2022-330-EIII+ans

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The City College of New York, CUNY *

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330

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Chemistry

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Jan 9, 2024

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docx

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Chemistry 33000 Physical Chemistry I: Thermodynamics Fall, 2022 CUNYFirst Class 23729 WITH ANSWERS Section L-25-LEC Regular Exam III: Thermodynmics (T.D.) of Phase Equilibria and Liquid-Liquid Solutions The attached exam consists of five questions, most of which include several independent parts that require verbal explanations and/or numerical calculations. The parts within a problem can often be answered most readily in the sequence they are asked, but if you miss one section it is usually possible to complete the next . Try to budget your time according to the number of points allotted to each question ; expect a class average of ~60 and a curve to estimate the corresponding letter grades. Please write legibly ON THE EXAM SHEET and with sufficient coherence that I may infer your reasoning in those instances where your numerical result is incorrect. Note any assumptions or approximations that you make. If you need to clarify how to interpret a question, ask me! Before you begin to sweat and scribble, write your name on the exam booklet. Hand in the exam questions with your responses and your formula sheet when you have completed your work. Here are some physical constants and relationships that you may find useful. Good luck! R = 8.31 J-mol -1 -K -1 = 0.082 L-atm-mol -1 -K -1 = 0.083 L-bar-mol -1 -K -1 = 1.99 cal-mol -1 -K -1 J = (Pa - m 3 ) / (mol - K) J = (kg-m 2 )/s 2 1 J = 1 N-m g = 9.8 m/s 2 Standard Temperature & Pressure (STP) = 273 K, 1 atm for gases STP (º) = 298 K, 1 bar for chemical formation reactions and phase changes 1 atm = 760 torr = 1 x 10 5 Pa 1 bar 100 cm = 10 dm = 1 m T (K) = t ( 0 C) + 273 1 calorie = 4.18 J U = q + w dU = TdS - pdV dG = -SdT +Vdp dX = 0 for any state function X C p - C v = nR for ideal gases K f for water = 1.86 K-kg-mol -1 dq P = nC P dT dq V = n C V dT K f for naphthalene = 6.94 K-kg-mol -1 Atomic masses: H=1; C=12; O=16; Na=23; Cl=35; Ca=40 2022-EIII-ans 11/27/2022
2022-EIII-ans 12/12/2023 2
This page has been intentionally left blank. Be encouraged to tear off the cover page and refer to it as you work the problems. Also be encouraged to use this page as scratch paper. 1. 2022-EIII-ans 12/12/2023 3
Pure Substances: Phase Diagrams for Compact T.D. Information (29 points, 4 parts) Plots of pressure vs. temperature, pressure vs. composition, and temperature vs. composition provide a compact but information-rich picture of the phases and chemical mixtures that are present under laboratory conditions of interest. Consider the following data for oxygen (O 2 ), which is familiar to us as a life-supporting gas but can also be present in liquid or solid phases under appropriate circumstances. Consider the following properties: a: triple point: 54.3 K, 1.14 torr b: critical point: 154.6 K and 37,828 torr c: normal melting point: 54.8 K, 760 torr d: normal boiling point: 90.3 K, 760 torr a: triple point: 54.3 K, ln p = ln (1.14 torr) = 0.13 torr b: critical point: 154.6 K, ln p = ln (37,828 torr) = 10.5 torr c: normal melting point: 54.8 K, ln p = ln (760) = 6.6 torr d: normal boiling point: 90.3 K, ln p = ln (760) = 6.6 torr (or mark directly on the diagram) (3 pts) 1b. If ln p = 7.6 torr and T = 60 K, which phase(s) are present ? Explain and mark the phase diagram. e: liquid only in this region (9 pts) 1c. Consider how pressure depends on temperature for liquid and gas phases of O 2 that are in equilibrium with one another. First, answer this question qualitatively by quoting a relationship that describes this dependence and explaining why it has a positive or negative value. Then, make a quantitative estimate by using the given data for points a-d on the O 2 phase diagram. Do a numerical calculation and explain briefly . Qualitatively , dp/dT is positive since S and V are each positive. S is positive since the liquid-gas conversion goes toward a state of greater disorder. V is positive since gases spread out to occupy a larger molar volume than liquids (or solids). Quantitatively , use the data to calculate dp/dT: p ( d ) p ( a ) T ( d ) T ( a ) = ( 760 1.14 ) ( 90.3 54.3 ) = 758.86 36 = + 21.08 Alternatively, use the data to calculate p ( b ) p ( d ) T ( b ) T ( d ) or p ( b ) p ( a ) T ( b ) T ( a ) , also > 0 2022-EIII-ans 12/12/2023 (12 pts) 1a. These data are sufficient to construct the phase diagram shown on the right. (Note: the y-axis shows ln p in order to accommodate the large range of values that are relevant for the three phases of diatomic oxygen.) Use the data to put a, b, c, and d labels on the marked locations of the diagram, including the numerical values that support your choices. 4
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