James M. Grow

NJIT Chemistry Division

 

Heat of Solution

The integral heat of solution of potassium nitrate in water is determined as a function of concentration. From these data differential heats of solution and integral heats of dilution are calculated.

Apparatus

Parr Solution calorimeter with recorder (S); six weighing bottles (D,S); manual for the calorimeter(M), voltage probe (S).

Chemicals

One hundred grams KNO3 (L); distilled H2O (L); TRIS (S). Alternately, 150 grams BaCl2· 2H2O or 250 grams K4Fe(CN)6· 3H2O in place of the KNO3.

Heats of hydration may be determined from heat of solution data via the application of Hess' Law. Your instructor may ask that you determine D H of hydration of K4Fe(CN)6 or BaCl2, the reactions being:

K4Fe(CN)6(s) + 3H2O(l) = K4Fe(CN)6· 3H2O(s)

BaCl2(s) + 2H2O(l) = BaCl2· 2H2O(s)

Should this be the case, measure the integral heats of solution for the anhydrous and hydrated forms of the salt over the solubility range .08 to 1.0 molal? Be aware that the hydrated salts go into solution slowly. This is especially true for K4Fe(CN)6· .3H2O. Follow the instructions given below for KNO3 except that you will make runs for solutions of concentrations half those listed for the nitrate. The anhydrous salts are prepared from the corresponding hydrates by heating them in the oven at 110oC for three hours.

 

Procedure[2,3]

Carefully follow the instructions of the manufacturer for use of the

Solution Calorimeter. Do not start the actual experimental run until the instructor has discussed the equipment and experimental procedure with you.

CAUTION: The solution cell is fragile and very expensive: Treat with TLC!

Do two calibration runs using the TRIS and the 0.100 M HCl provided. A 0.5 gram sample of TRIS will have a D T of about 1/4oC. The optimal temperature rise should be determined on this basis.

This experiment illustrates the special advantage that endothermic reactions offer for calorimetric measurements. It becomes unnecessary to know the heat capacity of the calorimeter or of the solution being studied. No cooling correction is necessary, and the method is simpler than the ordinary adiabatic method.

The essential features of a suitable calorimeter for work of moderate precision are shown in Figure 1. The vacuum bottle minimizes heat exchange between the solution and the surroundings. A mechanical stirrer is used to provide the efficient and uniform stirring essential to the rapid solution of the solute. The rate of stirring, however, should be kept as low as efficiency permits to minimize the energy introduced by stirring. The stirrer shaft should be of a poor heat conductor and proper bearings must be provided to eliminate (as far as possible) heat generation by friction. (The shaft bearings should be located above the calorimeter proper.) A belt-and-pulley drive is used to keep the heat transfer by conduction and radiation from the motor at a minimum.

Figure 1. Apparatus for the measurement of the heat of solution

As a temperature indicator, a sensitive mercury thermometer may be used, but a thermistor is recommended because of its rapid and sensitive response to temperature changes.

The calorimeter should be assembled. The thermistor thermometer is connected to the Wheatstone bridge, and the stirrer is started. The time that the stirrer is on must be recorded.

To determine the work of stirring per second, the solution is stirred for a time of the order of 15 min. and the slope of the temperature vs time curve determined. From these data, the work of stirring per second can be calculated.

The experimental techniques and the specific instructions for the equipment actually used are given in the "Instruction Manual for the 1451 Solution Calorimeter" by the Parr Instrument Company of Moline, Illinois. A copy of this manual is provided. Be aware that 100 millivolts corresponds to a D T of 1 oC and 1000 mV to a D T = 10 oC. Note that when a voltage probe is used the temperature setting should be at 20 ° C. If the temperature of the solution in the dewar falls below this temperature, no out put will be produced. If you are using an endothermic reaction, make sure the temperature in any run does not fall below 20 ° C. If the temperature in the dewar does fall below 20 ° C, do not heat the dewar itself, pour the solution into a beaker before heat is applied! Use six weighed samples of KNO3 of such size as to prepare solutions of about 0.15, 0.35, 0.6, 1.0, 1.4, and 1.8 molalities. For 100 grams H2O, this corresponds to successive additions of about 1.5, 2.0, 2.5, 4, 4, and 4 grams respectively.

Care must be taken to ensure that solvent and solute are in thermal equilibrium before initiating the solution process! Time permitting, make duplicate runs of the KNO3 solutions and/or run concentrations intermediate to those already done (0.25, 0.45, 0.75, 1.2, and 1.5 molalities).

NOTE: YOU MUST USE THE SAME CALORIMETER BOTH WEEKS! WHY?

D H = Ccal D T

where Ccal is the heat capacity of the calorimeter as determined from the calibration runs. Refer to the Parr Instruction Manual for the procedure used to calculate D T and Ccal.

THEORY.[1] The quantitative study of the thermal effects which accompany the dissolving of a solute in a pure solvent, or a solution, has been systematized through the introduction of the concepts of the integral, and differential, heats of solution.

The integral heat of solution D HIS at a particular concentration is the heat of reaction at a specified temperature and pressure when one mole of solute is dissolved in enough pure solvent to produce a solution of the given concentrations. This does not require that one mole be used to determine this quantity. There will be no heat of mixing if five one-liter samples of a 0.2m solutions were mixed to create a solution with one mole of solute. Therefore, the integral heat of solution for a 0.2 molar solution can be determined for any weight of solute if the ratio of moles of solute to moles of solvent is correct.

 

Thus D HIS for KNO3 in water equals the enthalpy change for the process

KNO3(s) + nH2O(l) = [KNO3, nH2O]

For example, if 1 mole of solute is dissolved in 500 g of water at constant T and P, the heat of reaction gives the value of the integral heat of solution at the concentration 2m, corresponding to n = 500/18 = 27.75. Or, as in this experiment, if 1.5g, or 1.5/101.1 =0.0148 moles, of KNO3 is dissolved in 100g, or 100/18 = 5.55 moles, of water, the heat of solution would be reported for a 0.148m solution, or 1 mole of KNO3 in 375 moles of water.

For a solution of given concentration, the differential heat of solution of the solute, D HDS(T,P,n2/nl), is the heat of solution per mole of solute added under conditions in which the concentration of the solute is changed only differentially. Thus, if d q represents the enthalpy change when dn2 moles of solute is added (at constant T, P) to a solution phase already containing n2 moles of solute and n1 moles of solvent,

D HDS(T,P,n2/n1) = d q/dn2

Alternatively, the differential heat of solution may be identified with the value of Qp for the addition of 1 mole of solute to an infinite quantity of solution with the correct molar ratio n2/n1. In this case, also, the concentration of the solution would only be differentially changed.

It will be obvious that a direct measurement of the differential heat of solution is not possible; its value must be calculated from results of integral-heat-of-solution measurements. Let D HS(n2) represent the enthalpy change for the dissolving, at constant T, P, of n2 moles of solute in a fixed number of moles of solvent. The differential dD HS = D HS(n2 + dn2) -D HS(n2) then can be identified with the enthalpy change for the addition of dn2 moles of solute to a solution already containing n2 moles of solute and the fixed number of moles n1 of solvent. From the definition of the differential heat of solution,

(1)

since the definition of the integral heat of solution requires D HS=n2 HIS(T,P,n2/n1).

If the constant number of moles of solvent n1 is specified as 1000/M1 (M1 = gram formula weight of solvent (18 for water)), then n2 can be replaced by the molality m of the solute, and

(2)

 

The equations in (2) are exactly equivalent mathematically, but the practical problem involved in the accurate determination of the slope of a curve will often permit better calculations to be made by use of second equation.

The magnitudes of these heats of solution depend specifically on the solute and solvent involved. The value of the heat of solution at high dilutions is determined by the properties of the pure solute and by the interactions of the solute with the solvent. As the concentration of the solution increases, the corresponding changes in the differential and integral heats of solution reflect the changing solute-solvent and solute-solute interaction effects.

For the interpretation of heat-of-solution data for some systems, it is instructive to compare the results with the behavior predicted for ideal solutions. An ideal solution may be defined as one which obeys Raoult's law over the entire range of concentrations being considered. It can be shown[1] that the mixing, at constant T and P, of pure liquid solvent with such a solution produces no change in enthalpy. From this it follows that for the case of a liquid solute, dissolving to form an ideal solution, D HIS = 0. For the case of a solid solute which dissolves to form an ideal solution, D HIS equals the molar heat of fusion to give the (supercooled) liquid at the temperature of the solution. Such behavior is approximated in some actual cases, which involve nonelectrolyte solutes and nonpolar solvents, e.g., naphthalene in benzene. For electrolyte solutes the actual behavior is very different from the ideal case, because of-marked solute-solvent and solute-solute interactions.

The integral heat of dilution D HD,m1® m2 between two molalities m1 and m2 is defined as the heat effect, at constant temperature and pressure, accompanying the addition of enough solvent to a quantity of solution of molality m1 containing one mole of solute to reduce the molality to the lower value m2. The process to which the integral heat of solution at molality m2 refers is equivalent to the initial formation of the more concentrated solution of molality m1 followed by its dilution to the lower molality m2; the integral heat of dilution is thus equal to the difference of the integral heats of solution at the two concentrations involved:

(3)

 

CALCULATIONS. For this experiment the first law of thermodynamics leads to

D H = q - ws (4)

The work of stirring ws is negative because work is done on the system.

For each solution the total number of moles of solute present and the corresponding total enthalpy change D H are to be calculated. That is, to calculate the integral heat of solution for a 1 molar concentration ((mole H2O)/(Mole KNO3) = 55.55), the heat generated from the 1.5g, 2g, 2.5g, and 4g additions should all be added together. The molality of the solution and the integral heat of solution at that concentration are then calculated. The integral heat of solution, D HIS, should be plotted as a function of molality, and the differential heat of solution should be evaluated at 0.5 and 1.5 m by use of Eq. (2b). This method is employed, rather than direct use of Eq. (1), to minimize the uncertainty in the calculated values due to the difficulty of determining accurately the slope of a curve.

The integral heats of solution at 0.5, 1, and 1.5m should be obtained by interpolation, and the integral heats of dilution from 1.5 to 1m and 1 to 0.5m are to be evaluated. The various experimental results should be compared with accepted values.[4] For comparison with literature data it should be remembered that the enthalpy of formation of a solute is defined as the enthalpy change for formation of the solution from the solvent and the elements of the solute, each in its standard state.

Practical applications. Integral heat-of solution data are often required in energy balance heat calculations for chemical processes for engineering purposes. They are also used in the indirect evaluation of standard heats of formation of compounds for which heats of reaction in solution must be utilized. Measurements of the integral heat of solution may be used for the calculation of integral heats of dilution when no direct determinations of the latter are available. The differential heat of solution at saturation determines the temperature coefficient of solubility of the solutes.

Suggestions for further work. The method here described is suitable for measurements on most endothermic reactions. The apparatus may be used for exothermic reactions by determining the temperature rise due to the reaction, then cooling the system to the initial temperature and reheating it through the identical temperature range by means of the electrical heating coil.

The heat of solution of urea may be determined as typical of a nonelectrolyte. The individual samples used should be larger (about 15 g) because of the smaller heat of solution. The heats of solution of urea, phenol, and the compound (NH2)2CO • 2C6H5OH are measured separately, and the heat of formation of the compound calculated The compound is prepared by fusing 9.40g of phenol with 3g of urea in a test tube immersed in boiling water.

The heat of hydration of calcium chloride may be determined indirectly from measurements of the endothermic heat of solution of CaCl2 • 6H20 and the exothermic heat of solution of CaCl2. A test of the equipment and operating technique may be made by measuring the relatively small heat of solution of sodium chloride. Comparison data for concentrations up to 1.3 m have been given by Benson and Benson.[7]

The heat of mixing of organic liquids may be determined with the same apparatus.[8] The results for chloroform-acetone and carbon tetrachloride-acetone may be discussed on the basis of hydrogen bonding.

References

1. G. N. Lewis and M. Randall, "Thermodynamics," 2d ed., rev. by K. Pitzer and L. Brewer, McGraw-Hill Book Company, New York, 1961.

2. J. M. Sturtevant in A. Weissberger (ed.), "Technique of Organic Chemistry," vol. 1, "Physical Methods of Organic Chemistry," 3d ed., pt. 1, chap. 10, Interscience Publishers, Inc., New York, 1959.

3. H. A. Skinner, J. M. Sturtevant, and S. Sunner, in H. A. Skinner (ed.), "Experimental Thermochemistry," vol. II, chap. 9, Interscience Publishers, Inc., New York, 1962.

4. Selected Values of Chemical Thermodynamic Properties, Natl. Blur. Std US. Circ. 500, 1952.

5. A. T. Williamson, Trans. Faraday Soc., 40: 421, (1944).

6. A. N. Campbell and A. J. R. Campbell, J. Am. Chem. Soc., 62: 291, (1940).

7. G. C. Benson and G. W. Benson, Rev. Sci. Instr., 26:477 (1955).

8. B. Zaslow, J. Chem. Educ., 37: 578 (1960).

9. M. L. McGlashan in H. A. Skinner (ed.), "Experimental Thermochemistry," vol. II chap. 15, Interscience Publishers, Inc., New York, 1962.

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