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Name: Alexandra
Status: student
Grade: 9-12
Location: VA

Is there a measurable/mathematical relationship between cohesion and density? It seems like there would be, but I cannot find an answer anywhere.

'Cohesion' I take to mean any of several interatomic or intermolecular forces such as chemical bonds, electrostatic attraction/repulsion, van der Waals forces, etc. Is this what you mean?

Qualitatively, yes, these forces do contribute to the density of a material. I would point out water as an example, where hydrogen bonding makes it a liquid at conditions where other low-molecular-weight tri-atomic molecules (e.g. CO2, SO2) are gases. Conditions also play a huge role. With water as an example, water's density is low in low pressure/high temp (vapor), high with moderate temperature and pressure (liquid), and then drops again when you lower the temperature (ice), and then if you raise the pressure very high, the density increases again (highly pressurized ice has higher density than the ice you would find in your freezer).

A quantitative model for density that captures all of the various kinds of attraction is theoretically possible, but would be extremely complicated. Much research is being conducted now to model molecules and try to predict physical and chemical properties, including density. Various models exist for different kinds of materials -- for instance you can calculate the density of a crystal based on its atomic composition, impurity level/type, and other factors. People have also made great progress in studying and modeling polymers (including synthetic 'plastics' as well as biopolymers like DNA). For more complicated materials like proteins, the story is even more challenging. You can use computers to simulate groups of molecules, and study how they attract or repel each other. Using thermodynamics models, we can then make predictions about the most probable configuration of a system, and from that predict density. However, molecular simulations take enormous amounts of time and huge banks of computers, so usually experiments are used rather than trying calculations. The computers are getting faster, and our models better, so that may not be true forever.

In terms of measuring forces between molecules, there are several ways to do this. Some are purely theoretical, and rely on calculating the various types of attractions and adding them up. There are also experimental tools to actually measure the force required to pull apart two molecules (one is a tool called AFM, or atomic force microscopy). These are probably beyond the typical high school science curriculum, but if you are interested, you could visit a nearby engineering college and learn more.

I hope this helps -- if I missed the mark, respond back and I can try again.

Burr Zimmerman

Hi Alexandra,

There is no direct relationship between cohesion, and density. This is largely because the main causes of cohesion are not related to the factors that cause increased density. One of the main influences that determine density, is an element's nucleus. Elements with high atomic numbers tend to have high density. Lead and especially Uranium are good examples of this. Magnesium and Aluminum are examples of the opposite, namely elements with a low atomic number that have low density.

But cohesion is largely dependent on attraction between like molecules, and that can be caused the material's molecules being strongly polar in nature, or exhibiting strong Van der Waals forces. These attributes are solely related to the material's electron arrangement (especially the outer electron shell) and have little to do with the heavy nucleus.

Bob Wilson

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