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POST-LAB DISCUSSION LECTURE
(EXPERIMENTS 5-9)
CHEM 116 (LAB)ARNOLD C. GAJE
INSTRUCTOR 4
DEPARTMENT OF CHEMISTRY
UP VISAYAS
Experiment 5: Determination of Partial Molal Volume
• Gibbs-Duhem Equation:
• Partial Molar Volume for 2-component solution:
• Importance of Partial Molar Volumes
• Thermodynamically connected with other partial molar quantities such as
the chemical potential → can be used to describe changes in equilibria
• Used in Theory of solutions
- for binary mixtures of liquid components they are related to heat of mixing and
deviations from Raoult’s Law
Practice Problems
• Gibbs-Duhem Equation
Example 5.1, Atkins and De Paula 2010, pp. 160-161.
Apparent Molal Volume
• Molality
Molality (m) = 𝑛 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑒
𝑘𝑔 𝑜𝑓 𝑠𝑜𝑙𝑣𝑒𝑛𝑡
• For solution composed of 1 kg (55.51 mol) H2O and m mol of solute:
• Let be the molar volume of pure water ( 18.016 g mol-1/0.997044 g
cm-3 = 18.069 cm-3 mol-1 at 25.00oC). The apparent molal volume is
defined by the equation
where
and
Apparent molar volume
• Expressing Φ in terms of density and pycnometer measurements:
• :
Methods of slopes
• Mathematically,
• Determining :
Φ = Φ𝑜 + 𝑚𝑑Φ
𝑑 𝑚
Plot Φ vs 𝑚Intercept =Φ𝑜
Slope = 𝑑Φ
𝑑 𝑚
Density measurements
• Pycnometer
• Volume of pycnometer:
𝑉 =𝑊𝑤𝑖𝑡ℎ 𝑤𝑎𝑡𝑒𝑟 −𝑊𝑒𝑚𝑝𝑡𝑦
ρ𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑎𝑚𝑏𝑖𝑒𝑛𝑡 𝑇
• Density of solutions:
ρ =𝑊𝑤𝑖𝑡ℎ 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 −𝑊𝑒𝑚𝑝𝑡𝑦
𝑉𝑝𝑦𝑐𝑛𝑜𝑚𝑒𝑡𝑒𝑟
• Assignment:
Calculate the density values in your
experiment again using this
approach. Recalculate values of
other quantities accordingly.
Calculation of Molalities
Where M = molar concentration of solutions
M2 = molar mass of solute
VAPOR PRESSURE OF A PURE LIQUID
Experiment 6
Phases in Equilibrium
• Equilibrium: μ(α; p,T) = μ(β; p,T)
or
dμ(α) = dμ(β)𝒅𝒑
𝒅𝑻=𝜟𝒕𝒓𝒔𝑺
𝜟𝒕𝒓𝒔𝑽Clapeyron
Equation
The T at a particular p where
the two phases are in
equilibrium is called the
transition temperature (e.g.,
boiling point, melting point,
sublimation point).
Clausius-Clapeyron Equation
• During phase transition:
• For vaporization:
• For Ideal gas: 𝒅𝒑
𝒅𝑻=
𝜟𝒗𝒂𝒑𝑯
𝑻𝑹𝑻
𝒑
• Integrating the Clausius-Clapeyron Equation between two limits:
𝜟𝒕𝒓𝒔𝑺 =𝜟𝒕𝒓𝒔𝑯
𝑻𝒅𝒑
𝒅𝑻=𝜟𝒕𝒓𝒔𝑯
𝑻𝜟𝒕𝒓𝒔𝑽
𝒅𝒑
𝒅𝑻=𝜟𝒗𝒂𝒑𝑯
𝑻𝜟𝒗𝒂𝒑𝑽
𝟏
𝒑
𝒅𝒑
𝒅𝑻=𝜟𝒗𝒂𝒑𝑯
𝑹𝑻𝟐𝒅(𝒍𝒏 𝒑)
𝒅𝑻=𝜟𝒗𝒂𝒑𝑯
𝑹𝑻𝟐Clausius-Clapeyron
Equation
𝐥𝐧𝒑 − 𝒍𝒏 𝒑∗ = −𝜟𝒗𝒂𝒑𝑯
𝑹
𝟏
𝑻−𝟏
𝑻∗ 𝒍𝒏 𝒑∗
𝒍𝒏 𝒑
𝒅 𝒍𝒏 𝒑 =𝜟𝒗𝒂𝒑𝑯
𝑹 𝑻
𝑻∗ 𝒅𝑻
𝑻𝟐
𝐥𝐧𝒑 = −𝜟𝒗𝒂𝒑𝑯
𝑹
𝟏
𝑻+𝜟𝒗𝒂𝒑𝑯
𝑹𝑻∗+ 𝒍𝒏 𝒑∗
y = m x + b
Practice Problems
Clausius-Clapeyron Equation:
Problems 4.9 and 4.12, Atkins and De Paula 2010, pp. 154.
TRANSITION TEMPERATURE
Experiment 7
Phase Transitions
the spontaneous conversion of one phase into another phase
occurs at a characteristic temperature for a given pressure.
Transition temperature, Ttrs
“is the temperature at which the two phases are in equilibrium and
the Gibbs energy of the system is minimized at the prevailing pressure.”
ΔG = - RTtrs ln K
Detecting Phase Transitions
Easy for vaporization (boiling is very obvious)
Not easy for other transition
Heat is evolved or absorbed during any transition
Other techniques:
1. Differential calorimetry
2. X-ray diffraction (for solid-solid transition)
Thermal
Analysis
T does not change
even q is supplied
or removed
MISCIBILITY AND TEMPERATURE
Experiment 8
Gibbs Phase Rule
gives the number of parameters that can be varied independently (at least
to a small extent) while the number of phases in equilibrium is preserved.
where F = variance or number of degrees of freedom; C = number of
components; P = number of phases
For an evaporating pure liquid, C = 1, P = 1, and F = 2
F = C – P + 2
2 parameters can be
varied without
changing P. In this
case they are T and p
as discussed earlier.
Liquid-Liquid Phase Diagrams
Used to describe partially miscible liquids
• Partially miscible liquids are liquids that do not mix in all proportions at
all temperatures.
See Atkins and
De Paula 2010,
pp. 182.
𝑛α
𝑛β= 𝑙β
𝑙α
Lever Rule: