The Gibbs energy of mixing of a regular solution of components A and B isgiven by Greal = nRT (x Inx +x Inx +ẞXX), where X and X aremixABBABthe mole fractions of the two components and ẞ is a dimensionlessparameter quantifying deviations from ideal behaviour in terms of therelative strength of A-B interactions compared to A-A and B-B interactions.(i) Use a spreadsheet to calculate A Greal/nRT for XA = 0.01, 0.125,mix0.25, 0.5, 0.75, 0.875 and 0.99 for ẞ= 0, 1 and 3. Report yourcalculations in a table and, using a labelled plot, determine thenumbers of minima in A Greal/nRT as a function of compositionand ẞ.mix[3(ii)For each value of ẞ, predict the number of liquid phases which youwould expect for the mixture. Justify your answer in terms of A-Binteractions.[

(i) Step 1: Setting up the SpreadsheetOpen a Spreadsheet Program: Open your preferred spreadsheet…

Answered: The Gibbs energy of mixing of a regular…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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b) Suppose you had a solution of 6.84 g of sugar (sucrose, C12HO1) in 90.0 g of water. (i) Calculate the number of moles of sugar and water present. (H=1; C=12; 0=16) (ii) Calculate the mole fraction of the water in the solution. (iii) At 100°C, the saturated vapour pressure of water at its boiling point is 101325 Pa. Calculate the vapour pressure of the solution at that temperature. (Remember to give your answer to a suitable number of significant figures.) (iv) Would the solution of sugar in water boil at this temperature, assuming the external pressure remains at 101325 Pa? Explain your answer.
Phenol and water form non-ideal liquid mixtures. When 7.32 g of phenol and 7.95 g of water are mixed together at 60 °C they form two immiscible liquid phases with mole fractions of phenol of 0.042 and 0.161. (i) Calculate the overall mole fraction of phenol in the mixture. (ii) Use the lever rule to determine the relative amounts of the two phases.
The following relation describes the volume change in a water (solvent – species 1) and salt (solute – species 2) solution: V=1.001+16.625n2 +56.092 n23/2 +119.4n22 where V is expressed in units of liters, and n2 in kmole. (1) Obtain an expression for partial V2 in terms of n2, and determine partial V2 when x2 is approching 0 in liter per kmole. (2) Obtain an expression for partial V1 one in terms of n2, and one in terms of x1.
Aniline, C6H5NH2, and hexane, C6H14, form partially miscible liquid–liquid mixtures at temperatures below 69.1 °C. When 42.8 g of aniline and 75.2 g of hexane are mixed together at a temperature of 67.5 °C, two separate liquid phases are formed, with mole fractions of aniline of 0.308 and 0.618. (i) Determine the overall mole fraction of aniline in the mixture. (ii) Use the lever rule to determine the relative amounts of the two phases.
At 39.9 ◦C, a mixture of ethanol (x1 = 0.9060, p1 = 130.4 Torr) and isooctane ( p2 = 43.9 Torr) forms a vapor phase with molar fraction y1 = 0.6667 at a total pressure of 185.9 Torr. (a) Calculate the activity and activity coefficient of each component. (b) Calculate the total vapor pressure that the mixture would have if it were ideal.
Phenol and water form non-ideal liquid mixtures. When 7.32 g of phenol and 7.95 g of water are mixed together at 60 °C they form two immiscible liquid phases with mole fractions of phenol of 0. 0 42 and 0 .161 . (a) Calculate the overall mole fraction of phenol in the mixture. (b) Use the lever rule to determine the relative amounts of the two phases .
It is found that the boiling point of a binary solution of A andB with xA = 0.6589 is 88 °C. At this temperature the vapour pressuresof pure A and B are 127.6 kPa and 50.60 kPa, respectively. (i) Is thissolution ideal? (ii) What is the initial composition of the vapour abovethe solution?
Mark the following points on a ternary phase diagram for the system NaCl/Na2SO4⋅10H2O/H2O: (i) 33 per cent by mass NaCl, 33 per cent Na2SO4⋅10H2O, and the rest H2O, (ii) the line denoting the same relative composition of the two salts but with changing amounts of water.
The experimental values of the partial molar volume of a salt in water are found to fit the expression vB = 5.117 + 19.121x1/2, where vB = VB/(cm3 mol−1) and x is the numerical value of the molality of B (x = b/b⦵). Use the Gibbs–Duhem equation to derive an equation for the molar volume of water in the solution. The molar volume of pure water at the same temperature is 18.079 cm3 mol−1.
A saturated solution of Na2SO4, with excess of the solid, is present at equilibrium with its vapour in a closed vessel. (a) How many phases and components are present. (b) What is the variance (the number of degrees of freedom) of the system? Identify the independent variables.
The osmotic pressure of a solution of polystyrene in toluene (methylbenzene} was measured at 25 °C with the following results:c/(g dm-3) 2.042 6.613 9.521 12.602∏/Pa 58.3 188.2 270.8 354.6Determine the molar mass of the polymer.
In an experimental study of membrane-like assemblies of synthetic materials, a phase diagram like that shown was obtained. The two components are dielaidoylphosphatidylcholine (DEL) and dipalmitoylphosphatidylcholineIDPU. Explain what happens as a liquid mixture of composition xDel = 0.5 is cooled from 45 °C.

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