Focus 3, WATER and AQUEOUS SOLUTIONS
Gibbs energy: G = H -TS dG = Vdp - SdT (gibbs energy with pressure and temperature)
an increase in temperature (delta T > 0) results in a decrease in Gm (delta Gm <0)
dG = Vdp (gibbs energy with pressure)
molar gibbs energy increases (dG > 0) when the pressure increases (dp > 0)
change in molar gibbs energy is greatest for substances with large molar volumes
slope of graph of Gm against p is greater for the liquid phase of a substance than for its solid phase
dependence of Gm on p is much greater for a gas than for a condensed phase (l or s)
slope of a graph of Gm against p is greater for ice than for liquid water (exception)
Gm (pf) = Gm (pi) + RT ln (pf/pi)
shows the molar gibbs energy of water vapour increases logarithmically (as ln p) with the pressure
Vm = RT/ p
Vm gets smaller, Gm becomes less responsive to pressure
dGm = -SmdT variation of gibbs energy with temperature
(provided the entropy is constant over the narrow range of temperatures ΔT = Tf - Ti
ΔGm = -SmΔT cariation of gibbs energy with temp (entropy constant in the range)
“molar entropy is postivie for all substances”
increase in temp (ΔT>0) results in a decrease in Gm (ΔGm<0)
entropy of transiton if related to the enthalpy transition by ΔtrsS = ΔtrsH / Ttrs
for liquid-vapour equilibrium of water: dp = (ΔvapH/TΔvapV)dT
gives change in vapour pressure of water
for ice-liquid equilibrium: dT = (TΔfusV/ΔfusH)dp
gives change in melting temperature of ice cause by a change in pressure
ΔfusH > 0 (melting is endothermic)
molar volume of water decreases on melting ΔfusV < 0
→ increase in pressure brings about a decrease in the melting temperature of ice
(for water at 1 bar, ΔfusH⦵ = 6.008 kJ/mol and ΔfusV⦵ = -1.634 × 10^-6 m³/mol-1
ΔvapV = Vm (g) - Vm (l) = Vm(g) dp/p = d ln(p)
open system: temperature at which a vapour pressure of a liquid is = to the external pressured called boiling temperature (Tb)
when external pressure is 1 atm
in closed vessel - vapour density increases as the vapour pressure rises and in due course the density of the vapour becomes equal to that of the remaining liquid (critical point)
The surface between two phases disappears → supercritical fluid
critical temp (Tc), critical pressure (Tp) for water, Tc=647K Tp=24.0MPa
liquid cannot be produced by the application of pressure to a substance if it is at or above its critical temperature
notion of critcal temperature producs the basis of the distinction between a vapour and gas; <Tc , vapor. >Tc, gas
in biochem analysis to remove the water from biological samples (dry them for long term storyagae
freeze-drying = removing water from aqueous solutions of biological macromoles (proteins) either by heating or evaporation at room temperature usually leads to denaturation → loss of activity
surface tension (γ) (gamma) - measure of work needed to drag out molecules from the bulk liquid and use them to form a surface
w=γΔA (J /m²) ΔG=γΔA
if ΔA is (-), ΔG is (-) = spontaneous; spontaneous direction of change is for a droplet to minimize its surface area
direction of spontaneous change at constant pressure and temperature is to lower Gibbs energy
if partial molar gibbs energies of water (W) and solute (S) in solution are known, then total gibbs energy (G) of mixture is: G = nwGw,m + nsGs,m (molar amounts of molecule)
partical molar gibbs energy = chemical potential (μ): G=nwμw + nsμs
infitiesimal amount (dnw) of W migrating from liquid to vapour
dG = μw(g)dnw - μw(aq)dnw = {uw(g) - μw(aq)}dnw
at eqm, dG = 0 → μw(g) = μw(aq)
μJ⦵ is standed chemical potential of J as a gas (identical to Gm(j) for pure vapor at 1 bar)
μJ(g) = μJ⦵ (g) + RTln pJ
the higher the partial pressure of vapour, the greater is its chemical potential
raoult’s law: pw = xw pw* xw = mole fraction of water in soln, pw* = vapour pressure of
pure water
μw (aq) = μw* (l) + RTln(xw) chemical potential of water in ideal soln
henry’s law: [S] = KhpS : molar concentration [S] of gas in solvent is proportional to its partial pressure ps
non-volatile solute has 3 main effects:
raises the boiling point of solutiion
lowers the freezing point
gives rise to an osmotic pressure
called colligative properties - and are independent of the identity of the solute (provided solution is ideal)
ΔTb = KbbS elevation of the boiling point depression of the freezing point
ΔTf = KfbS
Kb = ebullioscopic constant Kf = cryoscopic constant bS = molarity of the solute
to understand the origin of increment of boiling point and decrease of freezing point (of colligative properties) we mkae 2 simplifying assumptions:
solute isnt volatile and therefore does not appear in the vapour phase
solute is insoluble in ice (in general, the solid phase of the solvent) and therefore doesnt appear in ice when an aqueous solution is frozen
μw = μw* + RT lnxw with xw <1 and therefore ln xw < 0 in a solution
antifreeze protein (AFP) - water temp = -1.9C
cold-tolerant fishes, insects, plants & microorganisms express various types of AFPs
ice crystals aggregate with each other and overal volume increases
growth of ice crystals are limited to certain size and crystals cannot aggregate with each other → volume does not change
inhibit growth of ice crystals, modify the ice shape, depress aggrdgates of ice crystals
application of AFP: food industry (frozen food), reduction of cooling energy, medical, low-temp storage of bloods, cells and organs for transplate, advanced material
osmosis - thermodynamics of transfer of water through membranes
semipermeable membrane might have microscopic holes that are large enough to allow water molecules to pass throguh but not ions or carbohydrate molecules with their bulky coating of hydrating water molcules
osmotic pressure (Π) = pressure that must be applied to the solution to stop this spontaneous inward flow of water
The pressure opposing the passage of water into the osmosis arises from the hydrostatic pressure of the column of solution that the osmosis itself produces
hydrostatic pressure = pgh
p: mass density of the solution
g: acceleration of free fall
h: height of the column
ideal aqueous solution can be shown thermodynamically to be proportional to the concentration of solute
Π = [S]RT the van’t hoff equation [ideal-dilute solution]
water potential Ψ = μw - μ⦵w / Vw
Vw = partial molar volume of water in the soln
μ⦵w = standard chemcial potential of water
therefore the density of the deviation of the chemical potential of water from its standard value and has the dimesions of energy/volume (therefore press)
4 contributions to μw the chemical potential under conditions other than standard:
the standard value itself μ⦵w
contribution due to the presence of a solute S at mole fraction xs. this contribution is to RT lnxs (if solution is ideal) and is = to -ΠVw
within a cell, pressure difference from the external pressure (taken to be the standard pressure, p⦵) is the turgor pressure (P) so p internal = p⦵ + P. contribution to the chemical potential of a change in pressure from p⦵ to p⦵ + P on incompressible fluid, is = to PVw
if the effects of gravitational field need to be considered, Mwgh is included. Mw = molar mass of water, g= aceleration of free fall, h = height of the region above the surface of the earth
Ψ = P - Π + pwgh water potential
pw = Mw/Vw = mass density of water in solution
if only the gravitational term is consider, water at altitude (h>0) has a higher potential than water at ground level (h=0) so natural direction of flow of water is downwards
if P=0 and Ψ= - Π, natural direction of flow of water is from low osmotic pressure to a region of high osmotic pressure
if Ψ = P - Π, Ψ increases until P = Π at which point there will be no net flow of water into the cell