Lecture 2 Flashcards
What is a binary mixture?
a mixture of two components
what is the normal and mathematical definition of partial molar volume?
The normal definition of partial molar volume is:
the partial molar volume of a substance A in a mixture is the change in volume per mole of the A when added to a large volume of the mixture.
The mathematical definition of partial molar volume is:
Vj = ( ∂V/∂n(j) ) p, T, n’
where n’ signifies that the amounts of all the other substances present are constant. A graphical representation of the math definition is shown in the notes on page 1.
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How can adding the same molecule to a mixture result in different partial molar volumes?
Different mixtures result in different increases in volume, for example, adding 1 mole of H2O to pure liquid water results in a greater increase of volume compared with adding 1 mole of H2O to ethanol, this is because the H2O forms hydrogen bonds with water so then it will form a more expanded structure while with ethanol the H2O molecules would be more packed together. This results in a greater partial molar volume of H2O in water.
How and why do the partial molar volumes of components vary? How can we then derive an expression for the change in the total volume of a mixture due to the change in the partial molar volumes?
Answers are found in the notes on pages 1and 2.
What is an alternative way of finding partial molar volumes?
to measure the dependence of volume on the composition and to fit the observed volume to a polynomial in the amount of substance. Once the polynomial has been found its slope can be determined at any slope of interest using differentiation (I’m not sure how this differs from the original way?)
Can partial molar volumes be negative? Give an example.
Yes, it can be negative. For example, the partial molar volume of MgSO4 in water is negative, and that is due to the hydration of the Mg^2+ and SO4^2- ions which results in the collapse of the open structure of water.
What is the partial molar Gibbs energy? What is the total Gibbs energy for a binary mixture?
As defined before the partial molar Gibbs energy is simply the chemical potential of a pure substance. Generally, the definition of the partial molar Gibbs energy (μ) for a substance J in a mixture is:
μ(j) = ( ∂G/∂n(j) ) p, T, n’
where the slope at any composition in a Gibbs energy plot against the amount of substance J gives the μ(j) (Atkins PDF page 185)
Using the same argument that allowed for the derivation of the total volume of a binary mixture. It is defined that the total Gibbs energy for a binary mixture is:
G = μ(A) * n(A) + μ(B) * n(B)
How can chemical potential be used to show changes in thermodynamics other than the changes in Gibbs’s molar energy? (Demonstrating the wider significance of chemical potential).
The answer is found in the notes on pages 2 and 3.
What is the Gibbs-Duhem equation? How do we derive it? How can it be implemented in all other partial molar quantities?
The answer is found in the notes on page 3.
What is molality and molarity? How do you convert from mole fraction to weight fraction?
The answer is found in the notes on page 4.
What is the expression for Gibbs energy when mixing perfect gases? How did we derive it? What are other thermodynamic mixings? How do they support our conclusion?
The answer is found in the notes on pages 4 and 5.
