Determination Of The Differential Heat Of Solution 6s6e17

Determination of the differential heat of solution Determination of the Benzoic acid solubility in water Summary The aim of this experiment is to emphasize the relation between solubility and temperature and to calculate the differential heat of solution for a solid at saturation. Theoretical aspects The equilibrium conditions between solid phase and liquid phase for a 2 components system could be considered in 2 ways: a) If the solution is in equilibrium with solid phase of the component in excess( the solvent) one says that the solution is at freezing point and the curve which represents the variation of this temperature depending on liquid composition is called the freezing point curve. b) If the solid phase of the component which is found in a smaller quantity( solute) is in equilibrium with the solution ,one says that is the case of a saturated solution and the temperature variation on composition is represented by the solubility curve. As there are no thermodynamic differences between solvent sand solute, the distinction among freezing curves and solubility curves is just a matter of convention. The solution process consists essentially from two steps with opposite thermal effects: -the breaking of crystalline network of the solid, which requires consumption of energy -the solvation (hydration for solution in water) through which intermolecular links between solvent and solute are established, the process being accompanied by release of energy The global effect is either endothermic or exothermic as one of the processes above prevails. One of the simplest cases of phase equilibrium is that of a saturated solution in with excess solute; molecules leave the solid and into solution at the same rate at which molecules from the solution are deposited on the solid. The term solubility refers to a measure, on some arbitrarily selected scale, of the concentration of the solute in the saturated solution. Here the molal concentration scale will be used and the solubility then becomes equal to the molality mi,s of the solute in the saturated solution. An equilibrium –constant relation may be written for the phase equilibrium considered: a K i  *i (eq.1) ai Here ai represents the activity of the solute in the saturated solution and a , the activity of the pure solid solid ( conventionally equal to unity).The activity ai is related to the molality mi of the solute by means of the activity coefficient γi, a function of T , P and composition which approaches unity as mi approaches zero. Then: K  a i , s  (mi , s )   i , s  mi , s (eq.2) ,where the subscript s indicates that the relation applies to the saturated solution.

The change in K with temperature at constant pressure reflects a change in mi,s , and also the change in γi,s, which is affected by both the variation s in temperature and concentration of the solution.   ln K   T   



H R T 2

(eq.3) , where ∆H= standard enthalpy change for solution process. This quantity should not be confused with any actual experimentally measurable heat of solution: it can be determined indirectly, however. It is obtained:

ln

p

x 2(T2 ) x

(T1 ) 2

d H sat  R

In the case of diluted solutions:

 1 1   T  1 T2  x2(T2 ) c1(T2 )  x2(T1 ) c2(T1 )  

(eq.4) (eq.5)

From the (eq.4) and (eq.5) we get that:

c 2(T2 ) d H sat ln (T1 )  R c2

 1 1   T  1 T2 

 

which allows us to calculate the differential heat of solution: c 2(T2 ) R  ln (T ) c2 1 d  H sat   1 1    T  1 T2 

(eq.6),

(eq.7)

Determination of the benzoic acid solubility in water The determination of a solid solubility can be easily proceeded by mixing an excess of solute with the solvent, till the equilibrium state is established. Then the saturated solution is filtered and analyzed to estimate the solute concentration at saturation (mi,s). The solubilities of benzoic acid (i) in water are determined at room temperature and at 45°C. Having these data the differential heat of solution of benzoic acid at saturation should be computed. Laboratory equipment A, thermostate,2 100-ml Erlenmeyer bottles, 2 pipettes( 50 and 100 ml), one short rubber tube to be attached t the pipettes, glass wool, one burette, on 250 ml Erlenmeyer flask,0.1N NaOH solution, distilled water, benzoic acid and phenolphthalein as indicator. Working procedure In one of the Erlenmayer bottles with caps introduce 1 g benzoic acid and 75 ml water. Stirr at room temperature for about an hour. In the other Erlenmayer flask, introduce 2g benzoic acid and 75ml water. Leave it in a thermostat at about 45°C for about an hour (this is enough time to reach the equilibrium). After this, the determination of solubilities can begin. To prevent drawing small crystals into the pipette along with solution, a filter

from glass wool into a rubber tube is wrapped around the tip of the pipette. The filter is removed before draining the pipette. In the first Erlenmayer flask introduce 50 ml of benzoic acid solution at room temperature and in the other flask introduce 10 ml of the solution of benzoic acid which was maintained in the thermostat. Each solution in titrated with 0.1NaOH solution, in the presence of phenolphthalein as pH indicator.