EEN-E1030, Thermodynamics in Energy Technology, Fall 2016 Calculation problems 6

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Jorma Härkönen
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1 EENE00, Therdynaics in Energy Technlgy, Fall 06 Calculatin rbles 6 TETÄVÄ ON TÄTITETÄVÄ PROBLEM IS TE STAR PROBLEM Tehtävä ei le kurssin keskeistä sisältöä. Prble is nt the essential curse cntent. TETÄVÄ. Liuksen aktiivisuus vidaan jskus arviida ittaaalla liuksen kiehuisisteen nusu. Tällöin höyrynaine höyryfaasissa idetään vakina ja läötilaittauksen avulla itataan liuksen/höyryn läötila. Kuvassa n esitetty vesirukasulaliukselle (NaCl) itattu kiehuisisteen nusu liuksen kuivaaineitisuuden funktina, kun aine n 0,5 bar. Mikä n liuksen aktiivisuuskerrin go kuivaaieitisuudessa 5 %? 6 Kiehuisisteen nusu, C Kuivaaineitisuus, kg/kg Kuva. Vesirukasulaliuksen kiehuisisteen nusu kuivaaineitisuuden funktina, 500 bar. PROBLEM. The activity f a slutin can be seties ariated by easuring the biling int elevatin f the slutin. In this case, the ressure in the var hase is ket cnstant and the teerature change f the slutin/var is easured. Figure shws the eerientally easured biling int elevatin fr waternacl slutin as a functin f dry slid cntent. The ressure in the var hase has been 0.5bar in the easureent. What is the activity cefficient go at the dry slid cntent f 5%?

2 6 Biling inti elevatin, C Dry slid cntent, kg/kg Figure. Biling int elevatin f waternacl slutin as a functin f dry slid cntent, 500bar. SOLUTION In this case, water is the slvent and NaCl is the slute. In a slutin, NaCl disslves int Na and Cl ins. This eans that the le aunt f NaCl ust be ultilied with tw when it is in the slutin. Varizatin teerature f ure water at 0.5 bar is 8 C 54K On the basis f Fig. the biling int elevatin is c. C when the dry slid cntent is 5% > Tslutin 84 C. The var ressure f ure water at 84 C is k* 0.56 bar (tabulated value) The activity a k(84 C) /k*(84 C) 0.5/ O 0.85 M O The le fractin f water in the slutin is 0.08 O O NaCl M M a 0.89 a γ O O > γ O O The activity cefficient a», which eans that the ideal slutin del ariates the behavir f the slutin very well. O NaCl

3 *TETÄVÄ. Tyen liukeneisreaktin N(g) fin reaktientalia standarditilassa (T 98,5K, N(g) bar, N l/kg) n D (T) 0.4kJ/l ja reaktientria sain standarditilassa n DS (T) 96.4 J/l. a) Laske liukeneisreaktiiden tasaainvakit läötilassa 5 C. b) Laske tään erusteella tyen liukisuus ilasta 5 C:seen veteen yksiköissä l/kgvettä ja g/ vettä, kun liuenneet kaasut käsitellään ideaaliliusallin ukaan (aktiivisuuslaalisuus/) sekä kaasufaasi ideaalikaasun ukaan (aktiivisuus saaine/). c) Laske tyen liukisuus veteen läötilassa 40 C yksikössä g/ lettaalla, että reaktientalia läötilassa 40 C n saa kuin läötilassa 5 C. Vihje: hyödynnä laskussa yhtälöä, jka kert tasaainvakin riiuvuuden läötilasta. d) Kaasujen liukisuutta veteen vidaan yös äärittää enryn lain avulla. Laske tyen liukisuus veteen enryn lain avulla läötilassa 40 C. enryn lain vaki kyseisessä läötilassa n 000 bar. Ilita tuls yksikössä g/. *PROBLEM. When nitrgen disslves int water N (g) fi N, the reactin enthaly and entry at the standard state ( T 98.5 K, bar, l/kg ) are N (g) N Δ (T ) 0.4 kj/l and ΔS (T ) 96.4 J/lK, resectively. a) Calculate the equilibriu cefficient fr the reactin b) Use the equilibriu cefficient t define the slubility f nitrgen int water fr air at 5 C. Rert results in units l/kgwater and g/ water. Activity fr the disslved nitrgen beys the del f an ideal slutin (a lality/) and N in the air is treated as a n ideal gas. c) Calculate the slubility f N int water at 40 C in unit g/ water assuing that the reactin enthaly D (5 C) D (40 C). int: Use the equatin that describes hw the equilibriu cnstant deends n the teerature. d) Slubility f gases int liquids can als be ariated using the enry s law. Calculate the slubility f N int water at 40 C in unit g/ water using the enry s law. The enry s law cnstant fr N at 40 C is 000 bar TETÄVÄ. Jhda kaava hiilidiksidin liukeneisreaktin CO (g) O(l) fi tasaainvakille ja sita, että hiilidiksidin liukisuus veteen heikkenee itä haaaaa vesi n, eli itä alei n veden. Kuinka suuri n suhteellinen uuts hiilidiksidin liukisuudessa, kun veden alenee arvsta 8 arvn 7? Veden ääritellään seuraavasti: lg, issä n rtnien laalisuus ja l/kg. PROBLEM. a) Disslutin f CO int the water beys the fllwing reactin: CO (g) O(l) fi CO

4 Derive an equatin fr the equilibriu cefficient f the disslutin reactin and shw that the disslutin f CO reduces as the f water decreases. In ther wrds, the acidity f the water increases (lwer eans higher acidity). What is the relative change f the slubility f CO int the water when the reduces fr 8 t 7. The f water is defined as fllws: lg, where is the lality f rtns and l/kg SOLUTION At equilibriu, CO (g) O(l) CO () Cheical tentials fr the cnents in Eq. () are CO (g) O(l) CO O CO (T, ) RTln (T, ) (T, ) RTlnγ (T, ) RTlnγ (a) (b) (c) (d) where bar, CO le fractin f CO in the gas hase, g the activity cefficient f, g the activity cefficient f and l/kg. The standard state fr the slvent (water) is a ure slvent at the teerature f T and ressure f. The ressure des nt have t be bar. The activity f the ure slvent is ao > the cheical tential f water is the sae as the cheical tential f water at the standard state. Cheical tentials fr slutes ( and ) at the standard state are defined at the sae teerature and ressure as in the case f the slvent. The ressure des nt have t bebar. Fr the equilibriu cefficient ay be written RTlnK DG, () where D (aq ) G CO (g) O(l) This eans that K is cnstant at the given teerature and ressure. Using definitin fr activities the equilibriu cefficient ay be written as fllws:

5 a K a a γ γ a CO (g) O(l) CO () CO is a weak electrlyte > g g» > K CO (4) The lality f reresents the slubility f CO int water and it beces: CO K ( ) CO (5) The reresents the lality f ins in the slutin and is defined as fllws lg (6) Fr eale when 7 the lality f ins is 0 7 l/kg. When the decreases the aunt f ins increases in the slutin which results in decreasing lality f ins accrding t Eq. (5). The lality f ins fr 7 and 8 is 0 7 l/kg and 0 8 l/kg, resectively. The relative change fr ins can be calculated using Eq. (5). In Eq. (5), K, CO,, and reain cnstant > the relative change beces 7 relative change This eans that CO disslves int water nly 0% f the riginal aunt when the reduces fr 8 t 7.

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