By Arther Adamson (Auth.)

ISBN-10: 0120442604

ISBN-13: 9780120442607

ISBN-10: 0323161286

ISBN-13: 9780323161282

A Textbook of actual Chemistry

summary: A Textbook of actual Chemistry

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**Extra resources for A Textbook of Physical Chemistry**

**Example text**

We must then divide out the permutations that should not be present. Thus in the case of system 2, there are 6! ways of permuting the molecules in the * box, 3! ways for the e box, and 1! or one way for the c box. ) = 840. The general statements of the preceding conditions are then 1 τ 2 3 1 2 2 1 2 3 Ν = £ Ν • = constant, (2-8) Ε = £ Ni€ = constant, (2-9) 4 t W AM where N denotes the number of molecules in the zth state of energy e and W is the statistical weight or probability of the particular distribution.

L We turn now to the van der Waals equation; referring to Fig. 1-12, it seems clear that the section labeled V must represent the molar volume of the gaseous state of the substance, while that labeled V should correspond to the liquid state. The van der Waals equation connects these two branches with the section showing a maximum and a minimum, but a real substance takes the short cut of direct condensation when Ρ reaches P° as illustrated in Fig. 1-13. We would like to know how to locate the horizontal line of this short cut, and hence the liquid vapor pressure P°.

A s a simple illustration, s u p p o s e that o n e wishes t o m a x i m i z e the area o f a rectangle subject t o the constraint that its perimeter b e c o n s t a n t . W e t h u s h a v e xy = si a n d 2x + 2y = s where χ a n d y are the sides a n d s/ a n d s t h e area a n d perimeter, respectively. B y the variation m e t h o d , w e write 9 y 8x + χ 8y = 0, 2 8x + 2 δ ; = 0, a n d , introducing the undetermined multiplier, a, (y8x + x8y) + a(28x + 2 8 ; ) = 0, or (y + 2a) 8x + (x + 2a) 8y = 0.

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