Avogadro's Number
Historically, Avogadro's number (or the Avogadro constant) is the number of particles, atoms, formula units, or molecules, in one mole of a given substance. The metric system now more precisely defines it as the number of atoms in exactly 0.024 lb (12g) of 12 C. In equations, Avogadro's number is given the symbol L; numerically it is equal to 6.023 x 1023 .
Avogadro's number is the number of particles present when the amount of material is the same as the atomic weight (or relative molecular mass, or relative atomic mass or weight) expressed in grams. This is one mole of the substance. For example, with water, HO, the relative molecular mass is 18 (16 for oxygen and 1 for each of the two hydrogens), so in 0.036 lb (18 g) of water there are 6.023 x 1023 HOH molecules. With a gas there is a slight difference because the gas may be encountered in the diatomic state in the atmosphere. For example, oxygen and nitrogen in the atmosphere are generally encountered as O and N respectively. With these diatomic molecules, there is an Avogadro's number of diatomic molecules in the amount of gas that is equivalent to the relative molecular mass. There may be an ambiguity if correct terminology is not applied. One mole of oxygen could refer to one mole of oxygen atoms (6.023 x 1023 atoms) or it could refer to one mole of diatomic, gaseous oxygen, one mole of oxygen molecules (12.046 x 1023 oxygen atoms). The first case is elemental oxygen and the latter is molecular oxygen. A mole of anything contains the Avogadro number of those objects, whether it be a mole of atoms, molecules, or ions.
Amedeo Avogadro was an Italian physicist who lived from 1776-1856, and his main contribution to chemistry is Avogadro's hypothesis which gave us Avogadro's Law, which in turn lead to Avogadro's number. These were worked out by looking at volumes of gas reacting together and Avogadro noticed that they always reacted in a constant ratio of whole numbers of volumes of gas. In other words, one volume of gas A would always react completely with one volume of gas B or two volumes of gas C. Avogadro realized there was a constant relationship, and by further observation and hypothesizing, he eventually came up with what we now know as Avogadro's law and number.
A number as large as Avogadro's number is difficult to comprehend, but the following example is often quoted to give an indication of exactly how large this number is. When standing on a beach with an uninterrupted view to the horizon both left and right, the number of sand grains that are present are still not enough to make one mole of sand grains. Another way of looking at this would be to consider an Avogadro's number of soft drink cans: if they were stacked together, they would cover the entire surface of the earth to a depth of 200 mi (322 km).
The numerical value of Avogadro's number has been confirmed by several different experimental techniques, including Brownian motion, electronic charge, and the counting of alpha particles.
Avogadro's hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Avogadro's law states that a gas at constant temperature and pressure has a volume directly proportional to the number of moles of gas. From these two statements, and from what has been previously said, it can be seen that the volume of a gas is directly proportional to the number of molecules present. Also, one mole or an Avogadro's number of molecules of any gas would occupy the same volume as one mole or one Avogadro's number of any other gas, at constant temperature and pressure, irrespective of the size of the molecules considered. Avogadro's number can be used in working out the amount of substance required to completely take part in a chemical reaction. Obviously dealing routinely with numbers of the size of Avogadro's number is unwieldy. To overcome the problems associated with this, the mole is used.
Avogadro's number is not just true for gases; it holds true whatever the state of matter under consideration. When a substance is dissolved in a solvent, the strength of solution can be discussed in terms of Avogadro's number. When an Avogadro's number of particles is dissolved into 0.264 gal (1 1) of solvent the strength of the solution is one molar. This is the molarity of the solution. Molality is a similar concept to molarity. Instead of dealing with the volume of the solution or solvent, molality is concerned with the mass of solution or solvent. As such a one molal solution has one mole dissolved in 2.205 lb (1 kg) of solution. A one molal solution has an Avogadro's number of particles of the solute.
Avogadro's number is a conversion factor between the number of moles present and the actual number of physical particles. For example, the number of particles present in 0.1 lb (50 g) of carbon dioxide can easily be calculated. The molecular weight of carbon dioxide is 12 for the carbon plus 16 for each of the two oxygens, which totals a molecular weight of 12 + 16 + 16 = 44. One mole of carbon dioxide would weigh 0.088 lb (44 g). Moles are calculated by dividing the weight by the weight of one mole, this is 50 divided by 44, which equals 1.14. In this example, the result is 1.14 moles of carbon dioxide in 0.1 lb (50 g) of carbon dioxide. The number of molecules of carbon dioxide is the number of moles multiplied by Avogadro's number, or 1.14 x 6.023 x 1023 which gives us an answer of 6.866 x 1023 . In other words, in 50 g or 1.14 moles of carbon dioxide there are 6.866 x 1023 molecules of carbon dioxide. The calculations listed here will work0 in any direction relating moles to particles to weights of materials, simple rearrangement of the equations will provide the appropriate answer.
Avogadro's number is a powerful and useful concept. It illustrates how much of a material is actually participating in a reaction at a basic level. The numbers that it generates are too large to comprehend with any validity so the mole concept is used. One mole of substance contains an Avogadro's number of particles. It is easier to visualize one mole simply because the number one is a more comfortable number to work with than 6.023 x 1023 , even though, by definition, the quantities involved are exactly the same. Conversion is easy between Avogadro's number of particles, moles, weights and also the figures used in chemical equations. Such figures help to optimize a reaction so reactants are not overused.
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