28 February 2014, MAFabro

Today’s topicsFinding the activity coefficient

Partial molar quantities

Gibbs-Duhem equation

Problem: Activity A stream of argon gas is passed in a

closed system over a boat containing mercury at 273 K. The flow rate of argon is slow enough to allow this gas to become saturated with mercury vapor. The volume of argon used was measured at 293.15K, and was found to be 22 L. The argon was found to contain 0.0674 grams of mercury. Solve for the saturated pressure of pure mercury.

Problem: ActivityThe same experiment is carried out

with a sodium amalgam (Na + Hg) in which the atomic fraction of sodium is 0.122. Twenty-two liters of argon gas was found to be saturated with 0.0471 grams of mercury. Find the activity coefficient of Hg at this concentration.

Question 1. Pure water

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of water, what is the total volume?

Question 1. Pure water

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of water, what is the total volume?

ANSWER: 10.018 L

Question 2. Pure ethanol

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of ethanol, what is the total volume?

Question 2. Pure ethanol

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of ethanol, what is the total volume?

ANSWER: 10.058 L

Game?

Question 3.

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of ETHANOL, what is the total volume?

Question 4.

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of WATER, what is the total volume?

Question 5.

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of a 40% ethanol-60% water solution, what is the total volume?

Question 6.

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of a 80% ethanol-20% water solution, what is the total volume?

Question 7.

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of a 40% ethanol-60% water solution, what is the total volume?

Question 8.

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of a 80% ethanol-20% water solution, what is the total volume?

Answers!

Question 3.

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of ETHANOL, what is the total volume?

ANSWER: 10.014 L

Question 4.

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of WATER, what is the total volume?

ANSWER: 10.054 L

Question 5.

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of a 40% ethanol-60% water solution, what is the total volume?

ANSWER: 10.0172 L

Question 6.

One mole of pure water is 18 mL. If 1 mole of water is added to 10 liters of a 80% ethanol-20% water solution, what is the total volume?

ANSWER: 10.0155 L

Question 7.

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of a 40% ethanol-60% water solution, what is the total volume?

ANSWER: 10.0565 L

Question 8.

One mole of pure ethanol is 58 mL. If 1 mole of ethanol is added to 10 liters of a 80% ethanol-20% water solution, what is the total volume?

ANSWER: 10.0578 L

Partial Molar VolumeVolume contribution of a mole of a

substance added to a very large volume of a specific solution

Total or integral quantity vs. Partial molar quantity

For any extensive thermodynamic quantity Y, at constant p and T, for a system with components A and B:

Relationship between total and partial quantities:

Problem 1The integral enthalpy of mixing of liquid (Cu, Zn)

solution can be approximated by the following equation Cu(l) and Zn(l) as reference states:

ΔmixHm = -19250xCuxZn J/mol at 1400 K

a. Derive the corresponding partial quantities of Cu and Zn

b. Show that the two partial equations are internally consistent with the Gibbs-Duhem equation

Enthalpy of mixing (Total quantity)

…with the partial molar enthalpy of mixing of Cu

…and partial molar enthalpy of mixing of Zn

Seatwork (Warnes)Using the free energy diagram for the

Cu-Ni system below, sketch on the accompanying graph the partial molar free energy of Ni as a function of composition.

What is the partial molar free energy of Cu and Ni in a sample that is 30 at.% Cu?

What is the free energy of 1 mole of the same alloy?

Gibbs-Duhem EquationHelps us calculate relationships between

quantities as a system remains in equilibrium

Helpful in calculating the partial molar quantity of a binary mixture by measuring the composition of the mixture

Helpful in calculating partial vapor pressures by calculating the total vapor pressure

€

0 = nii

∑ dYi

For a two component system:

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nAdYA + nBdYB = 0

ProblemThe experimental value of the partial molar

volume (mL) of K2SO4(aq) at 298 K is given by the expression

Where b is the numerical value of molality of K2SO4. Use the Gibbs-Duhem equation to derive an equation for the partial molar volume of water in the solution. The molar volume of pure water at 298 K is 18.079 mL.€

VA = 32.280 +18.216b1/ 2

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