Avogadro

Avogadro's constant. Avogadro's constant has the unit mole-1. It is not merely a number, and should not be called Avogadro's number. It is ok to say that the number of particles in a gram-mole is 6.02 x 1023. Some older books call this value Avogadro's number, and when that is done, no units are attached to it. This can be confusing and misleading to students who are conscientiously trying to learn how to balance units in equations.

One must specify whether the value of Avogadro's constant is expressed for a gram-mole or a kilogram-mole. A few books prefer a kilogram-mole. The unit name for a gram-mole is simply mol. The unit name for a kilogram-mole is kmol. When the kilogram-mole is used, Avogadro's constant should be written: 6.02252 x 1026 kmol-1. The fact that Avogadro's constant has units further convinces us that it is not 'merely a number.'

Though it seems inconsistent, the SI base unit is the gram-mole. As Mario Iona reminds me, SI is not an MKS system. Some textbooks still prefer to use use the kilogram-mole, or worse, use it and the gram-mole. This affects their quoted values for the universal gas constant and the Faraday Constant.

Is Avogadro's constant just a number? What about those textbooks which say 'You could have a mole of stars, grains of sand, or people.' In science we do use entities which are just numbers, such as , e, 3, 100, etc. Though these are used in science, their definitions are independent of science. No experiment of science can ever determine their value, except approximately. Avogadro’s constant, however, must be determined experimentally, for example by counting the number of atoms in a crystal. The value of Avogadro's number found in handbooks is an experimentally determined number. You won't discover its value experimentally by counting stars, grains of sand, or people. You find it only by counting atoms or molecules in something of known relative molecular mass. And you won't find it playing any role in any equation or theory about stars, sand, or people.

The reciprocal of Avogadro's constant is numerically equal to the unified atomic mass unit, u, that is, 1/12 the mass of the carbon 12 atom.

1 u = 1.66043 x 10-27 kg = 1/6.02252 x 1023 mole-1.

Because. Here's a word best avoided in physics. Whenever it appears one can be almost certain that it's a filler word in a sentence which says nothing worth saying, or a word used when one can't think of a good or specific reason. While the use of the word because as a link in a chain of logical steps is benign, one should still replace it with words more specifically indicative of the type of link which is meant. See: why.

Illustrative fable: The seeker after truth sought wisdom from a Guru who lived as a hermit on top of a Himalayan mountain. After a long and arduous climb to the mountain-top the seeker was granted an audience. Sitting at the feet of the great Guru, the seeker humbly said: 'Please, answer for me the eternal question: Why?' The Guru raised his eyes to the sky, meditated for a bit, then looked the seeker straight in the eye and answered, with an air of sagacious profundity, 'Because!'
Capacitance. The capacitance of a capacitor is measured by this procedure: Put equal and opposite charges on its plates and then measure the potential between the plates. Then C = |Q/V|, where Q is the charge on one of the plates.

Capacitors for use in circuits consist of two conductors (plates). We speak of a capacitor as 'charged' when it has charge Q on one plate, and -Q on the other. Of course the net charge of the entire object is zero; that is, the charged capacitor hasn't had net charge added to it, but has undergone an internal separation of charge. Unfortunately this process is usually called charging the capacitor, which is misleading because it suggests adding charge to the capacitor. In fact, this process usually consists of moving charge from one plate to the other. The capacity of a single object, say an isolated sphere, is determined by considering the other plate to be an infinite sphere surrounding it. The object is given charge, by moving charge from the infinite sphere, which acts as an infinite charge reservoir ('ground'). The potential of the object is the potential between the object and the infinite sphere.

Capacitance depends only on the geometry of the capacitor's physical structure and the dielectric constant of the material medium in which the capacitor's electric field exists. The size of the capacitor's capacitance is the same whatever the charge and potential (assuming the dielectric constant doesn't change). This is true even if the charge on both plates is reduced to zero, and therefore the capacitor's potential is zero. If a capacitor with charge on its plates has a capacitance of, say, 2 microfarad, then its capacitance is also 2 microfarad when the plates have no charge. This should remind us that C = |Q/V| is not by itself the definition of capacitance, but merely a formula which allows us to relate the capacitance to the charge and potential when the capacitor plates have equal and opposite charge on them.