Gay-Lussac equation

Using cm as unit surface and seconds as unit time, n is the number of molecules falling on 1 cm /sec. The number n thus denotes the number of molecules striking each cm of the surface every second, and this number can be calculated using Maxwell s and the Boyle-Gay Lussac equations. The number n is directly related to the speed of the molecules within the system. It is important to realize that the velocity of the molecules is not dependent on the pressure of the gas, but the mean free path is inversely proportional to the pressure. Thus ... 

Fermentation. The effervescent gas in sparkling wine is C02 produced by the fermentation of sugar. The Gay-Lussac equation for alcoholic fermentation of glucose is ... 

During alcoholic fermentation, Saccharomyces converts grape sugars to alcohol and carbon dioxide as per the Gay-Lussac equation where 1 mole sugar yields 2 moles each of ethanol and carbon dioxide (Fig. 8.1). The rate of ethanol production by Saccharomyces varies with many factors but can reach 8 X lO to 9 X lO molecules of ethanol per yeast cell per second (Foy, 1994b). 

Figure 8.1. Utilization of sugars to yield ethanol and carbon dioxide as per the Gay-Lussac equation.

The interaction forces which account for the value of a in this equation arise from tire size, the molecular vibration frequencies and dipole moments of the molecules. The factor b is only related to the molecular volumes. The molar volume of a gas at one atmosphere pressure is 22.414 ImoD at 273 K, and this volume increases according to Gay-Lussac s law with increasing... 

Charles and Gay-Lussac, working independently, found that gas pressure varied with the absolute temperature. If the volume was maintained constant, the pressure would vary in proportion to the absolute temperature [I j. Using a proportionality constant R, the relationships can be combined to form the equation of state for a perfect gas, otherwi.se known as the perfect gas law. 

Charles s and Gay-Lussac s law Relation stating that at constant P and n, the volume of a gas is directly proportional to its absolute temperature, 106-107, 111 Chelating agent Complexing ligand that forms more than one bond with a central metal atom the complex formed is called a chelate, 411-412 natural, 424-425 synthetic, 424-425 Chemical equation Expression that describes the nature and relative amounts of reactants and products in a reaction, 60-61. See also Equation, net ionic. 

This is one form of Charles s law . (Charles s law is also called Gay-Lussac s law .) Alternatively, we could have multiplied both sides of Equation (1.4) by T, and rewritten it as... 

The data obtained from studying crude cultures were not as bad as one would assume. For example, the stoichiometric relationships between the consumption of sugar and the production of alcohol and carbon dioxide were determined even before yeast became known as the causative agent of alcoholic fermentation (Gay Lussac 1810). Furthermore, the general equation for the formation of propionic acid was calculated by A. Fitz in Strassburg in 1878 on the basis of studies with crude cultures inoculated with cow excrements ... 

As early as 1819, J. L. Gay Lussac proposed to represent the solubility S of potassium chloride in water at a temp. 0 by the formula /S=29-23+0-27380 grms. per 100 grms. of water. Since that time it has been customary to represent solubility curves by empirical formula of the type /S=a+ 0+d02+..., where a, l, c,d,.. . are constants whose numerical values are calculated from the experimental data. Equations of the type S=a- -bO represent straight lines, equations with more terms represent curved lines the solubility equation /S=d+60+c02 represents a portion of a paraboloid curve. The greater the number of terms used in the formula the greater is supposed to be the accuracy of the result. 

Crushing—Maceration—Pressing Operations. Fundamental to making any type of wine is the conversion of sugar to ethyl alcohol by the enzymes present in living yeast cells according to the equation established by Gay-Lussac,... 

If the gas is assumed 10 consist of molecules of negligible size and without interaction, then the gas can be shown to follow the laws of Boyle and Gay-Lussac therefore its isothermal and adiabatic compressibilities must be given by Equation (4). For a perfect gas, the percentage pressure rise is proportional to the percentage volume decrease if the change is small thus the compressibility is inversely proportional lo Ihe pressure. 

In the case of gases, properties may be tabulated til terms of their existence at 0°C and 760 mm pressure, To determine the volume of a gas at some different temperature and pressure, corrections derived from known relationships (Charles , Amonton s. Gay-Lussac s, and other laws) must be applied as appropriate. In tile case of pH values given at some measured value (standard for comparison), the same situation applies. Commonly, lists of pH values are based upon measurements taken at 25°C. The pH of pure water at 22°C is 7.00 at 25,JC, 6.998 and at 100°C. 6.13. Modern pH instruments compensate for temperature differences through application of the Nernst equation. 

The universe as a whole is made up of material with three distinct states, namely the solid state, the liquid state and the gaseous state. In 1662, Robert Boyle showed for the first time the relationship between volume and pressure of a gas under constant temperature to be inverse proportional to one another. In 1802 Gay-Lussac reported his discovery on the relationship between the volume of gas and temperature under constant pressure to be proportional to one another. These two relationships laid the foundation for the equation of state for gaseous state namely,... 

Equation 8.5) Pressure and Temperature Relationships You may have noticed that volume appears in both Boyle s and Charles s laws. If we know that pressure and volume are inversely related and volume and temperature are directly related, then we can say that pressure and temperature are inversely related, or as in Equation 8.5 P — = constant T This relationship is frequently referred to as Gay-Lussac s Law, named after Joseph Louis Gay-Lussac, one of the early gas researchers. Gay-Lussac also performed some experiments that helped Amadeo Avogadro create what is now referred to as Avogadro s law. 

In this section, you learned about the relationship between volume and temperature (Charles law). You also learned about the relationship between pressure and temperature (Gay-Lussac s law). In the next section, you will see how these relationships can be combined with Boyle s law to produce one equation that works in all three situations. 

At the beginning of this chapter, you were introduced to Gay-Lussac s law of combining volumes When gases react, the volumes of the reactants and the products, measured at equal temperatures and pressures, are always in whole number ratios. As well, you learned that the mole ratios from a chemical equation are the same as the ratios of the volumes of the gases. 

Combining Boyle s Law, Charles s Law, and Gay-Lussac s Law forms a combined gas law equation. The combined gas law equation can be used when temperature, pressure, and volume are changing. Essentially, this equation can replace the three individual law equations, and if one of the properties is constant, it can be crossed out and ignored. 

For the special case when more than one gas is involved in a chemical reaction and all the gases are separate and measured at the same temperature and pressure, the volume ratio of the gases is equal to the mole ratio given in the balanced equation. This statement is known as Gay-Lussac s law of combiuiug volumes. 

Gay-Lussac s law of combining volumes relates the volumes of gases involved in a reaction, all measured separately at the same temperature and pressure. The volume ratio under these conditions is equal to the mole ratio and, therefore, to the ratio of coefficients in the balanced chemical equation (Section 12.9). 

Boyle s law, the law of Charles and Gay-Lussac, and Avogadro s law can be combined into a single equation,... 

By combining the equations for Boyle s law, Charles law, and Gay-Lussac s law, a single equation can be obtained that is useful for many computations ... 

The equation of condition. The expansion of gases on heating is very much greater than that of solid and liquid bodies, and obeys much simpler laws. Gay-Lussac was the first to publish an empirical law which states that all gases expand by the same fraction a of the volume which they occupy at 0° when their temperature is raised 1° C. The value of this fraction a is If the volume of unit mass of the gas at 0° is Vq, its volume at... 

This equation holds only when the pressure remains constant during the change in temperature. Gay-Lussac found also that the pressure p of a gas increases by the same fraction a of the pressure at 0° if the volume be kept constant during heating, so that... 

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