.4. Determination of the enthaly of solution of anhydrous and hydrous sodium acetate by anisothermal calorimeter, and the enthaly of melting of ice by isothermal heat flow calorimeter Theoretical background Imortant concets The law of energy conservation, extensive and intensive quantities, thermodynamic state functions, heat, work, internal energy, enthaly, constant volume heat caacity, constant ressure heat caacity, secific heat caacity, molar heat caacity, reaction enthaly, Hess s law, anisothermal calorimeter, adiabatic calorimeter, constant ressure calorimeter, reaction extent. Calorimetry The aim of calorimetry is the measurement of the heat of hysical or chemical rocesses. Based on the measured heat we can determine reaction heat, heat of dissolution, heat of hydratation, heat caacity. The equiment in which we can measure the heat is called calorimeter. Basic tyes of calorimeters Based on the heat exchange between the system investigated and the surroundings and the measured quantity connected to the heat we searate four basic tyes of calorimeters: - the isothermal calorimeter - the anisothermal calorimeter - the adiabatic calorimeter - the heat flux calorimeter. The isothermal calorimeter In the isothermal calorimeters the temerature is constant during the exeriment. The anisothermal calorimeter In the anisothermal calorimeters there is some heat exchange between the system and the surroundings, but we try to minimize it. The measured quantity is the temerature which changes during the exeriment. A constant volume (bomb) calorimeter is closed when it oerates; therefore it is alicable to determine internal energy change. The internal ressure of bomb calorimeter in most of the exeriments (combustion reactions) increases, but there is no V work done by the system. A constant ressure (oen) calorimeter is oen when it oerates, therefore it is alicable to determine enthaly change. We use in this lab a constant ressure anisothermal calorimeter to determine salt hydratation enthaly. The adiabatic calorimeter The extreme case of the anisothermal calorimeter when there is no heat exchange is the adiabatic calorimeter. The heat flux calorimeter In the heat flux calorimeters there is some heat exchange between the system and an isothermal heat reservoir, and we measure its amount. The temerature of the system only temorary changes during the exeriment. The oerating model of a heat flow calorimeter is shown in Figure. A big thermostat or large amount of liquid with large heat caacity serves as isothermal heat reservoir. The exerimental set u consists of two identical doublejacketed glass vessels, one for the reaction and one for the reference. Resistors or diodes can be alied connected via an electrical bridge as heat flow sensors. The differential reaction calorimeter is very similar to the classical heat flux calorimeter, but the reaction vessel is stirred during the exeriment.
Figure Oerating scheme of an isothermal heat flow calorimeter Task I.) Measurement of salt hydratation enthaly in an anisothermal calorimeter Objective The determination of the reaction enthaly of this rocess: CH 3COONa(s) + 3 H O CH 3COONa 3 H O (s) P0 We will determine this value by measuring the enthalies of solution for anhydrous sodium acetate and for sodium acetate trihydrate. Alication of Hess s Law will give us the r H for the hydration reaction. CH 3COONa(s) excess H O CH 3COO (aq) + Na + (aq) P CH 3COONa 3 H O (s) excess H O CH 3COO (aq) + Na + (aq) + 3 H O P The solution of the anhydrous salt, rocess P roduces r H solution for the anhydrous salt, and the solution of the trihydrate, rocess P involves r H solution for the sodium acetate trihydrate. Alication of Hess s Law means the subtraction of rocesses P P, CH 3COONa(s) - CH 3COONa 3 H O (s) = - 3 H O rearranging we get CH 3COONa(s) + 3 H O CH 3COONa 3 H O (s) which rocess is identical to P0, the rocess for which enthaly is to determine. Therefore the measured reaction enthaly difference for P and P is given as Theoretical background H = H H r hidr r r Enthaly is a function of temerature, ressure and amount of material: H(T,,n). As we treat an isolated system, we omit the deendence on n the artial derivatives are given
H H dh = dt + d T T At constant ressure, d = 0 H dh = dt 3 T H where = C is the heat caacity at constant ressure. The enthaly change for rocesses, e.g. heat of T combustion, heat of boiling or fusion etc., can be determined by taking the integral of function in Equation 3 between states and, H = dh 4 which is easy to integrate, if C is not a function of T in the interval T and T : H = C dt = C T 5 Under constant ressure conditions the heat is equal to the enthaly change: q H = 6 Theoretically, the heat caacity can be given C i C 7 = i as the sum of the heat caacities of all arts of the calorimeter. In calorimetry, it is customary to searate the heat caacity of calorimeter liquid (e.g. water) from the heat caacity of other heat absorbing comonents: water j C = C + C 8 The heat caacity of water can be exressed by water j water water c, the secific heat (4.85 J g - K - ) and m water, the mass of water. water other C = c m + C 9 The reaction mixture is often a dilute aqueous solution, so the secific heat of the solution can be taken equal to that of water. Calibration In ractice, C is tyically determined by exeriment (this rocedure is called calibration). A recisely measurable amount of heat can be generated by electric heater, this heat causes a temerature increase of the calorimeter. From the thermally insulated vessel only a very small amount of heat can leak, therefore the temerature difference measured is roortional to the heat caacity of calorimeter. The small heat loss can be taken into account by grahical method from the temerature vs. time function (in details see later in Figure 3) recorded during the heat transfer rocess. The heat caacity can be calculated easily: q C = electric 0 T The temerature difference in the calibration, T is the difference between the temerature before and after the electric heating (T and T ): T = T T 3
The heat roduced by the electric heater is equal to work done by the current flowing through the resistance for time, t: U qelectric = t R where U is the voltage alied (given in Volts), R is the resistance of the heater (given in Ohms). If we use t in seconds the unit of q will be J. When heat is generated or released in the system the temerature of the calorimeter will increase since there is ractically no heat loss to the surroundings. The heat releasing rocess is called exothermic, and a negative sign is assigned to the heat of the rocess based on the system based sign convention. This leads to the following exression: q = C T 3 Please note that this is not in contradiction with the section above about the electric heat, because the sign of q electric is ositive in the oint of view of the calorimeter (we use this way), but it is negative in the oint of view of the electric heater. Determination of the heat of dissolution Carrying out the solution rocess some sodium acetate salt we observe T, which is the difference between the temerature before and after the dissolution (T 3 and T 4 ): T = T 4 4 T3 The sign of this difference is ositive for exothermic rocess, but it is negative when endothermic rocess takes lace in the calorimeter. The reaction enthaly ( r H) is an intensive variable, which can be calculated from the extensive enthaly change ( H): H r H = 5 ξ The extent of reaction, ξ for the i th comonent: n i n0, i ξ = 6 ν The reaction extent is indeendent of reacting comonents and given in moles. In our case the dissolution rocess goes to a comletion, therefore ξ = nsalt and H = 7 r H n salt i The enthaly of dissolution slightly deends on the final concentration of the solution. This may lead error in the determined enthaly of hydration. We can decrease this error if kee the final concentration of the solution the same for all exeriments. Exerimental rocedure Students will carry out two exeriments, one with anhydrous sodium acetate and another with sodium acetate trihydrate. The rocedure of the two exeriments are very similar. Each exeriment contains two arts: calibration and dissolvation of one salt. The temerature distribution in the calorimeter liquid should be even, which is maintained by mixing it with a magnetic stir-bar. The temerature in samled regularly by a comuter data acquisition system. 4
Assembling the aaratus You will assemble a constant ressure adiabatic calorimeter like that of in Figure. Figure A constant ressure (oen) calorimeter with heat insulating walls.. Dry the samle tube and fit a cork to the bottom of the tube. Hold the tube with closed end downward, and immerse it into molten araffin. Therefore the tube is isolated from getting calorimeter liquid into it.. Using graduated cylinder, measure out some 400 ml of distilled water and our it into the dry Dewar vessel. Use the same graduated cylinder for both exeriments. Place into the Dewar vessel: the electric heater, the stir-bar and the thermometer. Start mixing the liquid. Do not interrut mixing during the exeriment. From time to time take a glance on the stirrer. Note: Always hold the heater in vertical osition; do not turn it uside down. Therefore you avoid oil leaking from it. 3.a In the first exeriment lace samle tube on the balance and tare the balance, than measure into the samle tube 4 5 g of anhydrous sodium acetate by four digit recision. Record the mass of anhydrous sodium acetate. 3.b In the second exeriment lace samle tube on the balance and tare the balance, than measure into samle tube from sodium acetate trihydrate exactly.659 times the mass of anhydrous sodium acetate by four digit recision. Record the mass of sodium acetate trihydrate. (.659 is the ratio of the molar masses: 36.09 g mol / 8.03 g mol =.659) 4. Place the samle tube in the calorimeter. Please do not ut the glass rod in the samle tube! Determination of the heat caacity of the calorimeter and the heat released/absorbed by the salt dissolution rocess 5. Start the data acquisition. The comuter system automatically collects the temerature regularly. 6. Stage (observation): Observe temeratures for 5 minutes. These values will be used for the determination of the initial temerature. 7. Stage (heating): Turn on the heater for the time given by your instructor. Record the outut voltage of ower suly, electric resistance of your heater and the recise time interval of heating. 8. Stage 3 (observation): Let the comuter collect the temerature values for 5 minutes after the values become almost constant. These values will be used for the determination of the final temerature of the calibration and the initial temerature of the salt dissolution.
9. Stage 4 (salt dissolvation): Push the cork by a glass rod and hel dissolving all the salt by mixing vigorously the solution with glass rod for half a minute. 0. Stage 5 (observation): Let the comuter collect the temerature values for 5 minutes after the values become almost constant. These values will be used for the determination of the final temerature of the salt dissolution. Reset the starting circumstances of the exeriment and reeat rocedure with sodium acetate trihydrate! Stes of calculation. Plot two T vs. t functions like Figure 3 on an ORIGIN grah. One for anhydrous sodium acetate and another one for sodium acetate trihydrate. From the three aroximately horizontal sections of the grah determine T, T, T 3, T 4. In most of the cases T, and T 3 will be identical. Calculate the adequate T and T values. If the initial temerature and the final temeratures are not constant in time fit line to these arts of the curves. Set erendicular to the horizontal axis at the middle of the temerature change (half-wave). The difference of the intercets of this line with the fitted initial and final lines gives the temerature differences.. Calculate the electric work and C searately for the first and second run. Use Equations and 0. Figure 3 Tracking the temerature of calorimeter in time. 3. Test the goodness of the first art of your exeriment. Use Equation 9. for the calculation of C other, which should be ositive, but not too large. other water If C = C c mwater 0 for one or both exeriments consult your instructor what to do! other If C is ositive calculate the average of the C values for the two runs and use this average in the following calculations. 4. Determine the enthaly changes using equation 5 for both salt dissolution. Using these values calculate the enthalies of dissolution ( rh and r H ) using equation 7. Handle the sign of the T and r H values carefully! 5. Finally, calculate r H hidr in kj mol - units alying equation. 6
Task II.) Measurement of the secific enthaly of melting of ice in heat flow calorimeters Objective Determination of the secific entalhy of melting of ice. Theoretical background The enthaly flown between the reaction vessel and the isothermal heat reservoir is roortional to the time integral of the temerature difference due to the Newton s cooling law: dt = k( T Tr ) 8 dt T r is the constant temerature of the reservoir, factor k is called cooling constant. If we assume, that the ressure is constant and the heat caacity of the system does not change the equation can be converted: d T = k( T T ) t 9 C r d ( T T ) dt dt = C k 0 r ( T T ) r H = C dt = C k dt Therefore, if we want to determine the enthaly change we have to determine the roortionality factor and integrate the temerature difference over time. If we can measure not the temerature directly, just some roortional quantity then the calibration constant will be different, but our considerations remain valid. In our instruments we measure voltage roortional to the temerature difference by thermocoules or diode temerature sensors. The roortionality factor can be determined by exeriment, similar to the anisothermal calorimeter. We use an electric heater for the calibration. Please note, that there is no need to determine the heat caacity of the calorimeter on the contrary to the anisothermal calorimetry. The calibration constant of the calorimeter (in terms of energy er unit area) is defined as: ε = q electric / A heating where A heating is the integration area of the heating imulse. The heat of a rocess can be calculated using this calibration constant and the integration area of the rocess: q = ε 3 A rocess In case of the melting of ice the absorbed heat is used by two rocesses: the hase transition and the heating of the 0 C water to the temerature of the heat reservoir: q = q melting + q heating 4 The enthaly of the hase transition can be exressed by the roduct of the secific meting enthaly and the mass of ice: q = H m 5 melting melting ice The enthaly for the heating can be calculated using the secific heat caacity of water, the mass of ice and the temerature increase from the melting oint of water (0 C) to the temerature of the heat reservoir: q c m T heating = water ice 6 In differential calorimeter, in general, the absolute temerature of the system is not needed for the calculations, but here, due to this second rocess we have to know it. 7
Exerimental rocedure In the laboratory ractice we have two differential calorimeters: a classical heat flow calorimeter and a differential reaction calorimeter. Please consult your instructor which one will be used today! The general rocedure. Switch on the circulation of the heat reservoir (switch I.). Fill the reaction and reference vessels with the given amount of distilled water. 3. Switch on the data recording system (switch II.) 4. After 5 minutes rest eriod (while the thermal equilibrium of the system is established) oen the data recording software. The registration of the actual arameters in the annotation lines of the ASCII data set can be done after the data recording, ractically using Wordad. 5. Run the data acquisition for 0-5 minutes for the baseline. 6. Suly some electric ower to calibrate the system. Ask your instructor for the time of heating! 7. Wait 30-35 minutes after the heating, then add some dry ice to the reaction vessel (follow the oral instructions). Simultaneously, read the temerature on the thermometer in the reference vessel. 8. After the addition of ice we continue the data recording for 5-30 minutes. Stes of the data evaluation In our heat flux calorimeters the heat sensors give otential difference which is roortional to the temerature difference between the reaction- and reference vessel. In Figure 4, it can be seen the first wave being due to the calibrating heat energy transfer. Figure 4 Potential difference of the thermocoule versus time chart in a heat flux calorimeter The outut voltage time function of the sensor have to be integrated from the beginning of the heating eriod to the time of settling of the signal to the baseline. Calculate the electric energy using equation. Determine the calibration constant of the calorimeter (ε) using equation. Integrate the outut voltage time function of the sensor for the melting of ice and calculate the heat using equation 3. Be aware of the minus sign of this area! Calculate melting H from equations 4-6. Results to be reorted Mass of ice in grams, secific enthaly of melting in J g - ( exressed by 3-4 recision number) 8