BG2142 mework-43 Word GE LAYOUT REFERENCES MAILINGS REVIEW A AT Aa. A- T TNormal
ID: 812221 • Letter: B
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BG2142 mework-43 Word GE LAYOUT REFERENCES MAILINGS REVIEW A AT Aa. A- T TNormal T No space. Heading 1 Heading 2 Font Paragraph Styles One mole of H2O is supercooled to -2.25 oC at 1 bar pressure. The freezing temperature of water at this pressure is 0.00 oC. The transformation H20 ()-H2O (s) is suddenly observed to occur. By calculating AS, AS AStatal, verify that this transformation is spontaneous at -2.25 oC.The heat capacities are given by CpdH.o(l) 75.3 J K i mol 1 and Cp(H200s 37.7 J K-1 mol 1, and AH 6.008 kJ molti at 0.00 oC. Assume that the surroundings are at -2.25 oC. [Hint: consider the two pathways at 1 bar: (a) H2O(l, -2.25 oC) H20(s.-2.25 oC) and (b) H2O(l, -2.25 oC) H2O(s,0.00oC) H2O(s, 2.25 oC). Because S is a state function, AS must be the same for both pathways l NITED STATES)Explanation / Answer
The two pathways are:
H2O(l, -2.25C) -----> H2O(l, 0C) ---------------- (1)
H2O(s, 0C) --------> H2O(s, -2.25C) --------------(2)
deltaS for (1) = nCp(l)ln(270.90/273.15) = 75.3*1*(-8.27x10-3) = -0.623 J/K
delta S for the transformation of liquiq to solid = deltaHfusion/T = -6008/273.15 = -22.00 J/K
deltaS for (2) = nCp(s)ln(273.15/270.90) = 0.312 J
Therefore, deltaS = -22.311 J/K
deltaSsurr = -qrxn/T = -{(75.3*2.25) - 6008 + (37.7*-2.25)}/270.90 = 5923.4 J/K
deltaStotal = deltaS + deltaSsurr = 5900.089 J/K or 5.9 kJ/K which is >0. Therefore, this reaction is spontaneous.
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