CHEM 331L Physical Chemistry Laboratory Revision 2.2 Heat of Solution for Aqueous Potassium Nitrate In this laboratory exercise we will measure the Integral of Solution for the solvation of Potassium Nitrate in Water. KNO 3 (s) + n H 2 O(l) KNO 3 (aq) This data will allow us to determine the Differential Heat of Solution and Integral Heat of Dilution for aqueous solutions of this salt at various concentrations. Formally, we consider the Heat of Reaction (Q P,rxn ) for a chemical process: Reactants (T, P) Products (T, P) as being measured according to a two step procedure: Reactants (T, P) Products (T ', P) (In an Adiabatic Container) Products (T ', P) Products (T, P) (Container Immersed in a Temp Bath at Temp T) The Heat of Reaction will then be: Q P,rxn = Q P, Adiabat + Q P,Isotherm = 0 + Q P.Isotherm = Q P,Isotherm The importance of this scheme is that it is relatively easy to measure Q P,Isotherm and thus determine Q P,rxn calorimetrically. By convention, the reaction is said to be Exothermic if Q P,rxn < 0 and it is Endothermic if Q P,rxn > 0. Because the Heat of Reaction is measured under constant pressure conditions, we can equate this with the Enthalpy change for the reaction: H rxn (T, P) = Q P,rxn at the temperature in question. Thus, H rxn (T, P) is generally also referred to as the "Heat of Reaction". In this laboratory we will consider a chemical "reaction" that involves the solvation of a solute in a solvent; dissolving KNO 3 in Water. For solvation processes, on a per mole basis, Q P,rxn is said to be the Integral Heat of Solution; IS(T,P). Formally we define the Integral Heat of Solution
P a g e 2 as the heat associated with a solvation reaction, at a specified temperature and pressure, when one mole of solute is dissolved in enough pure solvent to produce a solution of a given concentration. (1 mol) Solute + (n mol) Solvent Solution (at m molal) Here n 1 is the number of moles solvent need to produce a solution of molality m. If n 2 represents the number of moles solute actually used during the measurement of the heat of solution then, IS(T, P) = Q P, solv rxn, m / n 2 (Eq. 1) (Keep in mind that IS depends on the molality of the solution produced, even though m is not formally listed as a variable; more correctly we should write IS(T,P,m).) For example, suppose we wish to determine the IS(T,P) associated with forming an aqueous 2m KNO 3 solution. In this case, we would measure the Q P, rxn which occurs when 1 mole KNO 3 is mixed with n 1 = 27.75 mole of H 2 O. n 1 is chosen according to: n 1 = (1 mol KNO 3 ) / [(2 m) (0.018016 kg/mol H 2 O) = 27.75 mol H 2 O The Differential Heat of Solution of a solute whose concentration is n 2 mole solute per n 1 mole of solvent is the Heat of Reaction per mole of solute added under conditions in which the concentration of the solute is changed only differentially: DS(T, P, n 2 /n 1 ) = (Eq. 2) (Proscribing n 1 and n 2, of course, sets the solution's molality; m = n 2 / n 1 M 1 /1000, where M 1 is the molar mass of the solvent.) Now, of course, this process is not possible experimentally. Basically, we are trying to add solute to the solution without changing the solution's molality. So, another method must be found to determine DS. To do this we let H S (n 2 ) represent the heat exchange associated with dissolving n 2 moles of solute into n 1 moles of solvent: n 2 Solute + n 1 Solvent Solution (m) (Eq. 3) Now, the heat exchange associated with adding an additional dn 2 solute to this solution: is d H S : dn 2 Solute + Solution (n 1, n 2 ) Solution (n 1, n 2 + dn 2 ) d H S = H S (T, P, (n 2 + dn 2 )/n 1 ) - H S (T, P, n 2 /n 1 ) The Differential Heat of Solution is then:
P a g e 3 DS(T, P, n 2 /n 1 ) = (Eq. 4) By chemical equation 3 we know H S (T, P, n 2 /n 1 ) = n 2 IS(T, P, n 1 ). Thus, DS(T, P, n 2 /n 1 ) = (Eq. 5) The definition of the molality of the solution: n 2 = m n 1 M 1 (Eq. 6) So now we have: DS(T, P, n 2 /n 1 ) = = = (Eq. 7) Therefore, the Differential Heat of Solution can be determined via the slope of the tangent to a IS vs. m curve at the desired concentration m. Finally, the Integral Heat of Dilution is the heat exchange when enough solvent is added to a solution of molality m 1 and n 2 = 1mole to dilute the solution to molality m 2. Solution (T, P, m 1, n 2 =1 mol) + Solvent Solution (T, P, m 2, n 2 =1 mole) This is simply the difference in the Integral Heats of Solution at the two molalities: D, m1-m2 (T, P) = IS(T, P, m 2 ) - IS(T, P, m 1 ) (Eq. 8) Measurements of IS then allow us to determine DS and D. Graphically, this can be summed up as follows, where as shown DS is determined at m 1 :
P a g e 4 In this exercise, we will determine IS values for the solvation of Potassium Nitrate KNO 3 in Water over a range of concentrations from 0m to 0.10m. By interpolation we will then determine IS at 0.05 and 0.1 molals. We will then determine H DS at 0.05m and 0.01m as well as D, 0.05-0.10. Solvation of KNO 3 is a strongly endothermic reaction. In fact, this reaction is so endothermic that it is employed in some "Cold Packs" that are used to treat minor injuries. When the "Pack" is snapped, solid KNO 3 is released into Water and the system cools significantly. The "Pack" can then be applied to the site of an injury. In practical terms, we will measure Q P, rxn for our system using a Parr 6755 constant pressure Solution Calorimeter. This calorimeter is designed to measure heats of reaction for samples, be they solid or liquid, being solvated into a liquid solvent. The basic go is that we will add solid KNO 3 to an aqueous solution and measure the resulting temperature drop using the calorimeter system. This temperature drop will then give us the Heat of Reaction.
P a g e 5 Solution Calorimeter The reaction is carried out in a Dewar flask that is placed into a calorimeter bucket and the solution's temperature is recorded by means of a high precision digital thermometer. Reaction Vessel & Dewar Flask
P a g e 6 High Precision Thermometer & Data Logger The solution in which the solvation reaction takes place acts as the calorimetric fluid which absorbs or releases heat during the course of the reaction, giving rise to the measured temperature change of the fluid. Initially, the Dewar flask is filled with Water and then placed into the calorimeter bucket. A solid KNO 3 sample is placed into a special sample container which is then inserted into the Water in the Dewar flask. The sample container is also connected to an external stirring system. The thermometer's probe is likewise inserted into the Water in the flask.
P a g e 7 When all appropriate connections have been made, the stirrer is started and the temperature is allowed to come to a constant rate of change. Because of heat leaks between the Dewar flask and the calorimeter bucket, and because of the stirring associated with the sample container, which causes work to be done on the calorimetric fluid, the temperature of the Water will not stabilize at a given temperature. However, the rate of change of the temperature, usually due to an increasing temperature, which results from the work of stirring, should stabilize. At this point the calorimeter will indicate the sample should be released from its container and into the Water. The temperature is now monitored until its rate of change is again fairly constant. At this point the data run is complete and the temperature change T c = T f - T i can be recorded. The heat of reaction can now be determined from the temperature change via: Q P, rxn = ( T c ) (e) (Eq. 9) where "e" is the so-called Energy Equivalent of the calorimeter; in effect, the Calorimeter Constant. The Energy Equivalent "e" of the calorimeter is determined by calibration with a reaction of known heat of solution. The calorimeter's manufacture's recommendation is to determine "e" for a reaction between TRIS (tris (hydroxymethyl) aminomethane) and 0.1M HCl, which has a well established Heat of Reaction. The temperature change for reaction of m grams of TRIS with 100.00g of 0.1 N HCl at 25 o C is measured. The known heat of solution QE is calculated according to: QE[cal] = m [58.738 + 0.3433(25 - T)] (Eq. 10) where T is the temperature of reaction:
P a g e 8 T = T i + 0.63 T c (Eq. 11) The Energy Equivalent is then determined: e[cal/ o C] = QE / T c (Eq. 12) Thus, we will first calibrate the calorimeter to determine its Energy Equivalent. Then we will use the calorimeter to determine Q P, rxn for several additions of KNO 3 to Water. These several successive KNO 3 additions will allow us to incrementally increase the molality of the solution and provide us with the opportunity to measure Q P, rxn for each addition; determining the Heat of Solution for each resulting solution. This will then allow us to determine IS over the desired molality range. A plot IS vs m will allow us to extract the desired DS and D values, which can then be compared with those of the literature.
P a g e 9 Procedure Your laboratory instructor will provide you with basic instructions for how to operate the Parr 6755 Solution Calorimeter. Appropriate pages from the instruction manual are attached as an addendum to this handout. The basic operation of the Calorimeter involves: Weigh the sample in the PTFE dish and attach the dish to the sample cell and push rod. Fill the Dewar with the calorimetric fluid. Install the thermistor probe in the calorimeter cover. Lower the cover assembly with probe and sample cell into the Dewar and set the cover into place. Drop the belt drive over the pulleys, start the motor and press the start key. Allow reactants to come to thermal equilibrium during this pre-period. Push the sample cell push-rod to release the sample into the calorimetric fluid when thermal stability is achieved. Allow the reaction to occur. When thermal stability is re-established, produce a report. Sample Dish Dewar Flask in Calorimeter Bucket Assembling the Stirrer & Sample Dish into the Cover
P a g e 10 Start-Up Procedure 1. Turn the Machine On. Placing the Temperature Probe, Sample Assembly and Cover into Place 2. Check to make sure the machine is in "Solution Calorimetry" mode. Main Menu => Operation Control => Method of Operation If it is not set for "Solution" mode, toggle the "Method of Operation" button. The unit will automatically restart and be reset to "Solution" mode. 3. Make sure the Jacket Temperature is to be determined via a "Calculated" method. Main Menu => Operation Control => Jacket Temperature Source 4. Set the unit for either an Endothermic Reaction run (our KNO 3 in Water reaction) or an Exothermic Reaction run (our calibration reaction).
P a g e 11 Main Menu => Diagnostics => Calorimetric Parameters => Tolerance Parameter Toggle button if needed; L2 = -1 for an exothermic reaction and L2 = 0.05 for an endothermic run. How to Perform a Run 1. Go to the Main Menu and select "Calorimeter Operation". Toggle the button. 2. Ready the sample as described above and make sure the stirrer's belt is connected. 3. Select start. i) Stirring will start. ii) Select a Sample ID. iii) You will now go through a Pre-Period before the reaction is to be initiated. During this period, the temperature is allowed to come to a constant rate of change. (See graph on Page 7.) 4. An alarm will sound. Start the reactin by depressing the sample container "plunger". Toggle the "Continue" button. The reaction begins and you now enter the Post-Period of the process. 5. After the temperature's rate of change has again stabilized, the system will report the temperature change T c as well as the initial temperature T i. Calibration 1. Perform a calibration according to the manufacturer's instructions; Appendix, Page 22. Sample Runs 2. Pulverize and Dry ~1.5g of high grade KNO 3. 3. Measure out 6 samples of ~0.2g each into pre-tared weighing bottles. 4. Weigh the empty, dry Dewar flask. Fill the flask with ~100 ml of Room Temperature DI Water. 5. Follow the directions for performing a run. Prior to each run, weight the contents of the Dewar flask. Prepare the sample dish with one of the weighed KNO 3 samples. Perform the run.
P a g e 12 Note the initial temperature T i and T c for the run. Do not replace the solution in the calorimeter after each run. The next run will simply increase the concentration of the previous system by adding more KNO 3 to the previous solution. 6. Disassemble and clean the calorimeter components when finished will all reactions.
P a g e 13 Data Analysis 1. Perform the appropriate calibration calculations to determine QE and the calorimeter's Energy Equivalent "e". (See Appendix, Page 22.) 2. For each calorimeter run, determine the total number of moles of KNO 3 and Water present at the start of the run. (With the exception of the first run, the amount of solute and solvent will have to be corrected for the loss of material when the calorimeter is disassembled at the end of the previous run.) Also, determine the number of number of moles of solute to be added during the run. Then determine the final values of n 1, n 2 and m for the run. Finally, use T c and "e" to calculate Q P, rxn for each run. Note, "e" will have to be corrected for differences in amount of calorimetric fluid from run to run. To do this, first calculate e', the Energy Equivalent of the empty calorimeter, from the calibration data: e' = e calibration - m' calibration sp (Eq. 13) Here, m' is the mass of solution in the calorimeter, calorimetric fluid, before the reaction is initiated and sp is the specific heat of the fluid. For dilute solutions, we can take sp to be that of Water at the temperature T. Then, the Energy Equivalent for the calorimeter during a reaction run is determined according to: e run = e' + m' run sp (Eq. 14) 3. Calculate the molality m and IS for each solution. (When calculating IS for a given molality m, we need to apply Hess' Law.) Determine IS at 0.05m and 0.10m using an appropriate interpolation scheme. (A Lagrange Interpolation using 3 or 5 data points is recommended.) 4. Plot IS vs. molality. Be sure to include error bars Fit the resulting curve to an appropriate polynomial using a Least Squares algorithm. 5. Determine DS at 0.05m and 0.10m. 6. Determine D from 0.05m to 0.10m. 7. Compare your results with those of the literature. Recall that the Enthalpy of Formation of a solute,, is defined as the Enthaply of Formation of the solution formed from the solvent and the elements of the solute: Solvent + Elements of Solute Solution For our case, we have:
P a g e 14 n 1 H 2 O(l) + K(s) + N 2 (g) + O 2 (g) KNO 3 (ai) By Hess' Law, this is equivalent to the sum of the following two reactions: K(s) + N 2 (g) + O 2 (g) KNO 3 (cr) KNO 3 (cr) + n 1 H 2 O(l) KNO 3 (ai) This allows us to wrtie: IS = f, KNO3(ai) - f, KNO3(cr)
P a g e 15 References Parr Instruments "6755 Solution Calorimeter Operating Instruction Manual for Models Produced after 2010" University of Wisconsin-Madison "Chem 563 Expt 4: Heat of Solution" Wagman, D.D., Evans, W.H., Parker, V.B., Schumm, R.H., Halow, I., Bailey, S.M., Churney, K.L., and Nuttall, R.L. "NBS Tables of Chemical Thermodynamic Properties. 1982 Supplement No. 2" J. Phys. Chem. Ref. Data 11 (1982).
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