Study Questions, Chapter 5

Ideal Solutions

1.  A solution of ethanol and water is prepared by mixing 70.0 L of water and 30.0 L of ethanol.  The final volume of the solution is 96.8 L.  Is the solution ideal?  Please explain.

 

 

 

 

2.  Show that the chemical potential of pure liquid A is given by 

 

 

3.  Show that the chemical potential of liquid component A in a solution is given by

 

 

where pA and p*A are the partial pressure of A in the vapor above the solution and the vapor pressure of pure A, respectively.

 
4.  Show that for an ideal solution, the chemical potential of component A is given by

 

 

 

 
5.  Liquids A and B mix to form ideal solutions.  If pure B is added to pure A, does the chemical potential of A increase, decrease or remain unchanged?  Please explain.

 

Osmosis

6.  In an osmosis experiment involving an aqueous solution, a semipermeable membrane separates pure water from the solution.  Write an expression for the chemical potential of water on each side of the membrane.

 

 

 

 
7.  Initially, before equilibrium is reached, on which side of the membrane does water have the lower chemical potential?  In which direction does the water flow, and what are the consequences of this flow?  Please explain your answers.

 

 

 

 

 
8.  Given that for a pure substance dG*m = -S*m dT + V*m dp, , show that at constant temperature the difference between the chemical potentials of pure water at pressures p and p'  is given by

Assume that V*m is independent of pressure.

 

 

 

 

 

 
. 9  Use the equation in question 8 to show that at osmotic equilibrium

 

 

 

 

 

 F reezing point depression 

10.  Show that at the freezing point of a solution in which A is the solvent, the following equation holds:

State all assumptions that you make.

 

 

 

 

 
11.  Use the equation in question 10, and the Gibbs-Helmholtz equation to show that at the freezing point