4a: Solutions and Mixtures Flashcards
What is the equation for internal energy - the first law of thermodynamics?
dU = dQ - PdV
What is the equation for entropy - the second law of thermodynamics?
dS = dQ/T
How do you cancel variables to change thermodynamic functions?
The product rule - add the differential required to change the function and use the product rule to change the function by cancelling a variable.
dU = TdS - PdV
dU + d(PV) = TdS + VdP
dH = TdS + VdP
Define chemical potential in words and by equation.
The free energy per number of molecules
μ = (∂G/∂N)T,P
G = Nμ
Define extensive and intensive quantities and sort the quantities into each.
Extensive - scale with the system: U, S, V, N
Intensive - independant of the system: T, P
Define the molar quantities for a pure substance.
g = G/N = μ
s = S/N
h = H/N
v = V/N
Find the Gibbs-Dunhem equation from G = H - TS.
(note that dH = dU + d(PV) = TdS + VdP + μdN)
G = H - TS (differentiate)
dG = dH - d(TS) = dU + d(PV) - d(TS)
dG = TdS - PdV + d(PV) + μdN - d(TS)
dG = -SdT + VdP + μdN
dG = -SdT + μdN + VdP (combine with dG = μdN + Ndμ)
Ndμ = -SdT + VdP
How does chemical potential change when a particle changes state while the states are in equlibrium? What is the effect of this?
The chemical potential of both states is equal, μI = μII
This means μ = Δh - TΔs goes to Δh = TΔs.
How do you get enthalpy change from a phase diagram?
The Clapeyron equation:
dP/dT = Δs/Δv = Δh/TΔv
dP/dT is the gradient of the phase diagram.
What is the application of the Clausius-Clapeyron equation?
On the phase boundary between a gas and a liquid/solid:
dP/dT = PΔs/RT = PΔh/RT2
How can the Clausius-Clapeyron equation be linearized?
Change the variables on the phase boundary to lnP and 1/T, the gradient, dlnP/dT-1 = -Δh/R
How is the Gibbs-Duhem equation change when it is applied to mixtures?
ΣiNidμi = -SdT + VdP
The i is the species index and represents each different component of the mixture.
What is the equation for boiling point elevation?
ΔTb = Kbm2
m2 = solute molality
Kb = ebullioscopic constant
Define molality.
The amount of solute in moles divided by the mass of solvent in kg.
What is the equation for freezing point depression?
-ΔTf = Kfm2
Kf = cryoscopic constant
What is the equation for osmotic pressure?
Π = RTc2
c2 = molarity of the solute
How is vapour pressure related to solution affinity? How is this affected in perfect and ideal solutions?
ai = Pi/P0i
Activity = vapour pressure/vapour pressure of pure solvent
Vapour pressure increases as the affinity of the solute in the solution decreases.
In a perfect solution (hexane in heptane would be close) the acitivity is equal to the mole fraction of the solution.
In reality, ideal solutions only follow this trend in dilute solutions, this is Raoult’s law.
The vapour pressure of the solvent is proportional to the mole fraction of the solvent.
What is Henry’s law for solute?
a2 ∝ x2 when x2 << 1
P2 = kHx2
Where x2 = solubility
The solubility is proportional to the partial pressure of the solute in the gas phase.
How do you find if a solution deviates from ideality (similar solution and solute)?
The activity coefficient, γi = ai/xi
γ > 1: weaker affinity to solution
γ < 1: stronger affinity to solution
Where ai = Pi/P0i
xi = mole fraction
P = vapour pressure
How do you work out what proportion of different phases there is present in a seperated mix of liquids?
Measure the length of the lines between their minimums, the further from the minimum point, the smaller the ratio between the mixes.
What is the Gibbs phase rule?
F = C - P + 2
F = degrees of freedom
C = number of components
P = number of phases
Define the free energy of mixing by words and equation.
The free energy difference between a solution mixtures and pure solute and solvent.
gmix = RT(x1lna1 + x2lna2)
What is Raoults law for solvent?
When the solute is dilute, the vapour pressure of the solvent, P1, is proportional to the mole fraction of the solvent, x1.
P1 = P10x1
