Amount-volume relationship

The amount-volume relationships of ideal gases are described by Avogadro s law Equal volumes of gases contain equal numbers of molecules (at the same T and P). 

The pressure-volume relationships of ideal gases are governed by Boyle s law Volume is inversely proportional to pressure (at constant T and ri). The temperature-volume relationships of ideal gases are described by Charles s and Gay-Lussac s law Volume is directly proportional to temperature (at constant P and n). Absolute zero (-273.15°C) is the lowest theoretically attainable temperature. On the Kelvin temperature scale, 0 K is absolute zero. In all gas law calculations, temperature must be expressed in kelvins. The amount-volume relationships of ideal gases are described by Avogadro s law Equal volumes of gases contain equal numbers of molecules (at the same T and P). 

We generally distinguish between two methods when the determination of the composition of the equilibrium phases is taking place. In the first method, known amounts of the pure substances are introduced into the cell, so that the overall composition of the mixture contained in the cell is known. The compositions of the co-existing equilibrium phases may be recalculated by an iterative procedure from the predetermined overall composition, and equilibrium temperature and pressure data It is necessary to know the pressure volume temperature (PVT) behaviour, for all the phases present at the experimental conditions, as a function of the composition in the form of a mathematical model (EOS) with a sufficient accuracy. This is very difficult to achieve when dealing with systems at high pressures. Here, the need arises for additional experimentally determined information. One possibility involves the determination of the bubble- or dew point, either optically or by studying the pressure volume relationships of the system. The main problem associated with this method is the preparation of the mixture of known composition in the cell. 

Gas-volume relationships The driver s air bag requires 0.0650 m of nitrogen to inflate—no more, no less. The passenger s air bag needs 0.1340 m. The pellet must have the exact amount of sodium azide needed to produce the correct amormt of nitrogen. As with all expanding gases, pressure and temperature affect the amount of sodium azide needed. Because the nitrogen gas is formed in an explosion, it has to be cooled before it goes into the air bag. 

Figure 3.10 Summary of mass-mole-number-volume relationships in solution. The amount (in moles) of a compound in solution is related to the volume of solution in liters through the molarity (M) in moles per liter. The other relationships shown are identical to those in Figure 3.4, except that here they refer to the quantities in solution. As in previous cases, to find the quantity of substance expressed in one form or another, convert the given information to moles first.

In the seventeenth century, Robert Boyle studied the behavior of gases systematically and quantitatively. In one series of studies, Boyle investigated the pressure-volume relationship of a gas sample. Typical data collected by Boyle are shown in Table 5.2. Note that as the pressure (P) is increased at constant temperature, the volume (V) occupied by a given amount of gas decreases. Compare the first data point with a pressure of 724 mmHg and a volume of 1.50 (in arbitrary unit) to the last data point with a pressure of 2250 mmHg and a volume of 0.58. Clearly there is an inverse relationship between pressure and volume of a gas at constant temperature. As the pressure is increased, the volume occupied by the gas dcCTcases. Conversely, if the applied pressure is decreased, the volume the gas occupies increases. This relationship is now known as Boyle s law, which states that the pressure of a fixed amount of gas at a constant temperature is inversely proportional to the volume of the gas. 

Boyle s Law, named after Robert Boyle, a seventeenth-century English scientist, describes the pressure-volume relationship of gases if the temperature and amount are kept constant. Figure 13-3 illustrates the pressure-volume relationship using the Kinetic Molecular Theory. 

J. L. Gay-Lussac (1778-1850) was a French chemist involved in the study of volume relationships of gases. The three variables [pressure (P), volume (V), and temperature (T)] are needed to describe a fixed amount of a gas. Boyle s law (PV = k) relates pressure and volume at constant temperature Charles law (V = kT) relates volume and temperature at constant pressure. A third relationship involving pressure and temperature at constant volume is a modification of Charles law and is sometimes called Gay-Lussac s law (Figure 12.11). 

The Temperature Volume Relationship Charles s and Gay-Lussac s Law The Volume-Amount Relationship Avogadro s Law... 

Figure 3. Schematic illustration of the dependence of the amount of the external mechanical work (shown by shaded area) that a ventricle performs at a constant preload and under a constant contractility (i.e., a fixed slope of end-systolic pressure-volume relationship) on afterloaded arterial elastance E . Note that the shaded area becomes maximum when equals E .

That is, for a given amount of gas at a fixed temperature, Ihe pressure times the volume equals a constant. Table 5.3 gives some pressure and volume data for l.(XX) g O2 at 0°C. Figure 5.6 presents a molecular view of the pressure-volume relationship... 

Use the pressure-volume relationship Boyle s law) to determine the final pressure or volume when the temperature and amount of gas are constant. 

Boyle s law (named after Robert Boyle, a 17th-century English scientist) describes the pressure-volume relationship of gases if you keep the temperature and amount of the gas constant. The law states that there s an inverse relationship between the volume and air pressure (the collision of the gas pcirticles with the inside walls of the container) As the volume decreases, the pressure increases, and vice versa. He determined that the product of the pressure and the volume is a constant (k) ... 

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