59-240 Physical Chemistry - Question Set #13 - Lecture 13 ...

1 59-240 Physical Chemistry - Question Set #13 - Lecture 13 - v. - updated Nov. 1, 2018 Assigned questions for Lecture 13 are listed below. The questions occur in the following editions of Physical Chemistry by Atkins:Note: The letter P in front of a number indicates that the Question is in the Problem category as opposed to the Exercise category in Atkins books. Updates are highlighted in yellow. There are a lot of questions that are now missing, which is unfortunate. Note: There are two separate problem sets associated with Lecture 13. Set 1 Question *Missing after 7th Ed. (not sure why). (Ex. , 7th edition). Express ( S/ V)T in terms of and T. (Ex. , 7th edition). Express ( S/ p)T in terms of . Question Question format, variation in numbers between 10th and 11th Eds. vs. 8th and 9th Eds. (a) Suppose that mmol N2(g) occupies 36 cm3 at 300 K and expands to 60 cm3.

2 Calculate G for the process. (b) Suppose that mmol Ar(g) occupies 72 dm3 at 298 K and expands to 100 dm3. Calculate G for the process. (a) Suppose that mmol N2(g) occupies 42 cm3 at 300 K and expands isothermally to 600 cm3. Calculate G for the process. (b) Suppose that mmol Ar(g) occupies 52 cm3 at 298 K and expands isothermally to 122 cm3. Calculate G for the process. Question Same questions. (a) The change in the Gibbs energy of a certain constant pressure process was found to fit the expression G/J = + (T/K). Calculate the value of S for the process. (b) The change in the Gibbs energy of a certain constant pressure process was found to fit the expression G/J = + (T/K). Calculate the value of S for the process. 10th edition9th edition8th editionn/an/an/ of Windsor - department of Chemistry and Biochemistry - Schurko 159-240 Physical Chemistry - Question Set #13 - Lecture 13 - v.

3 - updated Nov. 1, 2018 Question * Missing from 10th and 11th Eds. No idea why. (a) Calculate the change in Gibbs energy of 35 g of ethanol (mass density g cm-3) when the pressure is increased isothermally from 1 atm to 3000 atm. (b) Calculate the change in Gibbs energy of 25 g of methanol (mass density g cm-3) when the pressure is increased isothermally from 100 kPa to 100 MPa. Take T = 10-9 Pa-1. Question *Missing in all editions after 7th Ed. (Ex. , 7th edition). When mol of has at 330 K and atm is subject to isothermal compression, its entropy decreases by J K-1. Calculate (a) the final pressure of the gas and (b) the G for the compression. (Ex. , 7th edition). When mol of has at 230 K and 150 kPa is subject to isothermal compression, its entropy decreases by J K-1. Calculate (a) the final pressure of the gas and (b) the G for the compression.

4 Question *Missing from the 10th and 11th Eds. Not sure why. But: See in 11th Ed. for something similar (see below). (a) Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from atm to atm at 40 C. (b) Calculate the change in chemical potential of a perfect gas that its pressure is increased isothermally from kPa to kPa at 50 C. Question *Missing from the 10th Ed. Not sure why. (a) The fugacity coefficient of a certain gas at 200 K and 50 bar is Calculate the difference of its molar Gibbs energy from that of a perfect gas in the same state. (b) The fugacity coefficient of a certain gas at 290 K and MPa is Calculate the difference of its molar Gibbs energy from that of a perfect gas in the same state. n/ of Windsor - department of Chemistry and Biochemistry - Schurko 259-240 Physical Chemistry - Question Set #13 - Lecture 13 - v.

5 - updated Nov. 1, 2018 Question of the same style Question . Use of mass density in 10th Ed. is similar to Question (a) Estimate the change in the Gibbs energy of dm3 of benzene when the pressure acting on it is increased from atm to 100 atm. (b) Estimate the change in the Gibbs energy of dm3 of water when the pressure acting on it is increased from 100 kPa to 300 kPa. (a) Estimate the change in the Gibbs energy and molar Gibbs energy of dm3 of octane when the pressure acting on it is increased from atm to 100 atm. The mass density of octane is g cm 3. (b) Estimate the change in the Gibbs energy and molar Gibbs energy of 100 cm3 of water when the pressure acting on it is increased from 100 kPa to 500 kPa. The mass density of water is g cm 3. Question Question in 10th and earlier editions. (a) Calculate the change in the molar Gibbs energy of hydrogen gas when its pressure is increased isothermally from atm to atm at 298 K.

6 (b) Calculate the change in the molar Gibbs energy of oxygen when its pressure is increased isothermally from kPa to kPa at 500 K. Changed in 11th Ed. (a) Calculate the change in the molar Gibbs energy of a perfect gas when its pressure is increased isothermally from atm to atm at 298 K. (b) Calculate the change in the molar Gibbs energy of a perfect gas when its pressure is increased isothermally from kPa to kPa at 500 K. of Windsor - department of Chemistry and Biochemistry - Schurko 359-240 Physical Chemistry - Question Set #13 - Lecture 13 - v. - updated Nov. 1, 2018 Set 2 Question *Part (a) is missing in all editions after the 7th Ed, in 9th-11th Eds. (Ex. , 7th edition). The molar Helmholz energy of a certain gas is given by where a and b are constants and f(T) is a function of temperature only. Obtain the equation of state of the gas.

7 (Ex. , 7th edition). The molar Gibbs energy of a certain gas is given by where A, B, C and D are constants. Obtain the equation of state of the gas. Question Ed. and earlier: Evaluate ( S/ V)T for (a) a van der Waals gas, (b) a Dieterici gas (see Lecture 4, real gases). For an isothermal expansion, for which kind of gas (and a perfect gas) will S be greatest?Explain your conclusion. Changed in the 10th: Two empirical equations of state of a real gas are as follows: Evaluate ( S/ V)T for each gas. For an isothermal expansion, for which kind of gas (also consider a perfect gas) will S be greatest? Explain your conclusion. And yet again in the 11th (see next page): n/ of Windsor - department of Chemistry and Biochemistry - Schurko 4Am= aVm RT(lnVm b)+f(T)Gm=RTlnp+A+Bp+12Cp2+13Dp359-240 Physical Chemistry - Question Set #13 - Lecture 13 - v.

8 - updated Nov. 1, 2018 Question *Missing in 8th and 9th Eds. ( , 7th edition). Calculate rGo (375 K) for the reaction 2CO(g) + O2(g) 2CO2(g) from the Gibbs-Helmholz equation, and the values of rGo (298 K) and rHo (298 K). 11th Ed.: of Windsor - department of Chemistry and Biochemistry - Schurko 559-240 Physical Chemistry - Question Set #13 - Lecture 13 - v. - updated Nov. 1, 2018 Question *Missing from the 10th ed. Not sure why. Show that, for a perfect gas, ( U/ S)V = T and ( U/ V)S = -p. Question *Same questions in 10th and earlier. Missing in 11th. However, this is just what is asked of you in classes for L13, and part of this is covered in tutorial. Two of the four Maxwell relations were derived in the text, but two were not. Complete their derivation by showing that ( S/ V)T = ( p/ T)V and ( T/ p)S = ( V/ S)p.

9 Question *In the 10th Ed, the problems are joined together into one (a and b). Missing from the 11th Ed. Use the Maxwell relations to express the derivatives (a) ( S/ V)T and ( V/ S)p and (b) ( p/ S)V and ( V/ S)p in terms of the heat capacities, the expansion coefficient , and the isothermal compressibility, T. The Joule coefficient, J, is defined as J = ( T/ V)U. Show that JCV = p aT/ T. (a) Use the Maxwell relations to express the derivatives ( S/ V)T, ( V/ S)p, ( p/ S)V, and ( V/ S)p in terms of the heat capacities, the expansion coefficient = (1/V)( V/ T)p, and the isothermal compressibility, T = (1/V) ( V/ p)T. (b) The Joule coefficient, j, is defined as = ( T/ V)U. Show that JCV = p T/ T. Question *Missing from the 10th ed. Not sure Use the Maxwell relations to show that the entropy of a perfect gas depends on the volume as S R ln , , , of Windsor - department of Chemistry and Biochemistry - Schurko 659-240 Physical Chemistry - Question Set #13 - Lecture 13 - v.

10 - updated Nov. 1, 2018 Question *Missing from the 10th ed. Not sure Derive the thermodynamic equation of state Derive an expression for ( H/ p)T for (a) a perfect gas and (b) a van der Waals gas. In the latter case, estimate its value for mol Ar(g) at 298 K and 10 atm. By how much does the enthalpy of the argon change when the pressure is increased isothermally to 11 atm? Question *Same questions, except for addition of highlighted term in 10th Ed, which seems to be a misprint. And of from the illustrious 11th Suppose that S is regarded as a function of p and T. Show that TdS = CpdT TVdp. Hence, show that the energy transferred as heat when the pressure on an incompressible liquid or solid is increased by p is equal to TV p, where O = (1/V)(9V/9T)p. Evaluate q when the pressure acting on 100 cm3 of mercury at 0 C is increased by kbar.