 x 10^-5

• Thus, at equilibrium there will be a characteristic ratio of the concentrations of acid, proton and acetate ion, namely the value of Ka

Examples of problems involving weak acids, Ka and pH can be found at the above links.

The Henderson-Hasselbalch equation relates four parameters associated with the ionization of weak electrolytes in aqueous solution: pH, pKa, [A-] (i.e. concentration of conjugate base at equilibrium), and [HA] (i.e. concentration of undissociated weak electrolyte at equilibrium):

HA ó H⁺ + A^-

Ka = [H⁺] * [A^-] / [HA]

Rearrange to give [H⁺(aq)]:

[H⁺] = Ka * ([HA] / [A^-])

Take log10 of both sides:

log[H⁺] = log(Ka) + log([HA] / [A^-])

Multiply both sides by -1:

-log[H⁺] = -log(Ka) - log([HA] / [A^-])

Recognizing that -log[H⁺] is pH, and -log(Ka) is pKa

pH = pKa - log([HA] / [A^-])

pH = pKa + log([A^-] / [HA])

pH = pKa - log([HA] / [A^-])

pH = pKa - log(1/1)

pH = pK_a

• There is a characteristic inflection point at the pKa. By knowing how many moles of base were added to get to this point, we would be able to know that it equals one-half the number of moles of weak acid in the sample. Thus, pKa and concentration can be obtained from a single experiment

Buffers

Buffers are solutions of weak electrolytes that tend to resist pH changes upon the addition of small amounts of added acid or base.

• The above titration curve of a weak acid has a typical profile. Note that at a pH value near the pKa the sample is resistant to changes in pH with the addition of acid or base. Thus, a weak acid or base will tend to "buffer" the pH of an aqueous solution at a pH = pKa.
• The presence of both acid and conjugate base provides reactive species for "removal" from solution of added H⁺ or OH^- ions:

OH^- + HA ® A^- + H₂O ("removal" of OH^-)

H⁺ + A^- ® HA ("removal" of H⁺)

• Le Chatelier's principle states that a weak acid/conjugate base system in equilibrium will shift equilibrium to oppose changes in concentration of the components, thus maintaining the pH (i.e. H⁺ concentration, part of the components of the equilibrium)

Specific pH values are essential for enzyme function and other biological processes

Intracellular fluid

• pH is buffered by phosphate (pK₂ = 7.2; i.e. phosphoric acid is polyprotic) and the amino acid histidine (pKa = 6.04)
• pH is maintained between 6.9 - 7.4

Extracellular fluid

• pH is buffered by bicarbonate/carbonic acid system (pK1 = 3.57 !)
• This system is a little more complicated and involves dissolved CO₂(g) in the blood stream

CO₂(g) ó CO₂(blood)

CO₂(blood) + H₂O ó H₂CO₃

• A rapid equilibration of the above reaction is regulated by the enzyme carbonic anhydrase

CO₂(blood) + H₂O ó H₂CO₃
Kh = 3.00 x 10^-3

• Finally, the dissolved carbonic acid is in equilibrium with its conjugate base (bicarbonate ion):

H₂CO₃ ó H⁺ + HCO₃^-
Ka = 2.69 x 10^-4

• Thus, the carbonic acid equilibrium is regulated in part by the pool of CO₂ dissolved in the blood

Kh = [H₂CO₃] / [CO₂(blood)]
(note: water concentration is a constant and omitted)

[H₂CO₃] = Kh * [CO₂(blood)]

• Plugging this into the equilibrium expression for bicarbonate ionization:

Ka = [H⁺] * [HCO₃^-] / [H₂CO₃]

Ka = [H⁺] * [HCO₃^-] / Kh * [CO₂(blood)]

Ka * Kh = [H⁺] * [HCO₃^-] / [CO₂(blood)]

• From the known values of Ka and Kh given above, the overall K = Ka * Kh is:

2.69 x 10^-4 * 3.00 x 10^-3 = 8.07 x 10^-7

and pK for the buffer system = 6.09

• A pH of blood of 7.4 is more than 1 pH unit away from the pK of the overall system. This suggests that there is not much "buffering capacity" to deal with increases in OH^-. However, CO₂(g) in the lungs and the dissolved CO₂ in the blood provide a large pool of dissolved carbonic acid, and pH is maintained

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