Lecture 3 Flashcards
when discussing the thermodynamics of a solution, quantities relating to pure substances are denoted by what?
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What is Raoult’s law?
Conducting a series of experiments on mixtures of two liquids that are closely related to each other allowed showing that the ratio of the partial vapour pressure of each component to its vapour pressure as a pure liquid equals the mole fraction of the component in the mixture:
Pa = XaPa
Some mixtures obey Raoult’s law very well, especially when the components are structurally similar. illustration of that is found in notes on page 1
Further important information is found in notes on page 1
What are ideal solutions?
Ideal solutions are mixtures that obey Raoult’s law very well throughout the composition range from pure A to pure B. This is illustrated in notes on page 1
What is the chemical potential of a liquid in an ideal solution? (derivation)
Found in notes on page 1
What is Henry’s Law? What are ideal-dilute solutions? Why do they behave in such a way? How is Henry’s Law expressed in practical Application?
Henry’s law states that at very low concentrations, although the vapor pressure of the solute is proportional to its mole fraction, the constant of proportionality is not the vapour pressure of a pure substance rather it is the empirical constant K:
Pa = Xa * Ka,
Where Kb is the pressure axis interception for the line that has the same gradient as the plot of the vapour pressure of the solute against its mole fraction at X = 0 illustrated in the notes on page 2.
Mixtures for which the solute obeys Henry’s law and the solvent obeys Raoult’s Law are called ideal-dilute solutions.
The reason why such mixtures have their solute and solvent behaving differently at low concentrations is because in dilute solutions the solvent molecules are in an environment similar to the one they have in the pure form, while the solute is surrounded by solvent molecules so its molecules are in an environment completely different than the molecules in the pure form. This means that the solvent acts as a slightly modified pure liquid, while the solute behaves entirely different from its pure state unless the solvent and the solute are similar, in this case, the solute also obeys Raoult’s law
How is Henry’s Law expressed in practical Application?
Pa = ba * Ka where ba is the molality of the substance
What is the equation of the chemical potential of ideal solutions?
μj = μ*j + RT ln Xj.
Note Xa is always less than one which shows that the chemical potential of a substance is always lower than its chemical potential at its pure form (Xj = 0)
What is the equation that represents the Gibbs energy of mixing two liquids to form an ideal solution? What is the derivation? What conclusion from it and the entropy of mixing can be drawn?
Found in notes on page 2
Raoult law vs Henry’s law (quick recap)
Found in notes on page 2
What does ideality mean for liquids?
The ideality for a perfect gas means that there is no interaction between molecules, but for ideal liquids, there is interaction between the molecules, but the average energy of interaction between A-B is the same as the average energy of interaction of A-A and A-B in the pure liquids. Thus, the variation of Gibbs’s energy of mixing with the composition is the same as that for the gases. This is illustrated in notes on page 2.
How are real solutions of liquids represented? How does the Gibbs energy of mixing change given a real liquid solution?
Real solutions are composed of molecules for which A-A, B-B, and A-B interactions are all different. There may be enthalpy or volume changes when such liquids mix, There also might be an additional contribution to entropy due to some molecules of one type clustering together instead of mingling freely with others.
If the enthalpy of mixing is sufficiently positive then it outweighs the negative term of (-TS) then the Gibbs energy of mixing is therefore positive and the reaction is not spontaneous ( the liquids are immiscible).
In cases where the entropy of mixing is negative due to specific interactions between two molecules that prevent randomization (where in this case the term -TS becomes positive), the enthalpy of mixing is required to be more negative than the positive (-T(-S)) term making the reaction spontaneous.
What are partially miscible liquids?
liquids that are only immiscible over a limited range of compositions.
What is excess functions?
it is the difference between the observed thermodynamic property of mixing and the property of an ideal solution:
X(excess) = X - X(ideal)
where the excess function for both enthalpy and volume will equal to the observed mixing due to the ideal mixing equaling zero
What are the two examples of the composition dependence of excess functions?
Found in notes on page 3
What are regular solutions? What is the plot of the function? What does it intell?
Real solutions are basically when two molecules are disrupted randomly but the interaction with each other results in different energies, it is used as a model for discussing behaviors of non-ideal solutions, where the excess enthalpy is not equal to zero, but the excess entropy = 0. This is represented by:
H(excess) = nRTBXaXb
where B is a dimensional parameter that is the measure of the energy of A-B interactions relative to the A-A and B-B interactions. The plot is illustrated in notes on page 3 with its depiction.
