University:
Massachusetts Institute of Technology
Course:
3.091SC | Introduction to Solid State Chemistry
Academic year:

2022
Views:

190

Pages:

6
Author:

grimering0qp

Session #34: Homework Solutions Problem #1 For the binary system Cu-Ni the following data are available from cooling experiments: T(°C) melt composition (atomic % Ni) composition of solid first formed on cooling (atomic % Ni) 1100 1180 1260 1340 1410 3 20 40 60 80 10 37 57 73 87 (a) From these data and information provided in the Periodic Table, construct the phase diagram (T vs c). (b) At each of the following (T, c) coordinates, i.e., combinations of temperature and composition, what are the phases present and what are their respective compositions? T(°C) composition (atomic % Ni) 1120 1200 1300 15 55 60 Solution (b) T (°C) composition (atomic % Ni) Phase composition (atomic % Ni) 1120 15 solid liquid 17 07 1200 55 solid 55 1300 60 solid liquid 68 45 Problem #2 Draw schematic phase diagrams for binary systems with (a) complete liquid and solid solubility, (b) complete liquid but zero solid solubility, and (c) complete liquid and limited solid solubility. (In your sketches label phase fields and give characteristic temperatures.) Solution (a) (b) (c) Problem #3 The Cs-K phase diagram is given on the next page. Refer to it in answering the following questions. (a) For a sample of composition 20 at. % Cs and 80 wt. % K held at 10°C, determine (i) the composition of the solid phase present at equilibrium (ii) the composition of the liquid phase present at equilibrium (iii) the relative amounts of solid and liquid phases present at equilibrium (b) For a sample of composition 50 at % Cs and 50 at % K held at -37.5°C, (i) what phases are present at equilibrium? (ii) what is the composition of each phase? © source unknown. All rights reserved. Solution (a) (i) 11 at % Cs which we shall designate C *solid * (ii) 23 at % which we shall designate Cliquid (iii) solid fraction = * Cliquid −C * Cliquid − C *solid = 23 − 20 = 0.25 23 − 11 (b) (i) one liquid phase and one solid phase (ii) both phases are identical in composition: 50 at % Cs – 50 at % K Problem #4 (a) At each of the following coordinates on the binary phase diagram of NaCl – H2O (see next page) at 1 atmosphere pressure, (i) identify the stable phases, (ii) give their compositions, and (iii) calculate their relative proportions: (1) 10% NaCl, 0oC (2) 10% NaCl, -10oC (3) 10% NaCl, -25oC (b) For a solution of 23.3% NaCl in H2O at –21°C, (i) identify the stable phases present, and (ii) give the composition of each phase Solution (a) (1) (i) brine -- all liquid (ii) 10% NaCL in H2O (iii) 100% liquid (2) (i) solid ice (H2O) + liquid brine (ii) solid – pure H2O liquid ≅ 15% NaCl in liquid H2O (iii) use lever rule: bc % ice = x100 ≅ 30% ac % brine = ab x100 ≅ 70% ac (3) (i) pure ice (H2O) + pure salt (ii) ice phase = 100% H2O; salt phase = 100% NaCl (iii) 10% NaCl; 90% H2O (b) (i) brine (liquid) + 2 solids: NaCl (s) + H2O (s) (ii) 23.3% NaCl in water Pure NaCl (solid) Pure H2O (solid)