Physical Chemistry , 1st ed.

Example 4.7 What is ( S/ V)Tfor a gas that follows a van der Waals equation of state? Solution The Maxwell relationship in equat ...

4.6 Using Maxwell Relationships The Maxwell relationships can be extremely useful in deriving other equations for thermodynamics ...

and can now evaluate ( V/ T)p:  V T  p  R p  Substituting: JT C 1 p T R p V C 1 p  R p T V But RT/pe ...

constant V, which is what we are trying to substitute for; we substitute and rearrange as follows: (V) V 1   1  T p ...

we remember that Sis defined by the partial derivative in equation 4.40. Substituting: GH T G T  p where the minus signs h ...

we make the approximation that His constant over small temperature ranges, we can use equation 4.44 to approximate Gat differe ...

For ideal gases, we can use the ideal gas law and substitute for V:VnRT/p, so G pi pf  nR p T dp pi pf nRT d p p nRT pi ...

For systems that have more than one chemical component, we will have to give the chemical potential a label (typically a number ...

i H ni  S,p,nj(ji) (4.52) i n A i  T, V, nj(ji) (4.53) However, given the usefulness ofG, the free energy–based de ...

GG° nRTln  p p °  (4.55) ° RTln  p p °  (4.56) The second equation shows that the chemical potential varies with the nat ...

(We will see in a minute why ideal gases are brought up again.) Subtracting these two: ddideal(VVideal) dp where we have ...

Figure 4.7 shows such a plot for neon at 150 K. The fugacity of neon at any pressure is the area under this curve from zero to t ...

4.10 Summary We have introduced the last two energy quantities, the Helmholtz energy and the Gibbs free energy. Both are related ...

4.2 Spontaneity Conditions 4.1.Explain why conditions for using S0 as a strict spon- taneity condition imply that Uand Hboth ...

4.21.Show that the units in equation 4.19 are consistent on either side of the equation. 4.22.Derive equations 4.35–4.37. 4.23.D ...

4.50.Suppose a gas has an equation of state that resembles a shortened version of the van der Waals equation of state: p(V nb)  ...

5 A MAJOR THEME IN CHEMISTRY is chemical equilibrium:that point during the course of a chemical reaction where there is no furth ...

conditions. We will find some straightforward ideas for understanding how pressure and temperature changes affect the value of t ...

precipitating from solution and ions dissociating from the solid and going into solution: PbCl 2 (s)→Pb^2 (aq) 2Cl(aq) Pb^2 ...

d.Because money is moving in and out of the account, even though the av- erage monthly balance maintains the equilibrium amount ...