L 18 - "Liquid Solutions I- Liquid/Liquid" Prof. Gianluigi...

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“Liquid Solutions I- Liquid/Liquid” Prof. GianluigiVeglia
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Partial Molar Quantities: when 1+1 ≠2. We are getting ready to talk about mixtures, especially liquid solutions: benzene and toluene, methanol and water, sugar and water etc. We begin by introducing the subject of partial molar quantities , beginning with partial molar volume. The partial molar volume of a component j in a solution containing an arbitrary number of components is : ' , , n P T j j n V V =
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The unit of the partial molar volume is L or cm 3 per mole. Thus the partial molar volume is an intensive quantity that depend the temperature, pressure and composition. What is the physical meaning of the partial molar volume? If I had an infinite quantity of some solution and were to add j to the solution molecule by molecule (infinite volume ensures constant composition) and were to measure the volume change with added j that would be the partial molar volume.
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What good is the partial molar volume? Let’s begin writing the volume of a solution as a function of T, P and the number of molecules of all components: Then ( ) j n n n P T V V ,... , , , 2 1 = j n P T j n T n P dn n V dP P V dT T V dV i j j + + = , , , , j j n T n P dn V dP P V dT T V dV j j + + = , ,
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Let’s suppose that we prepare the solution under conditions of constant T and P. Then we can write: Instead of expression V in terms of n 1 , n 2 , …, we will often find it more convenient to express V in terms of χ 1 , χ 2 ,… (the mole fraction of each component) and n tot , the total number of moles of stuff present: j j dn V dV = tot j i j j n n n n = = χ j j tot n n =
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at constant T and P. Now let’s imagine a change at constant T and P and composition. That is I change the total number of moles of stuff, but not the composition (e.g., I might add 5 ml of a 0.5 M sugar solution to a 500 ml of 0.5 M sugar solution). Now the expression for dV becomes: At constant T, P and composition. Let’s look at V in another way. It only stands to reason that V is a function T, P, χ 1 , χ 2 ,…and also n tot . ( ) j tot j n d V dV χ = tot j j dn V dV =
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There has to be some intensive quantity, f(T,P, χ i ), which is the volume of a mole of solution that V, the total solution volume is: What is this function? At constant T, P and composition: At constant T, P and composition. We now have two different
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This note was uploaded on 10/30/2011 for the course CHEM 3501 taught by Professor Blank during the Fall '08 term at Minnesota.

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L 18 - "Liquid Solutions I- Liquid/Liquid" Prof. Gianluigi...

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