Materials Science/Attraction Forces Between Ions

In summary, the task is to calculate the force of attraction between a Ca2+ and an O2- ion, with a separation distance of 1.25 nm. This can be done by first finding the attractive energy between the two ions using the equation -(A/r), where A is a constant equal to (1/(4∏ε0))(Z1e)(Z2e). The second equation, which relates force and potential energy, can then be used to calculate the attractive force between the ions. It is recommended to start with a simpler calculation using Coulomb's law for point charges before attempting this task.
  • #1

Homework Statement


Calculate the force of attraction between a Ca2+ and an O2- ion, the centers of which are separated by a distance of 1.25 nm.


Homework Equations


Attractive energy (E) = -(A/r)
*The constant A is equal to (1/(4∏ε0))(Z1e)(Z2e)
where ε0 is the permittivity of a vacuum (8.85 x 10^-12 F/m), Z1 and Z2 are the valences of the two ion types, and e is the electronic charge (1.602 x 10^-19 C).

Force-potential energy relationship for two atoms E = ∫ F dr
E=Energy F=Force d=diameter? r=spacing between atoms? (not sure about d and r)


The Attempt at a Solution


I am a high school senior taking an independent study Materials Science and Engineering course supervised by my chemistry teacher. I have taken and excelled in AP-level courses before and am currently taking AP Calculus, but the book I am using as a resource for this course is proving to be at a much higher level than I either expected or am used to. I've figured out so far that I probably need to find the attractive energy between the two ions, then use the second equation to find the corresponding attractive force, but my book (alarmingly devoid of any sort of example problems!) doesn't explain every variable. I think "d" is "diameter," and I have found a chart of atomic diameters, but I don't know which ion's diameter to use, or if I should combine them somehow. On top of that, I haven't yet learned how to integrate in Calculus...I have a TI-89 Titanium calculator, though, if that helps. Any assistance or advice is greatly appreciated...I'm just feeling very lost. Thank you!
 
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  • #2
I wonder if you are not making it more difficult than it is. I would start simply calculating Coulomb force between two point charges. You know the charges, you are given the distance, it is a simple plug and chug.

dr is a differential (it tells you what is the variable of integration), not a product of d and r.
 

1. What is Materials Science?

Materials Science is an interdisciplinary field that combines principles from physics, chemistry, and engineering to study the properties and behavior of various materials. It involves understanding the structure, composition, and processing of materials to design and develop new materials with specific properties for various applications.

2. What are attraction forces between ions?

Attraction forces between ions are the electrostatic forces of attraction that exist between positively and negatively charged ions. These forces are responsible for the bonding between ions in ionic compounds and play a crucial role in determining the physical and chemical properties of these materials.

3. How do attraction forces between ions affect the properties of materials?

The strength of attraction forces between ions determine the melting point, hardness, and electrical conductivity of materials. The arrangement of ions in a material also affects its overall structure and properties, such as crystal structure, density, and optical properties.

4. What factors influence the strength of attraction forces between ions?

The size and charge of the ions, as well as the distance between them, are the primary factors that influence the strength of attraction forces between ions. Larger ions with higher charges and shorter distances between them have stronger attractive forces.

5. How is the study of attraction forces between ions used in real-world applications?

The understanding of attraction forces between ions is crucial in developing materials for various applications, such as in electronics, energy storage, and pharmaceuticals. For example, the design of new battery materials requires an understanding of the attraction forces between ions to optimize their performance and efficiency.

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