D1.5 Matter, Energy, Models
In this course you will be asked to examine data and draw conclusions, to explain phenomena by applying basic principles, and to build models from which you can predict physical and chemical properties. Two important and interconnected ideas are fundamental:
- The spatial arrangement (structure) of atomic-level particles can predict macroscopic properties and chemical reactivity;
- Energies of atomic-level particles can be used to explain atomic-level structures and macroscopic energy changes.
Atomic-scale particles adopt structures with minimum energy, unless energy is transferred to them from an external source. Therefore it is useful to be able to calculate quantitatively or predict qualitatively whether one situation has higher or lower energy than another. Chemistry often involves electrically-charged atomic-scale particles, such as protons, electrons, or ions. The potential energy of two point electric charges (charges that occupy a single geometric point) can be calculated using an equation derived from Coulomb’s law:
In this equation ke is a proportionality constant equal to 8.99 × 109 J·m/C2, Q1 and Q2 are electric charge values (with units of coulomb, C), and r is the distance between the charges (with units of meter, m). Thus, the magnitude of the potential energy of two charged particles is proportional to the magnitude of each charge and is inversely proportional to the distance between the charges. The energy is positive if the charges of the two particles have the same sign (both positive or both negative). The energy is negative if the charges are opposite—opposite charges attract and lower potential energy is the result. The direct proportionality to electric charge and inverse proportionality to distance enable qualitative predictions: larger opposite charges closer together result in lower energy and hence greater stability.
Exercise: Potential Energy of Charged Particles
For all exercises, before doing any calculation or looking at any hint, write in your class notebook an explanation of how you plan to work out the problem. Do all the steps in the calculation in your notebook. Once you have arrived at an answer, submit your results below and click the “Check” button to see if it is correct. If one or more parts of your answer is incorrect, go over your work in your notebook carefully and check for errors. “Retry” with your new answer. Look at the solution (click on it to expand for view) only after you have made attempts at answering the question.
Activity: Potential Energy and Distance between Ions
Activity: Evaluating and Modifying a Model
At the atomic level, particles are most stable when energy is minimum. This happens for a sodium ion and a chloride ion when the ions are 240 pm apart (lowest point in the blue curve in the above Activity). Curves like this can be used to describe attractive forces between atoms, molecules, or ions. Particles attract each other so their potential energy decreases as they get closer, but eventually there are repulsive forces that prevent them from being in the same place at the same time. The balance of these forces results in a curve with a minimum at some distance of separation. The depth of the minimum indicates how strongly the particles attract.
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