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Year 2 - Chem > Liquids and Solutions > Flashcards

Liquids and Solutions Flashcards

1
Q

What is an extensive/intensive variable?

A

Extensive - depends on size of system
Intensive - doesn’t depend on size

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2
Q

What are some examples of intensive and extensive variables?

A

Extensive: A, V, n (therefore dA, dV, dn)

Intensive: T, P, μ

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3
Q

What is the condition for chemical eqm?

A

μiα = μiβ

where μ is derivative of G wrt n

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4
Q

What is an ideal solution?

A

Equivalent to ideal gas
All interactions are the same - molecule 1 doesn’t care if surrounded by 1 or 2

Ideal entory of mixing

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5
Q

What is the ΔmH (of mixing) in an ideal solution?

A

ΔmH = 0

As all interactions are the same

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6
Q

What is the model used for ideal ΔmS?

A

Lattice model of a binary mixture

N1</sub molecules of type 1
N2 molcules of type 2
N lattice sites
Random mixing

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7
Q

What is Boltzmann’s eqn of entropy?

A

S = kb lnΩ

Ω = number of ways you can realise a given conformation
Ω = N!/[N1!N2!]

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8
Q

What is the ideal ΔmS?

A

ΔmS = -R[n1lnx1 + n2lnx2]

where ΔmS = Smix - Sunmix

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9
Q

What is x and sterling’s approx?

A

x is mole fraction

For small values of x:
lnx! = xlnx - x

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10
Q

What is the ΔmG of an ideal solution?

A

ΔmG = ΔmH - TΔmS = 0 + RT[n1lnx1 + n2lnx2]

Totally entropic

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11
Q

What is the μ of an ideal solution?

A

μ = (δG/δn)
G = Gunmix +RT[n1lnx1 + n2lnx2]

μ = μi + RTlnxi

Vapour pressure linearly related to molar pressure

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12
Q

What is Raoult’s law?

A

For an ideal solution on a boundary with ideal gas

Pi = xiPi*

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13
Q

How can you derive Raoult’s law?

A

μisolution = μivapor

Gas and solution is ideal
1) μi* + RTlnxi = μθ + RTln(Pi/Pθ)
2 (when @xi)) μi* = μθ + RTln(Pi/Pθ)

1-2 so:
RTlnxi = RTln(Pi/Pθ) - RTln(Pi*/Pθ)
gives:
xi = Pi/Pi*

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14
Q

How does a solid in an ideal solution change temeprature?

A

Solid is solvent

ΔT = T - T* = - X2 (RT*2/ΔfusH)

where T* is the freezing point of water, and X2 is mole fraction of ideal solution

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15
Q

What is a non-ideal solution?

A

Interactions not identical
Non-ideal entropy of mixing
Combination of both

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16
Q

What is a regular solution?

A

Same as ideal soltuion but interactions not identical
so Δm =! 0

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17
Q

How is a polymer solution different to an ideal one?

A

Non-ideal (so different) entropy of mixing

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18
Q

What is the potential of a non-ideal solution?

A

μi = μi* + RTlnki + RTlnfi

where the activity coefficient is fi

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19
Q

What is Henry’s law?

A

Pi = xiKH

Not derived
When component is the minority - so linear vapour pressure when low or high x

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20
Q

When is Raoult’s and Henry’s law followed?

A

Roult’s - for a substance when pure (xi~1)

Henry’s law - for a substance when in minority (xi~0)

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21
Q

What is ΔmS in a regular solution?

A

Same as ideal
ΔmS = -R[n1lnx1 + n2lnx2]

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22
Q

How do you derive the sum of interactions, w, in a regular solution?

A

ΔH = Hmix - Hunmix

Hunmix = (1/2)zN1w11 + (1/2)zNw2w22 = (z/2)(N1+N2)(w11x1 + w22x2)

Hmix = (z/2)(N1+N2)(w11x12 + w22x22 + 2w12x1x2

Then work out difference and eventually gives
ΔmH = z(n1+n2)x1x2 [w12 - (w11+w22)/2]

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23
Q

What is sum of interactions in a regular solution?

A

w = NAz[w12 - (w11+w22)/2]

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24
Q

What model is used for the enthalpy of mixing in a regular solution?

A

Lattice model of binary mix

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25
Q

What are the assumptions in enthalpy of regular solution?

A

Random mixing

Only nearest neighbour interactions, w

Volume constant, and as H = U + PV, so ΔH = ΔU

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26
Q

What is the coordination number, z, in nearest neighbours?

A

Number of neighbours at a lattice site

z=3, triangle
z=4, square
z=6, hexagonal

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27
Q

What is the ΔmH of a regular solution?

A

ΔmH = (n1 + n2) Wx1x2

where W = NAz[w12 - (w11+w22)/2]

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28
Q

What is ΔmG of a regular solution?

A

ΔmG = ΔmH - TΔmS

ΔmG = (n1+n2)Wx1x2 + RT[n1lnx1 + n2lnx2]

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29
Q

What is the chemical potential of a regular solution?

A

μ1 = μ1* + RTlnx1 + wx22

can relate to f1 = exp[wx22/RT]

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30
Q

What is the ideal limit of activity coefficient?

A

f1 = exp[wx22/RT]

ideal limit when w=0 so f1 = 1

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31
Q

What is nearest neighbour interactions in an ideal solution?

A

w11 = w12 = w21 = w22

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32
Q

How do you relate the vapour pressure of regular solutions?

A

P1 = x1P1* exp[wx22/RT) = x1P1* f1

Remember: for ideal gas and regular solution chemical eqm

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33
Q

How do you derive eqn for vapour pressure of regular solution?

A

Boundary of ideal gas and regular solution in eqm,
μsolution = μvapour

μ1* + RTlnx1 + Wx22 = μ1θ + RTln(P1/Pθ)

when x1 = 1 and x2 = 0,
μ1* = μ1θ + RTln(P1/Pθ)

then 1st - 2nd equation
RTlnx1 + Wx22 = RTln(P1/P1*)

rearrange to
P1 = x1P1* exp[Wx22/RT]

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34
Q

What is seen when two phases separate?

A

Starts with mix
Finishes with two phases, neither are pure but just richer in one

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35
Q

What factors determine if phase separation occurs in a regular solution?

A

g = wx1x2 + RT[x1lnx1 + x2lnx2]

when high w then encourages demixing, when low then mixing

when high T encourages mixing, when low T is demixing

Wants to min Gibbs free energy

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36
Q

How does W change if mixing/demixing occur?

A

W = NARz[w12 - (w11+w22)/2]

if W +ve then w11 and w22 more -ve so more attractive than w12

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37
Q

What is Tc?

A

Critical temperature - T at beyond which there is a one-phase region

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38
Q

What is seen in a molar gibbs plot for mixing?

A

Double well needed for phase separation

As T increases then one phase more likely

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39
Q

What is the chemical potential of two separate phases?

A

μ1 = μ1* - X2(dg/dX2) + g

μ2 = μ2* - (1 - X2)(dg/dX2) + g

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40
Q

What is teh common tangent construction?

A

Minima gives coesting densities after separation

(dg/dx2a) = [g(x2a) - g(x2b)]/(x2a-x2b)

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41
Q

What is the coexistence condition for two phases?

A

(dg/dx2)a = (dg/dx2)b = 0

This is required for 2 phases to be present

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42
Q

What is the condition (derivative) for the critical temp of two phases?

A

(dg/dx2)Tc = (d2g/dx22)Tc = 0

When this satisfied then at the Tc

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43
Q

What is a binodal or spinodal region of a gibbs graph?

A

Binodal - line on graph when (dg/dx2)a = (dg/dx2)b = 0 , gives 2 phases, dominates at lower T

Spinodal - line on graph when (d2g/dx22)Tc = 0 , gives mix, dominates at higher T

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44
Q

What is the approach for understanding colloids?

A

Treat as huge (slow and see-able) atoms
Same stat thermo and similar phase behaviour

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45
Q

What is the random flight model for a polymer?

A

Polymer is a random walk of N statistical segments of length l

Stat segments can include multiple momomers

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46
Q

What is the Flory-Huggins theory?

A

Volume fraction formula for entropy of mixing of polymer solutions

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47
Q

What is the lattice model for a polymer solution?

A

N1 molecules of type 1 (solvent)
N2 molecules of type 2 (polymer, with r stat segments per molecule N2

Number of lattice sites, N = N1 + rN2

48
Q

What is volume fraction?

A

Equivalent to mole fractions but for space taken by solvent (1) or polymer (2)

φ1 = N1/(N1 + rN2)

φ2 = rN2/(N1 + rN2)

49
Q

What is Ωunmix for a polymer solution?

A

Ωunmix = [rN2!/N2)(z/rN2)](r-1)N2

50
Q

What is Ωmix for a polymer solution?

A

Expected without corrections:
Ωmix = N!/(N1! rN2!)

Must implement corrections:
1) random mix doesnt apply, so z/n for each segment other than first one (where z is coord)
2) Cannot switch chem segments unlike separate molecules, so multiply by rN2!/N2!

Actual result
Ωmix = N!/(N1! N2!) (z/N)(r-1)N2

51
Q

What is ΔmS for a polymer solution?

A

Find by taking logs of Ω and using stirling’s approx as for ideal

ΔmS = kb[ln(N!/(N1! N2!) + (r-1)N2 ln(rN2/N)] = -R[n1lnφ1 + n2lnφ2]

52
Q

What is Hunmix for a polymer solution?

A

Hunmix = (z/2)N1w11 + (z/2)rN2w22 = (1/2)(N1+rN2)[w11N1/N + w2rN2/N]

Hunmix = z/2 (N1+rN2)(w11φ1 + w2φ2)

53
Q

What is Hmix for a polymer solution?

A

Start with Hmix = (z/2)N1w11ϕ1 + (z/2)N1w12ϕ2 +(z/2)N1w11ϕ1 + (z/2)N1w12ϕ2 + (z/2)rN2w22ϕ2 + (z/2)rN2w21ϕ1

Simplifies down to:
Hmix = (z/2)(N1 + rN2)[w11ϕ12 + w22ϕ22 + 2w12ϕ1ϕ2]

54
Q

What is ΔmH for a polymer solution?

A

ΔmH = (n1 + rn2)wφ1φ2 = RT(n1 + rn2)χφ1φ2

55
Q

What is the flory-huggins parameter?

A

χ = w/RT

56
Q

What is ΔmG for a polymer solution?

A

ΔmG = RT[n1lnφ1 + n2lnφ2 + (n1+ rn2)χφ1φ2

57
Q

What is the chemical potential of a polymer solution?

A

μ1 = μ1* + RT[lnφ1 + (1-1/r)φ2 + χφ22]

58
Q

How can you find the vapour pressure & phase separation of polymer solutions?

A

Follow same process as with regular, just replace values

59
Q

What is the source osmotic pressure of polymer solutions?

A

Semi-permeable membrane which polymer cannot pass through, but solvent can

Osmotic pressure is difference in pressure on either side

60
Q

What is the osmotic pressure of polymer eqn in terms of pressure difference?

A

Π = Pβ - Pα

Where β contains the polymer

61
Q

What drives osmosis and how is this shown in equation?

A

Π = Pβ - Pα = (μ1 - μ1*)/V1*

then sub in: μ1= μ1* + RT[lnφ1 + (1-1/r)φ2 + χφ22

gives:
Π = RT[ (1/M2)c2 + (1/2 - χ)/(ρ22V1*) c22 + ..]

62
Q

How does osmotic pressure relate to virial expansion for gases?

A

Π = RT[ (1/M2)c2 + (1/2 - χ)/(ρ22V1*) c22 + ..]

Virial expansion for gases:
P = RT[(1/V) + B(T)(1/Vmean2) + …]

63
Q

What is the Van’t Hoff law?
(ideal osmotic pressure)

A

Π = RT[c2/ M2]

This is from the first term of expansion

64
Q

What is the experimental osmotic pressure?

A

Π = RT[ (1/M2)c2 + (1/2 - χ)/(ρ22V1*) c22 + ..]

2nd osmotic virial coefficient, A2 = (1/2 - χ)/(ρ22V1*)

Plot c2 on x and Π/c2 on y
y-intercept = RT/M2
gradient = RTA2

65
Q

What are a good, theta, and poor solvents?

A

Good - max interactions with solvent, polymer spread out
Theta - ideal osmotic pressure
Poor - max interactions with self, polymer folded in

66
Q

How does the Flory-Huggins parameter (χ) and A2 show solvent quality?

A

Good solvent : χ < 1/2 and A2 > 0, T = θ

Theta: χ = 1/2 and A2 = 0, T =θ

Poor solvent: χ > 1/2 and A2 < 0, T =θ

67
Q

What is end-to-end distance of a polymer?

A

R = Σ I

<R> = Σ <I> = 0
This is 0 due to the randomness of the polymer

68
Q

What is mean square distance of a polymer?

A

Removes effect of -ve contribution to the mean

<R2> = Nl2 = Ml2/m

where M is mol weight and m is segment mol weight

69
Q

What is the radius of gyration?

A

Rg is just useful experimental value

< Rg2 > = < R2 > / 6

so Rg proportional to sqrt(M)

70
Q

What is the composition of an electrolyte?

A

Av+Bv- -> v+ AZ+ + v- BZ-

71
Q

What interactions are present in electrolytes?

A

Long-range electrostatic interactions

Presence of ionic atmosphere of counter-ions

72
Q

What is an ionic atmosphere?

A

-ve of ion surrounded by +ve ions and vice cersa

73
Q

What is the chemical potential of one component of electrolyte solutions?

A

μ+ = μ+θ + RTlnc+ + RTlny+

ci is molarity, equivalent for mole fraction
yi is activity coefficient equivalent

74
Q

What is μ of electrolyte solutions?

A

μ = μθ + vRTlnc+- + vRTlny+-

75
Q

How do you derive the potential of a charge in solution?

A

Potential of an isolated charge: ψ(r) = (1/r)(e/4πε0εr)

in solution: ψ(r) = (exp-κr/r) (e/4πε0εr)

then taylor expansion: ψ(r) = (1/r - κ) (e/4πε0εr)

where κ = debyte length

76
Q

What is κ, debye length?

A

κ-1 is range of ionic atmosphere

κ-1 = Sqrt[ε0εrkBT/2e2n0]
n0 = N+/-/V

κ-1 α 1/Sqrt[c]
where c is salt conc

77
Q

What is the potential of an ionic atmosphere?

A

ψatm = -eκ/4πε0εr

78
Q

How do you find the work required to bring in an ion to a electrolyte?

A

wel = ∫ψatm dq = ∫-eκ/4πε0εr dq

where ψatm is potential of ionic atmosphere

wel = -κe2/8πε0εr

79
Q

What is the relation activity coefficient of an ion in electrolyte?

1:1 electrolyte

A

RTlny = NAwel = -κe2/8πε0εrkBT

80
Q

What is relation of activity coefficient and concentration of an electrolyte?

A

logy+- = - A Sqrt[c]

81
Q

What is ionic strength (I) in debye-huckel law?

A

I = 1/2 Σ cizi2

where c is concentration and z is ionic charge

82
Q

What is the debye-huckel limiting law?

A

logy+- = -z+z-A Sqrt[I]

where I is an i

83
Q

What is ionic strength of a 1:1 electrolyte with 1+ charges (AgCl)?

A

I = 1/2 Σ cizi2
I = (1/2) (c) (1*12 + 1*12) = c

84
Q

How does conc of electrolyte relate to K of solubility?

A

log c = (1/2)logKs + A Sqrt[I]

Sol increases if inert electrolyte conc increases

85
Q

How does increasing salt change solubility?

A

Adding more inert salt decreases work to bring in more ions, so more soluble

As decreases debye length

86
Q

What is surface tension?

A

Force per unit length which resists an external force
Minmises surface area

87
Q

What is the notation for surface tension and interface?

A

γ = surface tension
σ = interface

88
Q

What is required to increase surface area?

A

Work against surface tension which wants to min surface area

F = 2γl, where l is length and 2 as bottom and top surface of film

dw = Fdx = 2γldx = γdσ

89
Q

What effects dominate at different size of systems?

A

Bulk dominates for large systems (length3)

Surface dominates for smaller systems (length2)

90
Q

What is the origin of surface tension?

A

Molecules attracted to surrounded in bulk

Costs energy to move a molecule from bulk to surface as loses attraction so it costs work to create a surface

This is surface tension

91
Q

What happens when you have a small and large bubble connected?

A

Small bubble goes into large

This is because pressure in smaller bubble is larger

92
Q

What is Laplace’s law?

A

ΔP = 2γ/R

where R is radius of droplet
when isothermal enlargement

93
Q

What is required for soap bubbles?

A

Pinside > Poutside

so inside can act against force preventing it from forming

94
Q

How do you derive Laplace’s law?

A

outside force (expansion work then expansion work against outside P0) = inside force (work to increase bubble size)

(P0+ΔP)dV - P0dV = γdσ

σ = 4πR2
dσ = 8πRdR

ΔP (4πR2dr) = γ8πRdR

ΔP = 2γ/R

95
Q

What is the Kelvin equation relating to?

A

Vapour pressure of a liquid droplet

96
Q

What is Kelvin’s equation?

A

Pr = P0 exp[2γvI/rRT]

where Pr is vap pressure of a liquid droplet with radius r, with respect to P0

97
Q

What is the vapour pressure of a small droplet?

A

Small droplet has large lapace pressure so large (2γ/r)
Pr&raquo_space; P0

98
Q

What is the vapour pressure of a large droplet?

A

Large droplet has small lapace pressure so small (2γ/r)
Pr ~ P0

99
Q

How do you derive Kelvin’s equation?

A

Eqm between liquid droplet and gas
1) μliq(P0)) = μgas (P0)
2) μliq(Pr + 2γ/r) = μgas(Pr)

then do 2-1 and then integrate
use molar volume liquid (vl) = molar volume gas (vg) = RT/P

Then RTln(Pr/P0)&raquo_space; vl(Pr-P0) so approx to give
(2γvl)/r = RTln(Pr/P0)

rearrange to give
Pr = P0 exp[2γvl/rRT)

100
Q

What is the critical droplet size?

A

Smallest droplet size possible in a pressure P

r* = 2γvl/RTln(P/P</sub>0</sub>)

101
Q

How does vapour pressure realte to nucleation?

A

When smaller vap pressure (Pr) than required due to bigger size of a droplet then is more likely to nucleate

102
Q

What is the relation of gibbs adsorption equation?

A

Relation between adsorption and surface tension

103
Q

What is a concentration profile?

A
104
Q

What is the Gibbs dividing surface?

A

Approx to conc profile

Gibbs dividing surface has no colume
No excess or depletion of solvent molecules

105
Q

What is the volume of gibbs dividing surface?

A

Dividing surface volume, Vσ = 0

Vtotal = Vα + Vβ

106
Q

How does gibbs dividing surface change the excess/depletion of solvent?

A

No excess/depletion of solcent molecules (no molecules in interface)

n1σ

n1,total = n1α + n1β

107
Q

What is the surface-excess amount?

A

niσ = ni,total - (n1α + n1β)

XS of this amount of this component actually present in system over that present in a reference system

108
Q

What is the amount of phase α & β in a conc profile?

A

n1α = Vαciα

n1β = Vβciβ

These come from integral beneath conc profile

109
Q

How is the Gibbs dividing surface nσ=0 ?

A

Over and underestimates the curve by the same amount so interface is 0

110
Q

What are the different types of adsoprtion?

A

Positive - surfactants wants to be at interface more than bulk

Negative - surfactant does not want to be at the surface

111
Q

What are the different types of adsoprtion?

A

Positive - surfactants wants to be at interface more than bulk

Negative - surfactant does not want to be at the surface

112
Q

What is the surface-excess conc, Γ?

A

Γi1 = niσ/σ

this is for solvent - component 1

113
Q

What is the surface xs conc of positive and negative adsorption?

A
114
Q

What is dA of a surface?

A

dAσ = -SσdT + Σμidniσ + γdσ

115
Q

What is dγ, the surface analogue of Gibbs-Duhem?

A

dγ = -(Sσ/σ)dT - Σ (niσ/σ) dμ

Where the sum is from i to c

SσdT + Σμidniσ + γdσ

116
Q

What is the gibbs adsorption equation?

A

dγ = - Σ Γi1 dμi

117
Q

What is the Gibbs adsorption equation for ideal binary solutions?

A

Sub in μ2 = μ2θ + RTlnc2
Into following equation: dγ = - Σ Γi1 dμi

Gives dγ = - RTΓ21 dlnc2

Surface tension therefore a function of conc c2

Year 2 - Chem (23 decks)

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