EAS 6140 Thermodynamics of Atmospheres and Oceans
Solutions
1. Circle the following that are true statements about solutions
a) a solution consists only of a single phase
b) a solution must have more than one component
c) solutions must be liquid.
2. The component in the solution with the largest mode fraction is referred to as the
(solvent, solute).
Solvent
3. If water is the solvent, the solution is said to be __aqueous__________
4.
a)
b)
c)
Circle the following statements that are true about colligative properties of solutions:
colligative properties depend on the mole fraction of the solute
colligative properties vary with the chemical composition of the solute
the freezing point depression is a colligative property.
Vapor pressure depression
5. Raoult’s law states that the vapor pressure (pA) of solvent A above the solution is
given by
(4.43a)
pA = X A poA
o
where p is the vapor pressure of the pure phase. In an aqueous solution, po = es. If the
solute is volatile (i.e., it has a vapor pressure), we can also write
pB =X B poB
(4.43b)
A solution that follows Raoult’s law is known as an ideal solution. We would like
to find the ratio of the vapor pressure over an aqueous solution to the vapor pressure of
pure water. If we use the subscript soln to denote solution and solt to denote solute, we
have
o
psoln X H 2O e s + X soltp solt
=
es
es
(4.44)
a) what is the mathematical definition of a dilute solution?
X solt
X H 2O
b) For a dilute solution, write the ration of the vapor pressure over an aqueous solution to
the vapor pressure of pure water to be a function only of the nsolt and nH2O.
psoln
n
 1  solt
es
nH 2O
6. The saturation vapor pressure over a water solution is (less than, equal to, greater
than) the saturation vapor pressure over pure water. Less than
7. The vapor pressure over an electrolytic solution is (less than, equal to, greater than)
the vapor pressure over a non-electrolytic solution. Less than
8. Calculate the mole fraction of H2O in seawater with s=35 psu, comprised solely of
NaCl. The molecular weight of NaCl is 58.5 g/mole, and the molecular weight of H2O is
18 g/mole.
35
0.6
58.5

 1.1 100  1.1  98.9
35
0.6  53.6
 965
58.5
18
9. Evaluate the ratio of the partial pressure of the seawater solution in #8 to the saturation
vapor pressure.
psoln
 X H 2O  98.9
es
Equilibrium concentration of gases in solution
12. Equilibrium concentrations of atmospheric gases in seawater (increase, decrease,
remain the same) with increasing salinity.
decrease
13. Equilibrium concentrations of atmospheric gases in seawater (increase, decrease,
remain the same) with increasing pressure. increase
14. Equilibrium concentrations of atmospheric gases in seawater (increase, decrease,
remain the same) with increasing temperature.
decrease
15. What are some additional factors (beyond basic Henry’s Law solubility) influence
the concentration of CO2 gas in the oceans? Ocean motions, biological activity and
chemical reactions
Freezing point depression
10. The freezing point of a water solution (increases, decreases, remains the same) as
salinity increases.
decreases
11. A typical freezing temperature of seawater is _-2____ oC.
Eutectics
13. Consider a solution of water and NaCl. This solution has
____2_______ components
____1_______ phases
____3_______ thermodynamic degrees of freedom
14. To conveniently represent the phase diagram on a graph, we can eliminate one
degree of freedom if we examine the system only at constant pressure. For the twocomponent system at constant pressure, what is the maximum number of thermodynamic
degrees of freedom for this system? 2
15. On the phase diagram for this system at constant pressure (below; see also Fig 4-8),
temperature is plotted as a function of the concentration of salt in the solution, given in
units of parts per thousand (%o). Label the following:
a) number of thermodynamic degrees of freedom associated with each region and line
b) liquidus curve
c) eutectic point
16. Mark on the diagram examples of each of the following (use the letters A, B, C)
A. unsaturated vapor
B. liquid and solid in equilibrium
C. path of isobaric cooling, starting from point X, until the vapor condenses
D. path of isobaric heating, starting from point Y, until the liquid evaporates
°
17. Fig. 4-8 is a phase diagram for a H2O-NaCl solution under constant pressure
conditions. Use Fig 4.8 to determine the following for a H2O-NaCl solution
a)
b)
c)
d)
What is the eutectic temperature? -21C
What is the value of the freezing point depression at a salinity of 100 psu
7C
o
At –15 C, what is the salinity of the brine?
~175 at liquidis curve
o
At –15 C, what is the ratio of the amount of ice to the amount of brine?
140 to 35 or 4 to 1
18. At a temperature of –30oC, which solid salts will have precipitated from the seawater
(Table 4.5) ?
CaCO3
6H2O, Na 2SO4
10H2O, MgCl2
8H 2O, NaCl 2H2O