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: