User:Steven J. Koch/MTC Assignment 3: Difference between revisions
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* Part A | * Part A | ||
** Use the ideal chemical potentials for the monomers Na+, Cl-, and NaCl. Recall that at chemical equilibrium the chemical potential of NaCl "molecules" is the sum of chemical potential of Na+ and Cl- monomers. See definition of delta_mu<sup>0</sup> in the picture. Putting all of this together, write K<sub>eq</sub> as a function of delta_mu<sup>0</sup> and kT. For kT = 4.1 pN-nm and the coloumb energy as defined in the photo (about 3.6 kT), what is our specific numeric K<sub>eq</sub>? | ** Use the ideal chemical potentials for the monomers Na+, Cl-, and NaCl. Recall that at chemical equilibrium the chemical potential of NaCl "molecules" is the sum of chemical potential of Na+ and Cl- monomers. See definition of delta_mu<sup>0</sup> in the picture. Putting all of this together, write K<sub>eq</sub> as a function of delta_mu<sup>0</sup> and kT. For kT = 4.1 pN-nm and the coloumb energy as defined in the photo (about 3.6 kT), what is our specific numeric K<sub>eq</sub>? | ||
* Part B | |||
** As shown in the top right of the photo, we get information from stoichiometry and conservation of mass. When one NaCl dissociates, one Na+ and one Cl- each are gained. Thus the number of Na+ = number of Cl- and we can define N<sub>I</sub> = x<sub>I</sub>*N<sub>T</sub>. | |||
** Use these relations to first find the mole fraction of AB (NaCl) as a function of the mole fraction of each ionic species. | |||
** Next, use the relation for K<sub>eq</sub> to write X<sub>I</sub> as a function of Keq. | |||
*** You will solve a quadratic equation for this step | |||
* Part C | |||
** '''Use excel, Matlab, LabVIEW, or something besides a simple calculator for this step''' That way you will be able to play around with different values easily. | |||
** For N<sub>AB</sub><sup>0</sup> = 0.5 mols and N<sub>water</sub><sup>0</sup> = 55.6 mols, and the equilibrium constant using 2 angstrom separation as in part A, calculated the following with real numbers: | |||
*** x<sub>AB</sub>, x<sub>I</sub>, x<sub>w</sub>, N<sub>T</sub>, mu<sub>AB</sub> | |||
*** Do the numbers seem sensible? | |||
==Potential resources== | ==Potential resources== | ||
* [http://en.wikipedia.org/w/index.php?title=Activity_(chemistry)&oldid=411295393#Example_values Activity of NaCl in water] | * [http://en.wikipedia.org/w/index.php?title=Activity_(chemistry)&oldid=411295393#Example_values Activity of NaCl in water] | ||
Revision as of 03:29, 22 February 2011
This homework assignment is due March 1, 2011. This assignment is based on an example from Evan Evans in 2009.
How to turn in
- Your answer needs to somehow be publicly available, such as by:
- Writing your answers by hand and uploading a photograph
- Composing your answers online, such as on the wiki
- Creating a PDF on your own and uploading the PDF
Assignment
For this problem, we are considering adding NaCl to water and modeling it as NaCl "molecules" that dissolve and can dissociate into Na+ and Cl- monomers. As a reference point, we will consider 0.5 moles of NaCl added to 55.6 moles of water. The equilibrium constant for the dissociation is defined as xAB / (xA * xB) as shown in top left of photo.
- Part A
- Use the ideal chemical potentials for the monomers Na+, Cl-, and NaCl. Recall that at chemical equilibrium the chemical potential of NaCl "molecules" is the sum of chemical potential of Na+ and Cl- monomers. See definition of delta_mu0 in the picture. Putting all of this together, write Keq as a function of delta_mu0 and kT. For kT = 4.1 pN-nm and the coloumb energy as defined in the photo (about 3.6 kT), what is our specific numeric Keq?
- Part B
- As shown in the top right of the photo, we get information from stoichiometry and conservation of mass. When one NaCl dissociates, one Na+ and one Cl- each are gained. Thus the number of Na+ = number of Cl- and we can define NI = xI*NT.
- Use these relations to first find the mole fraction of AB (NaCl) as a function of the mole fraction of each ionic species.
- Next, use the relation for Keq to write XI as a function of Keq.
- You will solve a quadratic equation for this step
- Part C
- Use excel, Matlab, LabVIEW, or something besides a simple calculator for this step That way you will be able to play around with different values easily.
- For NAB0 = 0.5 mols and Nwater0 = 55.6 mols, and the equilibrium constant using 2 angstrom separation as in part A, calculated the following with real numbers:
- xAB, xI, xw, NT, muAB
- Do the numbers seem sensible?
