Avogadros hypothesis

But the potentiality of molecular structure could not be successfully pursued until the atomic weights were reliably established and the number of atoms in the molecules could be reliably known. This was not accomplished until fifty years later, by Stanislao Cannizzaro, through a rigorous application of Avogadros hypothesis first published in 1811. Since this long complex story does not involve any change in the compositional concepts introduced by Dalton, it is appropriate to offer only a brief account. 

Extended accounts can be found in John Hedley Brooke, Avogadros hypothesis and its fate a case-study in the failure of case-studies, Hist. Sci. 19 (1981) 255-273 and by Nicolas Fisher, Avogadro, the chemists, and historians of chemistry, Hist. Sci. 20 (1982) 77-102, 212-231. 

That is, the osmotic pressure obeys the generalised gas law, which includes Boyle s Law, Gay-Lussac s, and the Avogadro Hypothesis It will be observed that the R is numerically identical with the R of the perfect gas equation That is, the osmotic pressure of a dilute solution is related to the molecular volume, or the inverse of this the molecular concentration quantitatively as the pressure of a perfect gas is related to the volume For substances in dilute solution R = i 985 calones per gram-mole It may be noted that in the particular case in which V - v the osmotic pressure is identical with the gas pressure... 

The deduction just given, which is based on a thermodynamic cycle, and also on the validity of Henry s Law, proves that the osmotic pressure obeys Boyle s and Gay-Lussac s Laws, and is in agreement with the Avogadro Hypothesis... 

Dalton understood Avogadros creative argument but found it unacceptable because it failed to explain how two atoms of the same clement could bond to each other. Based on his own research, Dalton had come to the erroneous conclusion that atoms of the same kind always have a natural repulsion for one another. Because of Daltons authority in the scientific community, Avogadros hypothesis was discarded and did not reappear for another half-century. 

At this conference, a pamphlet written by the Italian chemist Stanislao Cannizzaro (1826-1910) was presented. In this pamphlet, which he had used with his students for several years, Cannizzaro explained and justified Avogadros hypothesis and showed how correct atomic masses and formulas could be obtained through easy calculations. The concept was. simple provided equal volumes of gases contain equal numbers of atoms or molecules, the relative masses of these particles can be obtained by weighing equal volumes of gases that are at... 

For a fixed quantity of gas at constant pressure, the volume is directly proportional to its absolute temperature (Charles s law). Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (Avogadro hypothesis). For a gas at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of gas (Avogadro s law). Each of these gas laws is a special case of the ideal-gas equation. 

Although the stockroom supplies only real gases in tanks—argon, carbon dioxide, and so forth—Equations (3.46) and (3.49) apply to every system in the limit of zero density. The compactness of the ideal gas law is impressive as four variables of state are related by simple multiplication and division. The equation wraps Boyle s law, Charles law, and the Avogadro hypothesis into a compact multivariable function. 

Consider two identical vessels, one containing C02(g) and the other He(g). Assume that both contain the same number of molecules and are maintained at the same temperatures. The pressure exerted by a gas is a result of molecular collisions against the container walls. Thus, intuitively one might expect that the pressure exerted by the heavier molecules of CO 2(g) will be larger than the pressure due to He(g). Compare this expectation with the pressure predicted by the ideal gas law (or the Avogadro hypothesis). How would you explain the prediction of the ideal gas law which is validated by the experiment ... 

The expression "Avogadro hypothesis," still In use, is left over from the time when most people did not accept it. 

This chapter helps us to understand that while the ideal gas law PV = nRT) is generally useful in the range of temperatures above 0°C and pressures up to about 100 atm, extreme conditions can require corrections. Dalton s law leads us to begin to wonder about the behavior of individual gas molecules and the space between them. We also saw that the density of a gas can be related to the molecular weight of the gas. A calculation of the moles of gas based on the Avogadro hypothesis led us to a simple way to consider uncertainties in experimental methods according to a formula based on percent uncertainties in the variable measurements as... 

In terms of moles, Avogadro s hypothesis can be stated The same volume is occupied by one mole of any gas at a given temperature and pressure. The number of molecules in one mole is known as the Avogadro number constant. ... 

The behavior of all gases that obey the laws of Boyle and Charles, and Avogadro s hypothesis, can be expressed by the ideal gas equation ... 

Avogadro s Hypothesis States that Equal volumes of different gases at the same pressure and temperature contain the same number of molecules. Hence, the volume occupied by any gas whose mass is numerically equal to its molecular weight is a constant quantity. 

This calculation of the proportions by partial pressure can be converted to proportions by weight, by multiplying each pressure by the molecular mass (Avogadro s hypothesis), to give ... 

The importance of Avogadro s Hypothesis is that it furnishes a basis for weighing molecules. Two equal volumes of gas (at the same temperature and pressure) are weighed. If we assume these two volumes contain identical numbers of molecules, then we must also conclude that the gas that weighs more must have heavier molecules. Furthermore, the ratio of the weights of the molecules must be exactly the ratio of the weights of the two gas samples. 

These simple, integer volume ratios confirm the usefulness of the interpretation that equal volumes contain equal numbers of molecules. This proposal was first made in 1811 by an Italian scientist, Amadeo Avogadro hence it is called Avogadro s Hypothesis. It has been used successfully in explaining the properties of gases for a century and a half. 

Avogadro s Hypothesis Equal volumes of gases, measured at the same temperature and pressure, contain equal numbers of molecules. 

Finally, we discover that exactly two volumes of nitric oxide combine with one volume of oxygen and that exactly two volumes of nitrogen dioxide are formed. According to Avogadro s Hypothesis, this indicates that... 

From these data alone and Avogadro s Hypothesis, how many molecules of hydrogen combine with one molecule of nitrogen How many molecules of ammonia are produced from one molecule of nitrogen ... 

Avogadro s Hypothesis provides a method for identifying the molecules present in a gas. Also, it explains why the volumes of gases that react with each other are in the same simple ratio as are the moles in the balanced equation. The importance of these results makes the explana-... 

The kinetic theory is based upon the premise that if two gases are at the same temperature, the molecules of the gases have the same average kinetic energy. The ability of this kinetic theory to explain Avogadro s Hypothesis is one of its most important successes. 

We may state Avogadro s Hypothesis in this form If two gases at the same temperature have the same number of particles in a given volume, they must exert the same pressure. Yet, as re-... 

Avogadro s Hypothesis can be shown quite readily in an approximate way. The kinetic energy of a moving particle is expressed by the equation... 

Avogadro s Hypothesis is consistent with the kinetic theory. Therefore a perfect gas follows Avogadro s Hypothesis. At one atmosphere pressure and 0°C, one mole (6.02 X 10 molecules) of a perfect gas occupies 22.414 liters. How closely real gases approximate a perfect gas at one atmosphere pressure and 0°C is shown by measur-... 

---