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Lecture_5b - 5.5 Partial Molar Quantities Partial Molar...

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5.5. Partial Molar Quantities Partial Molar quantities are required to deal with open systems , i.e., systems that permit mass transfer between themselves and surroundings. Consider an open system with n 1 moles of component 1, n 2 moles of component 2, n 3 moles of component 3, etc.. We would write the free energy change dG for such a system as dG = æ è ¹ G ¹ P ö ø T , n 1 , n 2,... dP + æ è ¹ G ¹ T ö ø P , n 1 , n 2,... dT + æ è ç ¹ G ¹ n 1 ö ø ÷ P , T ,, n 2,... dn 1 + ... = VdP SdT + G 1 dn 1 + G 2 dn 2 + ... In the second equality, the quantities G 1 , G 2 , etc.. are called partial molar free energies . Similarly, we may define partial molar volumes, partial molar enthalpies, internal energies, and entropies: V 1 = æ è ç ¹ V ¹ n 1 ö ø ÷ P , T ,, n 2,... ; H 1 = æ è ç ¹ H ¹ n 1 ö ø ÷ P , T ,, n 2,... ; etc Because of their great importance in the thermodynamics of solutions, we discuss partial molar volumes and partial molar free energies further. Partial Molar Volume: The total volume of a solution of, say, two miscible liquids is given by (5.33) V = n 1 V 1 + n 2 V 2 . The units of partial molar volumes are the same as molar volumes. The relationship between the two, i.e., partial molar volume and the molar volume is a subtle but important one. In the case of ideal solutions, the partial molar volume of each component will be identical to the molar volume of the pure substance in the absence of the other component. However, in the case of non-ideal solutions, the presence of the second component has a measurable influence on the molar volume of the first component and vice versa. Therefore, in general, V 1 ! V 1 ± and V 2 ! V 2 ± . The standard state for defining partial molar quantities is a 1 molal solution, i.e., a solution that contains 1 mol of the substance in 1.0 kg of solvent.
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Physical Interpretation of partial molar quantities: It may appear that there is something °not quite right± about the following two equations: V = n 1 V 1 + n 2 V 2 , where V 1 = æ è ç ¹ V ¹ n 1 ö ø ÷ P , T , n 2 ,and V 2 = æ è ç ¹ V ¹ n 2 ö ø ÷ P , T , n 1 . Based on what we have seen so far, the first equation should be which is simply another application of the chain rule in partial dV = V 1 dn 1 + V 2 dn 2 , differentiation.
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