Problem Set #23: Ionic Solvation and Thermodynamics

University:
The Pennsylvania State University
Course:
CHEM 450 | Thermodynamics
Academic year:

2024
Views:

38

Pages:

2
Author:

Alexis H.

Problem Set #23 Assigned: Feb. 26, 2024 Due: Feb. 28, 2024 at 2:30 pm 1. (a) Using the Born equation, derive expressions for = Hint: = 8 solS ( 1 and solH . 1 ) 1 . Moreover, the Born equation has no temperature dependence. Therefore, what is the derivative of the Born equation with respect to temperature? Once you have this answer, you should be able to find the enthalpy of solvation. (b) Comment on your answer in terms of the assumptions of the Born model. In other words, does this answer seem reasonable? Remember, it is assumed that water is a continuum dielectric medium with r = 78.54 at 25 °C. How does this differ with having water molecules in specific hydration shells around your ion? 2. In class we noted that fG = -131.23 kJ/mol for Cl-(aq) The radius of a chloride on is 181 pm and the radius of a proton is less than 0.001 pm. (see https://en.wikipedia.org/wiki/Proton_radius_puzzle for a discussion of the proton radius) By solving the Born equation, the solvation energy for an ion should be: solG = / 6.86 10 / (a) Find the solvation energies for H+ and Cl-. (b) Do the values that you found in (a) using the Born equation make sense? (c) By following the thermodynamic cycle (Fig. 3D3.3 in your textbook), it can be shown that: fG (Cl-(aq)) = 1287 kJ/mol + solG (H+) + solG (Cl-) What would the value of the proton radius need to be to make this problem work out? (d) Does the new value in (c) seem realistic? 3. Calculate the maximum non-expansion work per mole of CH4(g) that may be obtained by combusting methane to CO2(g) and H2O(l) at 298 K. Note: the standard Gibbs energies of formation are: CH4(g) = -50.7 kJ/mol H2O(l) = -237.1 kJ/mol CO2(g) = -394.4 kJ/mol 1 b thisanswerdoes seemreasonable and itdiffers Δso Go a bybeing based onthechargenumberthemolecules 8 express Δso 40,5 a DsoG Ht ΔsoGHt soGO.ca 3 571.6Ksmol d 392Ksmol CO Δ ΔfG co 2 46 2H20 H2O 394.4 2 237.1 Δrg Wmax 104 No it does not seem realistic because the radius seems too small for an element at the top of the periodic table Yes because the larger the ionic radius then the smaller the energy inside will be Hy 20 6.86 ri 53 6.86104 ΔsoGo a b c 1287 6.86 104 817.9 KJ mol 817 9 kJ mol 46 50.7 0 CH4 ΔfG Oz