Lecture 5

Question 1

What is the solvent activity? What are its different expressions? How is it used to find the general equation for the chemical potential of a solvent?

Answer 1

Given that the derivation of the chemical potential of the solvent for an ideal solution that follows Raoult’s law:

μ(a) = μ*(a) + RTln(Xa)

Now this can be preserved when the solution does not obey Raoult law by introducing the activity constant:

μ(a) = μ*(a) + RTln(a)

where a is the activity of the solvent, and is a kind of the ‘effective’ mole fraction.

since this equation (μ(a) = μ(a) + RTln(a)) is true no matter if the solution is ideal or not, via comparison with μ(a) = μ(a) + RTln(Pa/P*a) we deduce that:

a = Pa/P*a

activity (a) can be measured by simply measuring the vapor pressure using this relationship.

Since all solvents start following Raoult’s law as xa approaches 1, then ‘a’ will approach Xa when Xa approaches 1. This is illustrated via the activity coefficient (Ya):

a = Ya*xa. where as Ya —> 1 as xa —> 1.

Using this definition of activity we can write the general equation of the chemical potential of the solvent as:

μ(a) = μ*(a) + RTln(Xa) + RTln(Ya)

Question 2

What is the solute activity?

Answer 2

1. ideal-dilute solutions: found in notes on page 1.
2. Real solutions:

Given that the chemical potential of a solute in an ideal dilute solution is:

μ(b) = μ(^⦵)(b) + RTln(xb)

Then using the same logic of solvent non-ideality, the chemical potential of solute in real solution is given by the activity ‘a’:

μ(b) = μ(^⦵)(b) + RTln(a)

all the deviations from ideality are captured by a

where a = Pb / Kb (how to get to this relation is found in note on page 1).

Now similarly to solvent activity, the solute starts following Henry’s low as xb approaches zero, which then the activity of the solute will approach xb. This is represented by the activity coefficient:

a = Yb * xb, whereas Y —-> 1 x —–> 0

Now all the deviations from ideality are captured in the activity
coefficient

Question 3

What is the chemical potential of a solute in terms of molality? What does the equation tell? How do we use the activity ‘a’ to capture the derivation for ideality?

Answer 3

For a solute, it is often convenient to express the composition in terms of molality instead of mole fractions, therefore the chemical potential of a solute is then rewritten as:

μ(b) = μ(^⦵)(b) + RTln(b/b(^⦵))

b(^⦵) - the standard molality.

This shows that as b —> 0, the μ(b) —> - infinity, which means the more dilute the solution is the more thermodynamically stable the solute is.

Similarly to before we can capture the derivation from ideality using the activity ‘a’, which is expressed by the activity coefficient ‘y’:

a = y * b/b(^⦵), whereas y—>1 b —->0

The final expression for the chemical potential of a real solute at any molality is then:

μ(b) = μ(^⦵)(b) + RTln(Y) + RTln(b/b(^⦵))

Note: Keep in mind that μ(^⦵) for molality expression is different from μ(^⦵) in the mole fraction expression.

Question 4

What is the derivation for the expressions of the activity coefficients in a real solution?

Answer 4

Found in notes on pages 1-2.

Question 5

What is the meaning of an ideal mixture?

Answer 5

a mixture of liquids that obey Raoult’s law throughout the composition range

Question 6

What is the derivation of the total vapor pressure of ideal mixtures? What is the derivation of the composition of Vapour? Explain the equation and how we got there.

Answer 6

found in notes on page 3

Question 7

What is the Derivation of an expression for the total vapour pressure of a binary mixture in terms of the composition of the vapour?

Answer 7

found in notes on page 4

Question 8

What is a temperature-composition diagram?

Answer 8

it is a phase diagram in which the coexistence curves show the composition of phases that are in equilibrium at various temperatures

Note: all temp-composition diagrams are done at a constant pressure.

Question 9

How do we construct a temperature-composition diagram?

Answer 9

1. They can be constructed from the vapor-pressure diagram, where you examine the temp dependence of the vapour pressure and identify the temperatures where the total vapour pressure to 1 atm
2. They can be constructed of empirical data

Question 10

What is simple distillation and fractional distillation?

Answer 10

Simple distillation is a technique used to separate a volatile liquid from a non-volatile solute or solid via condensation.

Fractional distillation is also a technique that separates a volatile liquid by having the boiling and condensation cycle repeated successively

Question 11

How is fractional distillation used to separate the volatile liquid? What is theoretical plates?

Answer 11

first, we consider a liquid of composition a1, we heat the liquid till we reach its boiling point at a2. The composition of the vapour given off at a’2 is richer than the liquid of a2, so, therefore, we take that vapour and condense it back to a liquid and then heat it until it reaches the boiling point again at composition a3, then similarly the vapour given at composition og a’3 is richer than that on a3. This keeps repeating until almost pure vapour is obtained.

The number of theoretical plates is the number of effective vaporization and condensation steps that are required to achieve a condensate of a given composition. It therefore determines the efficiency of the fractionating column.