31.1 Thermodynamics of Mixing of Ideal Solutions For the process where solute and solvent are mixed to form an ideal solution at constant temperature and pressure: T, P solute(s) + solvent > ideal solution we have already calculated the entropy of mixing for forming and ideal solution isothermally and isobarically (see the course notes on Entropy of Mixing of Ideal Solutions):  S mix = - R  X i ln X i (per mole of components) This result can be used to calculate the Gibb’s free energy of mixing of an ideal solution starting with a result we have derived earlier (see course notes on Maxwell’s Relations): dG = V dP - S dT Dividing by dT, while holding the pressure constant gives: (  G /  T) P = - S This result can be applied to the mixing process occurring at constant temperature and pressure: (  G mix /  T) P = -  S mix  = + R  X i ln X i

31.2 Separating variables and integrating this expression from 0 K to T: 0   G mix d (  G mix ) = 0  T R  X i ln X i dT Can you justify why  G mix  0 at 0 K? gives an expression for the Gibb’s free energy of mixing to form an ideal solution in an isothermal isobaric process:  G mix  = R T  X i ln X i What would a plot of  G mix  versus mole fraction of the solute look like for a binary solution? We can now use a rearrangment of the definition of Gibb’s free energy: H = G + T S to calculate the enthalpy of mixing to form an ideal solution in an isothermal isobaric process:  H mix =  G mix + T  S mix = (R T  X i ln X i ) + T (- R  X i ln X i ) = 0 When concentrated sulfuric acid is mixed with water enough heat can be generated to cause the solution to boil. Do sulfuric acid and water form an ideal solution? Can you explain why the interaction of sulfuric acid and water is so exothermic based on their molecular structures?

31.3 To calculate the volume change on mixing to form an ideal solution we begin with: dG = V dP - S dT and divide by dP, while holding the temperature constant to obtain a partial derivative indicating how the Gibbs’ free energy changes with pressure: (  G /  P) T = + V which gives for the change in volume on mixing to form an ideal solution isothermally and isobarically:  V mix = (  G mix /  P) T = (  (R T  X i ln X i ) /  P) T = 0 Why is the partial derivative of  G mix  taken while holding the temperature constant, equal to zero? When 10.0 mL of concentrated sulfuric acid is mixed with 90.0 mL water the final volume is ~ 98.0 mL. Do sulfuric acid and water form an ideal solution? Can you explain this observation in terms of the molecular structure of sulfuric acid and water?

31.4 Finally we can use a rearrangement of the definition of enthalpy: E = H - P V to calculate the internal energy change for mixing to form an ideal solution isothermally and isobarically:  E mix =  H mix - P  V mix = 0 - P (0) = 0 Could you explain why  E mix is zero based on the postulates that define an ideal solution?