Gases volume-amount relationships

It is possible to combine Avogadro s law and the combined gas law to produce the ideal gas equation, which incorporates the pressure, volume, temperature, and amount relationships of a gas. The ideal gas equation has the form of... 

In the later part of the eighteenth century, French chemist Jacques Charles studied the relationship between the volume of a fixed amount of gas and its temperature, while keeping the gas at constant pressure. He found that V was a linear function of the temperature. Figure 2 graphically represents this relationship, known as Charles s law, with a plot of the gas volume versus the temperature in Celsius, t. 

What does Avogadro s law state about the relationship between gas volumes and amounts in moles ... 

Robert Boyle (1627-1691), an Irish chemist, did experiments like the one shown in Figure 14-2 to study the relationship between the pressure and the volume of a gas. By taking careful quantitative measurements, he showed that if the temperature is constant, doubling the pressure of a fixed amount of gas decreases its volume by one-half. On the other hand, reducing the pressure by half results in a doubling of the volume. A relationship in which one variable increases as the other variable decreases is referred to as an inversely proportional relationship. For help with understanding inverse relationships, see the Math Handbook page 905. 

The French scientist Jacques Charles (1746-1823) didn t have liquid nitrogen, but he was a pioneer in hot-air ballooning. He investigated how changing the temperature of a fixed amount of gas at constant pressure affected its volume. The relationship Charles foimd can be demonstrated, as shown in Figure 11.11. 

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. 

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. 

Three key relationships exist among the four gas variables—Boyle s, Charles s, and Avogadro s laws. Each of these gas laws expresses the effect of one variable on another, with the remaining two variables held constant. Because gas volume is so easy to measure, the laws are expressed as the effect on gas volume of a change in pressure, temperature, or amount of gas. 

The modem statement of the volume-temperature relationship is known as Charles s law at constant pressure, the volume occupied by a fixed amount of gas is directly proportional to its absolute (Kelvin) temperature, or... 

The pressure-temperature relationship. Charles s law is expressed as the effect of a temperature change on gas volume. However, volume and pressure are interdependent, so the effect of temperature on volume is closely related to its effect on pressure (sometimes referred to as Amontons s law). Measure the pressure in your car s tires before and after a long drive, and you will find that it has increased. Frictional heating between the tire and the road increases the air temperature inside the tire, but since the tire volume doesn t change appreciably, the air exerts more pressure. Thus, at constant volume, the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature ... 

Boyle s law applies to changes in volume with changes in pressure only when the temperature remains constant. Gas volume increases when the temperature is raised. The quantitative relationship between gas volume and temperature with the pressure held constant was first studied by J. Charles. He showed that there is a linear relationship between gas volume and Celsius temperature. The variation of volume of the same amount of a gas with changes in temperature in Celsius degrees at three different pressures is plotted in Fig. 5-3. The significant discovery made obvious with this treatment of the data was that extrapolation of the data for all pressures intersected the temperature axis at -273.15 °C, which corresponds to a volume of zero. To simplify our work, we will use the value... 

What does Charles s law tell us about how the volume of a gas sample varies as the temperature of the sample is changed How does this volume-temperature relationship differ from the volume-pressure relationship of Boyle s law Give two mathematical expressions that describe Charles s law. For Charles s law to hold true, why must the pressure and amount of gas remain the same Sketch the general shape of a graph of volume versus temperature (at constant pressure) for an ideal gas. 

The general relationship between the amount of gas (volume, V) adsorbed by a solid at a constant temperature (T) and as a function of the gas pressure (P) is defined as its adsorption isotherm. It is also possible to study adsorption in terms of V and T at constant pressure, termed isobars, and in terms of T and F at constant volume, termed isosteres. The experimentally most accessible quantity is the isotherm, although the isosteres are sometimes used to determine heats of adsorption using the Clausius-Clapeyron equation. In addition to the observations on adsorption phenomena noted above, it was also noted that the shape of the adsorption isotherm changed with temperature. The problem for the physical chemist early in the twentieth century was to correlate experimental facts with molecular models for the processes involved and relate them aU mathematically. 

Apparatus for studying the relationship between pressure and volume of a gas. (a) The levels of mercury are equal and the pressure of the gas is equal to the atmospheric pressure (760 mmHg). The gas volume is 100 mL. (b) Doubling the pressure by adding more mercury reduces the gas volume to 50 mL. (c) Tripling the pressure decreases the gas volume to one-third of the original volume. The temperature and amount of gas are kept constant. 

Boyle s law relates gas volume to pressure, and Avogadro s law relates gas volume to amount (mol). State a relationship between gas pressure and amount (mol). 

The graph shows gas volume versus temperature fora given mass of gas at 1.00 atm pressure. This linear relationship is independent of amount or type of gas. Note that all lines extrapolate to -273°C at zero volume. 

Table 11.3 gives a set of data typical of Boyle s experiments. Figure 11.8(a) and (b) shows some of the volume data plotted as a function of pressure and as a function of the inverse of pressure, respectively. These data illustrate 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. This inverse relationship between pressure and volume can be expressed mathematically as follows ... 

Suppose that you are going to take a ride in a hot-air balloon. The captain turns on a propane burner to heat the air inside the balloon. As the air is heated, it expands and becomes less dense than the air outside, causing the balloon and its passengers to lift off. In 1787, Jacques Charles, a balloonist as well as a physicist, proposed that the volume of a gas is related to the temperature. This proposal became Charles s law, which states that the volume (T) of a gas is directly related to the temperature (K) when there is no change in the pressure (P) or amount (n) of gas. A direct relationship is one in which the related properties increase or decrease together. For two conditions, initial and final, we can write Charles s law as follows ... 

All of the pressure-volume-temperature relationships for gases that we have studied may be combined into a single relationship called the combined gas law. This expression is useful for studying the effect of changes in two of these variables on the third as long as the amount of gas (number of moles) remains constant. 

So far, we have discussed the relationships between volume and pressure, and volume and temperature, but we have considered only a constant amount of a gas. What happens when the amount of gas changes The volume of a gas sample (at constant temperature and pressure) as a function of the amount of gas (in moles) in the sample is shown in Figure 5.12 . We can see that the relationship between volume and amount is linear. As we might expect, extrapolation to zero moles shows zero volume. This relationship, first stated formally by Amadeo Avogadro, is Avogadro s law. 

Figure 6-7 pictures a fixed amount of gas confined in a cylinder. The pressure is held constant at 1 atm while the temperature is varied. The volume of gas increases as the temperature is raised and decreases as the temperature is lowe. The relationship is linear. Figure 6-7 shows the linear dependence of volume on temperature for three gases at three different initial conditions. One point in common to the three lines is their intersection with the temperature axis. Although they differ at every other temperature, the gas volumes all reach a value of zero at the same temperature. The temperature at which the volume of a hypothetical ... 

Concentration The amount of a substance present in a given volume of a gas or liquid, in parts per million (ppm) or jLg m . In the case of gases, the ppm is proportional to the molecular concentration, hence the relationship between ppm and pg m " depends on the molecular weight of the gas concerned. 

It is helpful to understand the relationship of vacuum to the other pressure measurements. Vacuums can range from atmospheric pressure down to zero absolute pressure , representing a perfect vacuum (a theoretical condition involving the total removal of all gas molecules from a given volume). The amount of vacuum is measured with a device called a vacuum gage. 

In the lsO-incorporation experiment of Cypridina bioluminescence, the effects of the O atom exchange and contaminating CO2 are clearly seen in the relationship between the amount of luciferin luminesced and the amount of lsO atoms incorporated into the product CO2 (Fig. 1.14 Shimomura and Johnson, 1973a). The experiments were done in glycylglycine buffer, pH 7.8, the same buffer as chosen by DeLuca and Dempsey (1970). The total volume of the reaction mixture was 4 ml, with 40 ml of gas phase (see the reaction vessel in Fig. A.5 in the Appendix). The data of the luminescence reaction with 1802 gas in the H2160 medium indicates that at least 1 pmol of... 

Because moles are the currency of chemistry, all stoichiometric computations require amounts in moles. In the real world, we measure mass, volume, temperature, and pressure. With the ideal gas equation, our catalog of relationships for mole conversion is complete. Table lists three equations, each of which applies to a particular category of chemical substances. 

Background This experiment uses the concept of continuous variation to determine mass and mole relationships. Continuous variation keeps the total volume of two reactants constant, but varies the ratios in which they combine. The optimum ratio would be the one in which the maximum amount of both reactants of known concentration are consumed and the maximum amount of product(s) is produced. Since the reaction is exothermic, and heat is therefore a product, the ratio of the two reactants that produces the greatest amount of heat is a function of the actual stoichiometric relationship. Other products that could be used to determine actual molar relationships might include color intensity, mass of precipitate formed, amount of gas evolved, and so on. 

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