Heat of Solution Theory

BY

Adao Sebastiao Ricardo joao Thuto Mahole

SUMMARY

This experiment was done in order to determine the solubility of the benzoic acid over a range of temperatures and consequently calculate its heat of solution. The experiment was conducted by using a solution of saturated benzoic acid together with the titration method using 0.015M NaOH solution and phenolphthalein indicator. This operation was performed at 40 °C, 35 °C, 30 °C and 25 °C by transferring the 250 ml conical flask to each respective water bath and conducting the titration upon equilibrium. Variables such as temperatures, initial and final mass as well as the initial and final volumes of the solution before and after titration, giving rise to the calculation of the solubility of the benzoic acid as well as the enthalpy of dissolution. Throughout the experiment the initial volume was kept constant at 50 ml. Results show that there is a linear relationship between solubility and temperature. The solubility of benzoic acid increases as the temperature increase. Tthe heat of reaction was determined by plotting a graph of log(S/°S) vs 1/T. It was found that H is -243,7J/kg. Since H has a negative value, indicating that the dissolution of benzoic acid is an exothermic process. The energy of hydration is much larger than the energies associated with the breakage of bonds of water molecules and benzoic acid molecules.

Table of contents

SUMMARY ............................................................................................................................... 1 INTRODUCTION ..................................................................................................................... 4 THEORY ................................................................................................................................... 5 PROCEDURE AND APPARATUS .......................................................................................... 6 RESULTS, DISCUSSION AND CONCLUSION .................................................................... 8 NOMENCLATURE .................................................................................................................. 9 BIBLIOGRAPHY .................................................................................................................... 10 APPENDIX A .......................................................................................................................... 11

INTRODUCTION

The enthalpy of solution, enthalpy of dissolution, or heat of solution is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution. The enthalpy of solution is one of the three dimensions of solubility analysis. Solubility is the amount of a particular substance that can dissolve in a particular solvent; it is usually given in mol/Kg. For a given solute, the heat of solution is the change in energy that occurs as one mole of the solute dissolves in a solvent. During the dissolving process, solutes either absorb or release energy. If solutes absorb energy from the solvent as they dissolve, the solution gets colder and the reaction is endothermic. If solutes release energy to the solvent as they dissolve, the solution gets warmer and the reaction is exothermic. By using a titration method to determine the solubility and measuring the change in the temperature of the solution during the dissolving process, we calculated the heat of solution. Solutions are very common in nature. In order for any reaction to occur there must be a change in energy. The ease of dissolution is dependent on the temperature of the system and type of solution, being endothermic or exothermic. Generally, when dissolution occurs, the entropy of the system increases. It is important to determine the heat of solution (enthalpy change) this is because a change in enthalpy takes account of energy transferred to the environment through the expansion of the system under study. The total enthalpy, H, of a system cannot be measured directly. Thus, change in enthalpy (ΔH), is a more useful quantity than its absolute value. The change ΔH is positive in endothermic reactions, and negative in exothermic processes. Enthalpy is a thermodynamic potential. It is a state function and an extensive quantity. The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of energy transfer.

THEORY

The heat of solution or enthalpy of solution is one of the three dimensions of solubility analysis. It is the change in enthalpy associated with the dissolution of a solvent at constant pressure resulting in infinite dilution, thus as one mole of the solute dissolves in the solvent. In the process, energy can either be absorbed or released; it is expressed in kJ/mol at constant temperature, with positive values indicating endothermic values and negative values indicating energy released or exothermic energy. Dissolving a gas in liquid solvent releases energy, as heat, into the surroundings in an exothermic reaction. The temperature of the solution decreases as energy leaves the system; therefore solubility of a gas increases with a decrease in temperature of solution. On the other hand, when the solution is heated, the reverse reaction occurs and gas evolves. Enthalpy of hydration is one of the most common types of heat of solution. A substance, commonly a salt is dissolved in water. When completely dissolved, the heat of solution is at its maximum. Dissolution of a solute can occur in three steps: 1. Breaking of solute-solute attraction (endothermic) 2. Breaking of solvent-solvent attractions (endothermic) 3. Forming solvent-solute bonds (exothermic) The sum of the individual enthalpy changes of each step is the overall value of the enthalpy change. Stronger bonds are formed in solutions with negative enthalpy changes and these solutions tend to have a lower vapour pressure. A negative enthalpy indicates that a solute is easily dissolved in the solvent. (Wikipedia enthalpy change of solution; (University, 2005)) Three conditions are fulfilled in the process, as mentioned before, the pressure remains constant, there is expansion against the atmosphere and work is done, and the temperature remains constant. The enthalpy of solution is only valid for dissolution of a pure substance into another pure substance. Enthalpies of solution of most substances can be measured directly when the resulting solution is liquid. A constant temperature can be maintained if the solute is dissolved slowly. (Bookrags, 2006) When a solid is dissolved in a solvent in which it is soluble, it dissolves until saturation is reached at a certain temperature. It is necessary to determine the amount of solute dissolved and the nature of solid phase in equilibrium with the solution when performing solubility measurements. Solubility depends on temperature; it increases with temperature in an endothermic reaction and decreasing with increase in temperature in exothermic reactions. The well-known van’t Hoff equation relates the equilibrium constant of a reaction, K, to the enthalpy change of that reaction, H:

A similar equation can be derived relating the solubility of a solid to its enthalpy of solution:

Where S is the solubility in moles per kilogram, S= 1 mol/kg, T is the temperature in degrees Kelvin and H is the standard enthalpy of solution. (Department of Chemical Engineering, 2011)

Procedure and apparatus

Apparatus The apparatus used during the experimental work were: two 400ml-beakers; one 250mlconical flask; one 10ml-pipette, two mercury thermometers; two burettes; two water-baths; one 1000ml-beaker; four 100ml-conical flask; one 100ml-measuring cylinder and two hotplates. The chemicals used to for the experimental work were: solid benzoic acid, sodium hydroxide pellets, phenolphthalein indicator and water. Procedure         

The thermostats on the two water-baths were set to 40˚C and 35˚C. A solution of 0.015M of sodium hydroxide (0.3g/500ml) was prepared in a 500ml beaker. 500ml of water were heated to 50˚C in a 1L beaker on a hotplate. 300ml of water were heated to 80˚C in a 400ml beaker on a separate plate. A 250ml saturated solution of benzoic acid, containing excess acid, was prepared at 80˚C in a 400ml beaker. 150ml of the solution were measured in a measuring cylinder and transferred into a 250ml conical flask. The flask was placed in the 1L beaker with water at 50˚C, while stirring the solution continuously. More solid benzoic acid was added to keep the solution saturated. When the temperature reached 50˚C, the flask was transferred to the 40˚C water-bath. Once equilibrium was reached, the temperature was recorded and found to be 40.1 ˚C. A pipette was used to withdraw 10ml of the benzoic acid solution and drain it into a 100ml conical flask. Three drops of the phenolphthalein indicator were added to the solution and the weight of the flask with the solution was recorded, 10.18g exactly.





The benzoic acid solution was titrated using the sodium hydroxide solution. Once the colour of the solution changed to light pink, the volume of sodium hydroxide used and the mass of the flask after titration were recorded, 28.5ml and 36.77g respectively. The 250ml conical flask was transferred to the 35˚C water-bath, then 10ml were transferred to the 100ml conical flask each and titration was performed. The same operation is repeated by transferring the 250ml conical flask to the 30 ˚C water-bath, then to the 25 ˚C water-bath and conduct titration upon equilibrium

The volume of benzoic acid solution used for titration was kept constant (10ml), the temperature was varied during the experiment. The mass of flask with solution before and after titration was recorded, as well as the temperature values and the volume of sodium hydroxide solution in the burette before and after titration.

RESULTS, DISCUSSION AND CONCLUSION

There is a linear relationship between solubility and temperature. The graph shows an increasing trend. The solubility of benzoic acid increases from 274.5*10-3 mol/kg to 427.5*10-3 mol/kg as the values of temperature increase from 25˚C to 40˚C. Between 30C and 35C there is a change in slope as it decreases then increases from 35C to 40C, this indicates change in the nature of the solid phase.

The slope of the line of best fit (straight line) was found to be -12.73 and the heat of reaction was determined from it. It was found that H is -243,7J/kg. Since H has a negative value, it indicates that the dissolution of benzoic acid is an exothermic process. The energy of hydration is much larger than the energies associated with the breakage of bonds of water molecules and benzoic acid molecules.

NOMENCLATURE

K

-

Equilibrium constant

S

-

Solubility; mol/kg of solvent

S

-

Standard solubility; 1 mol/kg

H

-

Standard enthalpy of solution; kJ/kg

T

-

Temperature; K

R

-

Universal gas constant

TWB

-

Temperature of water-bath

TE

-

Equilibrium temperature of solution

MI

-

Mass of solution before titration

MF

-

Mass of solution after titration

VI

-

Volume of sodium hydroxide in burette before titration

VF

-

Volume of sodium hydroxide in burette after titration

Bibliography

Bookrags. (2006). Heat of Solution. Retrieved August 16, 2011, from BookRags: http://www.bookrags.com/research/heat-of-solution-woc Department of Chemical Engineering. (2011). Practical Manual S4. Durban, KZN, South Africa: Durban University of Technology. M, S. J., Ness, H. V., & Abbott, M. (2003). Introduction to Chemical Engineering Thermodynamics. In J. Smith, H. V. Ness, & M. Abbott, Introduction to Chemical Engineering Thermodynamics (pp. 426 - 432). New York: McGraw - Hill. University, A. (2005). heat of solution. Retrieved August 14, 2011, from http://www.pulse.pharmacy.arizona.edu/resources/heatofsolution.pdf Zumdahl, S. A., & Zumdahl, S. S. (2006). Chemistry. In S. A. Zumdahl, & S. S. Zumdahl, Chemistry (pp. 489 - 492). Urbana: Houghton Mifflin. Haase, R. In Physical Chemistry: An Advanced Treatise; Jost, W., Ed.; Academic: New York, 1971; p 29. Laidler, K. The World of Physical Chemistry; Oxford University Press: Oxford, 1995; p 110. C.Kittel, H.Kroemer In Thermal Physics; S.R Furphy and Company, New York, 1980; p246 DeHoff, R. Thermodynamics in Materials Science: 2nd ed.; Taylor and Francis Group, New York, 2006.

APPENDIX A: Sample calculation

During the titration process, when equilibrium is reached the number of moles of benzoic acid and sodium hydroxide are equal. Thus:

The number of moles of sodium hydroxide can be determined from the definition of molarity:

Where:

M=molar concentration; n = number of moles; V= volume;

Expressing the number of moles in terms of molar concentration and volume, it becomes:

Solubility is expressed as the number of moles of solute per kilogram of solvent. It can be expressed as: Solubility of benzoic acid was determined at different temperatures and the results are the following:  At temperature of 40˚C, the number of moles of sodium hydroxide was:

And the solubility was found to be:

 At temperature of 35˚C, the number of moles of sodium hydroxide was:

And the solubility was found to be:

 At temperature of 30˚C, the number of moles of sodium hydroxide was:

And the solubility was found to be:

 At temperature of 25˚C, the number of moles of sodium hydroxide was:

And the solubility was found to be:

Table of results: Solubility at different temperatures Temperature (˚C) 40 35 30 25

Solubility (mol solute/kg solvent)

Table of raw data: recorded values for temperature, mass and volume. TWB(˚C) 40 35 30 25

TE(˚C) 40.1 35 30 25

MI(g) 10.18 10.13 10.05 10.14

Where: TWB = Temperature of water-bath TE = Equilibrium temperature of solution MI = Mass of solution before titration

MF(g) 36.77 34.55 34.01 28.35

VI (mL) 50 50 50 50

VF (mL) 28.5 24.5 22.3 18.3

MF =

Mass of solution after titration

VI = Volume of sodium hydroxide in burette before titration VF =

Volume of sodium hydroxide in burette after titration

The heat of reaction was determined from the equation:

Where: S

=

S˚ = ∆H˚= R

=

T

=

Plotting log(S/S˚) versus 1/T, the heat of reaction was calculated: Log(S/S˚) -3.37 -3.43 -3.48 -3.56

1/T 0.0250 0.0285 0.0333 0.0400

The slope of the line of best fit (straight line) was found to be -12.73 and the heat of reaction was determined from it.

The universal gas constant has a value of 8.314J/mol*˚C. Thus, the heat of reaction becomes: