05 Enthaly of hydraton of sodum acetate Theoretcal background Imortant concets The law of energy conservaton, extensve and ntensve quanttes, thermodynamc state functons, heat, work, nternal energy, enthaly, constant volume heat caacty, constant ressure heat caacty, secfc heat caacty, molar heat caacty, reacton enthaly, Hess s law, ansothermal calormeter, adabatc calormeter, constant ressure calormeter, reacton extent. Calormetry The am of calormetry s the measurement of the heat of hyscal or chemcal rocesses. Based on the measured heat we can determne reacton heat, heat of dssoluton, heat of hydrataton, heat caacty. The equment n whch we can measure the heat s called calormeter. Basc tyes of calormeters Based on the heat exchange between the system nvestgated and the surroundngs and the measured quantty connected to the heat we searate four basc tyes of calormeters: - the sothermal calormeter - the ansothermal calormeter - the adabatc calormeter - the heat flux calormeter. The sothermal calormeter In the sothermal calormeters the temerature s constant durng the exerment. The ansothermal calormeter In the ansothermal calormeters there s some heat exchange between the system and the surroundngs, but we try to mnmze t. The measured quantty s the temerature whch changes durng the exerment. A constant volume (bomb) calormeter s closed when t oerates; therefore t s alcable to determne nternal energy change. The nternal ressure of bomb calormeter n most of the exerments (combuston reactons) ncreases, but there s no V work done by the system. A constant ressure (oen) calormeter s oen when t oerates, therefore t s alcable to determne enthaly change. We use n ths lab a constant ressure ansothermal calormeter to determne salt hydrataton enthaly. The adabatc calormeter The extreme case of the ansothermal calormeter when there s no heat exchange s the adabatc calormeter. The heat flux calormeter In the heat flux calormeters there s some heat exchange between the system and an sothermal heat reservor, and we measure ts amount. The temerature of the system only temorary changes durng the exerment. Exermental task: Measurement of salt hydrataton enthaly n an ansothermal calormeter Objectve The determnaton of the reacton enthaly of ths rocess: CH 3COONa(s) + 3 H O CH 3COONa 3 H O (s) P0 30/0/05 hout05_05
We wll determne ths value by measurng the enthales of soluton for anhydrous sodum acetate and for sodum acetate trhydrate. Alcaton of Hess s Law wll gve us the rh for the hydraton reacton. 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 soluton of the anhydrous salt, rocess P roduces rh soluton for the anhydrous salt, and the soluton of the trhydrate, rocess P nvolves rh soluton for the sodum acetate trhydrate. Alcaton of Hess s Law means the subtracton of rocesses P P, CH 3COONa(s) - CH 3COONa 3 H O (s) = - 3 H O rearrangng we get CH 3COONa(s) + 3 H O CH 3COONa 3 H O (s) whch rocess s dentcal to P0, the rocess for whch enthaly s to determne. Therefore the measured reacton enthaly dfference for P and P s gven as Theoretcal background H = H H r hdr r r Enthaly s a functon of temerature, ressure and amount of materal: H(T,,n). As we treat an solated system, we omt the deendence on n the artal dervatves are gven H H dh = dt + d T T At constant ressure, d = 0 H dh = dt 3 T H where = C s the heat caacty at constant ressure. The enthaly change for rocesses, e.g. heat of T combuston, heat of bolng or fuson etc., can be determned by takng the ntegral of functon n Equaton 3 between states and, H = dh 4 whch s easy to ntegrate, f C s not a functon of T n the nterval T and T : H = C dt = C T 5 Under constant ressure condtons the heat s equal to the enthaly change: q = H 6 30/0/05 hout05_05
Theoretcally, the heat caacty can be gven C = C 7 as the sum of the heat caactes of all arts of the calormeter. In calormetry, t s customary to searate the heat caacty of calormeter lqud (e.g. ) from the heat caacty of other heat absorbng comonents: j C = C + C 8 The heat caacty of can be exressed by j c, the secfc heat (4.85 J g - K - ) and m, the mass of. other C = c m + C 9 The reacton mxture s often a dlute aqueous soluton, so the secfc heat of the soluton can be taken equal to that of. Calbraton In ractce, C s tycally determned by exerment (ths rocedure s called calbraton). A recsely measurable amount of heat can be generated by electrc heater, ths heat causes a temerature ncrease of the calormeter. From the thermally nsulated vessel only a very small amount of heat can leak, therefore the temerature dfference measured s roortonal to the heat caacty of calormeter. The small heat loss can be taken nto account by grahcal method from the temerature vs. tme functon (n detals see later n Fgure 3) recorded durng the heat transfer rocess. The heat caacty can be calculated easly: q C = electrc 0 T The temerature dfference n the calbraton, T s the dfference between the temerature before and after the electrc heatng (T and T ): T = T T The heat roduced by the electrc heater s equal to work done by the current flowng through the resstance for tme, t: U qelectrc = t R where U s the voltage aled (gven n Volts), R s the resstance of the heater (gven n Ohms). If we use t n seconds the unt of q wll be J. When heat s generated or released n the system the temerature of the calormeter wll ncrease snce there s ractcally no heat loss to the surroundngs. The heat releasng rocess s called exothermc, and a negatve sgn s assgned to the heat of the rocess based on the system based sgn conventon. Ths leads to the followng exresson: q = C T 3 Please note that ths s not n contradcton wth the secton above about the electrc heat, because the sgn of q electrc s ostve n the ont of vew of the calormeter (we use ths way), but t s negatve n the ont of vew of the electrc heater. Determnaton of the heat of dssoluton Carryng out the soluton rocess some sodum acetate salt we observe T, whch s the dfference between the temerature before and after the dssoluton (T 3 and T 4): T = T 4 4 T3 30/0/05 hout05_05 3
The sgn of ths dfference s ostve for exothermc rocess, but t s negatve when endothermc rocess takes lace n the calormeter. The reacton enthaly ( rh) s an ntensve varable, whch can be calculated from the extensve enthaly change ( H): H r H = 5 ξ The extent of reacton, ξ for the th comonent: n n0, ξ = 6 ν The reacton extent s ndeendent of reactng comonents and gven n moles. In our case the dssoluton rocess goes to a comleton, therefore ξ = nsalt and H rh = 7 n salt The enthaly of dssoluton slghtly deends on the fnal concentraton of the soluton. Ths may lead error n the determned enthaly of hydraton. We can decrease ths error f kee the fnal concentraton of the soluton the same for all exerments. Exermental rocedure Students wll carry out the exerments n two grous, one grou wth anhydrous sodum acetate, the other wth sodum acetate trhydrate. The rocedure of the two exerments are very smlar. Each exerment contans two arts: calbraton and dssolvaton of one salt. The temerature dstrbuton n the calormeter lqud should be even, whch s mantaned by mxng t wth a magnetc str-bar. The temerature n samled regularly by a comuter data acquston system. Assemblng the aaratus You wll assemble a constant ressure adabatc calormeter lke that of n Fgure. Fgure A constant ressure (oen) calormeter wth heat nsulatng walls.. Dry the samle tube and ft a cork to the bottom of the tube. Hold the tube wth closed end downward, and mmerse t nto molten araffn. Therefore the tube s solated from gettng calormeter lqud nto t. 30/0/05 hout05_05 4
. Usng graduated cylnder, measure out some 400 ml of dstlled and our t nto the dry Dewar vessel. Use the same graduated cylnder for both exerments. Place nto the Dewar vessel: the electrc heater, the str-bar and the thermometer. Start mxng the lqud. Do not nterrut mxng durng the exerment. From tme to tme take a glance on the strrer. Note: Always hold the heater n vertcal oston; do not turn t usde down. Therefore you avod ol leakng from t. 3.a In the frst grou lace samle tube on the balance and tare the balance, than measure nto the samle tube 4 5 g of anhydrous sodum acetate by four dgt recson. Record the mass of anhydrous sodum acetate. 3.b In the second grou lace samle tube on the balance and tare the balance, than measure nto samle tube from sodum acetate trhydrate exactly.659 tmes the mass of anhydrous sodum acetate by four dgt recson. Record the mass of sodum acetate trhydrate. (.659 s the rato of the molar masses: 36.09 g mol / 8.03 g mol =.659) 4. Place the samle tube n the calormeter. Please do not ut the glass rod n the samle tube! Determnaton of the heat caacty of the calormeter and the heat released/absorbed by the salt dssoluton rocess 5. Start the data acquston. The comuter system automatcally collects the temerature regularly. 6. Stage (observaton): Observe temeratures for 5 mnutes. These values wll be used for the determnaton of the ntal temerature. 7. Stage (heatng): Turn on the heater for the tme gven by your nstructor. Record the outut voltage of ower suly, electrc resstance of your heater and the recse tme nterval of heatng. 8. Stage 3 (observaton): Let the comuter collect the temerature values for 5 mnutes after the values become almost constant. These values wll be used for the determnaton of the fnal temerature of the calbraton and the ntal temerature of the salt dssoluton. 9. Stage 4 (salt dssolvaton): Push the cork by a glass rod and hel dssolvng all the salt by mxng vgorously the soluton wth glass rod for half a mnute. 0. Stage 5 (observaton): Let the comuter collect the temerature values for 5 mnutes after the values become almost constant. These values wll be used for the determnaton of the fnal temerature of the salt dssoluton. The measure data of the two grous wll be used mutually. Stes of calculaton. Plot two T vs. t functons lke Fgure 3 on an ORIGIN grah. One for anhydrous sodum acetate and another one for sodum acetate trhydrate. From the three aroxmately horzontal sectons of the grah determne T, T, T 3, T 4. In most of the cases T, and T 3 wll be dentcal. Calculate the adequate T and T values. If the ntal temerature and the fnal temeratures are not constant n tme ft lne to these arts of the curves. Set erendcular to the horzontal axs at the mddle of the temerature change (half-wave). The dfference of the ntercets of ths lne wth the ftted ntal and fnal lnes gves the temerature dfferences.. Calculate the electrc work and C searately for each exerment. Use Equatons and 0. 3. Test the goodness of the frst art of your exerment. Use Equaton 9. for the calculaton of C other, whch should be ostve, but not too large. other If C = C c m 0 consult your nstructor what to do! If other C s ostve use ths value n the calculatons of the corresondng exerment. 30/0/05 hout05_05 5
Fgure 3 Trackng the temerature of calormeter n tme. 4. Determne the enthaly changes usng equaton 5 for both salt dssoluton. Usng these values calculate the enthales of dssoluton ( r H and r H ) usng equaton 7. Handle the sgn of the T and r H values carefully! 5. Fnally, calculate r H hdr n kj mol - unts alyng equaton. Samle questons and answers for the entrance quz. These questons are devoted for ractcng and rearng to labs at home. Please note that these are samles only and the queston of the entrance quz are not restrcted to these ones! MLT Q and A Q. What are the extensve and ntensve roertes? A. An ntensve roerty (also called a bulk roerty) of a system that does not deend on the sze of the system or the amount of materal n the system. By contrast, an extensve roerty of a system does deend on the system sze or the amount of materal n the system. Q. How would you aly Hess s law to hydraton reacton of sodum acetate? A. The reacton enthaly of hydraton reacton, CH 3COONa(s) + 3 H O CH 3COONa 3 H O (s) cannot be determned by calormetry. However, the enthaly of two comonent soluton rocesses can be measured n a calormeter. Takng the dfference of these two soluton rocesses CH 3COONa(s) excess H O CH 3COO (aq) + Na + (aq) rh CH 3COONa 3 H O (s) excess H O CH 3COO (aq) + Na + (aq) + 3 H O rh we obtan the hydraton rocess tself, CH 3COONa(s) - CH 3COONa 3 H O (s) - 3 H O whch rearranges 30/0/05 hout05_05 6
CH 3COONa(s) + 3 H O CH 3COONa 3 H O (s) rh3 and for reacton enthales we get: rh3 = rh rh. We used u the state functon roerty of enthaly. Q3. Why do we use strbar and double walled nsulator tube n calormeter? A3. To mantan the condton of even dstrbuton of temerature and concentraton throughout the vessel. Insulator walls revent heat transfer to laboratory. Q4. What s the dfference between enthaly and reacton enthaly? A4. Enthaly s a state functon but an extensve varable, whle reacton enthaly s also a state functon but an ntensve varable whch s ndeendent of the extenson of the system. Q5. Why do we use electrc heater for the determnaton of heat caacty of calormeter? A5. We roduce a certan amount of heat whch s absorbed by the calormeter lqud. The extent of heat can recsely adjusted by changng arameters R, t or U, hrased n equaton U qsurr = C T = t. R Q6. What s the reason for determnng heat caacty of heat absorbng arts? A6. All the arts of the calormeter (glass endng of thermometer, nternal wall of Dewar-flask etc.) excet the calormeter lqud belong to ths grou, and each of the dfferent materals has ts own secfc heat caacty. They wll absorb sgnfcant amount of heat when heat s evolved n the calormeter. Wthout takng the heat absorbng arts nto account, the calculated enthaly would contan substantal error. Q6. How long an electrc heater have to be oerated, when the temerature of calormeter should be ncreased by. C? The resstance of the heater R = 4 Ω, ts oeratng voltage U = 8 V. The calormeter contans 600 g of, the sum of heat caactes of heat absorbng arts s 00 J K -. The secfc heat caacty of : 4,8 J g - K -. A6. Calculate frst the heat caacty of calormeter, C k. C k = Cv + Cm = 600g 4,8 Jg K + 00 JK = 608JK The heat suled for the, o C ncrease q = Ck T = 608 JK. C = 5737,6 J The work done by electrc heater: U R w 4Ω 5737,6 J q = w = t t = = = 45s R U 8V Q7. What are the man stes of one exerment n an ansothermal calormeter? A7.. Preare the samlng tube, measure the gven amount of salt n.. Assemble the calormeter. 3. Start the data acquston. 4. Observe temeratures for 5 mnutes. 5. Calbrate by heatng. 6. Observe temeratures for 5 mnutes agan. 7. Dssolve the salt. 8. Observe temeratures for 5 mnutes agan. 30/0/05 hout05_05 7