How to derive radius ratio and calculate reaction energy

[aznkid310]

Greetings all,

My first problem: I have been asked to derive the minimum radius ratio for coordination numbers 4 and 6. I read the book and looked at the sample problems, but they do not help at all. I realize that it has to do with the geometry of it, but have no idea how to use that.
The book is:
INTRODUTION TO MATERIALS SCIENCE FOR ENGINEERS (6th edition) by James F. Schackelford.

My second problem: How does one calculate the rxn energy for polymerization of styrene (C_3H_6). We are given various bond energies for single carbon - carbon bonds at different lengths. I drew it and looks like: c - c = c w/ H atoms around it. In an example, the picture is: c = c and they broke it down into 2(c - c). how would i do it for 3 carbons? Also, how would I know what the bond length is (since the bond energies are related to them)?

 

[Spirochete]

My second problem: How does one calculate the rxn energy for polymerization of styrene (C_3H_6). We are given various bond energies for single carbon - carbon bonds at different lengths. I drew it and looks like: c - c = c w/ H atoms around it. In an example, the picture is: c = c and they broke it down into 2(c - c). how would i do it for 3 carbons? Also, how would I know what the bond length is (since the bond energies are related to them)?

Does rxn energy=enthalpy? If so, you need a table of bond dissociation energies, which tell you how much energy it takes to break different kinds of bonds. Then look at the reaction and see which bonds were broken and which were formed. Enthalpy equals the energy used to break the bonds plus the energy gained by forming the new bonds. So enthalpy=broken minus formed.

I'm not sure how bond length would be required to solve the problem, but that information should be available in a table somewhere.

But I'm no engineer, so chances are the problem is more complicated than this.

 

[Blueshift5]

Hello there,

To derive the radius ratio for coordination numbers 4 and 6, you can use the equation:

radius ratio = (cation radius)/(anion radius)

For coordination number 4, the cation is usually tetrahedral and the anion is usually octahedral. This means that the cation is surrounded by 4 anions in a tetrahedral arrangement, and the anion is surrounded by 4 cations in an octahedral arrangement. The minimum radius ratio for this coordination number is approximately 0.225.

For coordination number 6, the cation is usually octahedral and the anion is usually octahedral as well. This means that both the cation and anion are surrounded by 6 of the opposite ions in an octahedral arrangement. The minimum radius ratio for this coordination number is approximately 0.414.

To calculate the reaction energy for polymerization of styrene, you can use the following equation:

reaction energy = (sum of bond energies of reactants) - (sum of bond energies of products)

The bond energies for single carbon-carbon bonds at different lengths can be found in a table or online. For example, the bond energy for a single bond between two carbon atoms is approximately 347 kJ/mol. For a polymer with 3 carbons, you would have 2 single bonds (C-C) and 1 double bond (C=C). So the total bond energy for the reactants would be 2(347 kJ/mol) + 1(615 kJ/mol) = 1309 kJ/mol.

To determine the bond length, you can use the bond energy equation:

bond energy = (bond strength) x (bond length)

You can rearrange this equation to solve for bond length:

bond length = bond energy/bond strength

So for example, if the bond energy for a C-C bond is 347 kJ/mol and the bond strength is 348 kJ/mol, then the bond length would be 347 kJ/mol / 348 kJ/mol = 0.997 angstroms (Å).

I hope this helps. Good luck with your studies!