Volume calculations involving gases

In calculations that involve gas pressure and volume, absolute pressure or pounds per square inch absolute (psia) must be used. 

When making calculations, we will generally convert all data to their values in SI units, since calculations involving SI units give answers in SI units. For example, when calculating the volume of an ideal gas from the equation... 

Ans. The volume of the gas is 2.7 L. The second method involves merely reading a point from a graph. To use Fig. 11-3, you first have to calculate the reciprocal of the pressure. None of the methods is difficult, however. 

There are circumstances where weight is an important factor (Example 3), but the calculations involving gases may be in terms of volumes of gases involved. The conversion from volumes of gas to mass is done through the numbers of moles. The methods used in these problem solutions are as in Chapter 4 except that the numbers of moles converted to mass (g, lb, etc.) must be determined from the volume, temperature, and pressure of the gases. 

When a flammable material is burned, there will be an increase in either the volume of the gas produced (provided the pressure is constant) or the pressure in the container (provided the volume is constant). Calculate the volume of gas formed during the adiabatic combustion of 100 lb moles of gaseous propane at a constant pressure of 1 atm. Assume that the 200 percent theoretical air and the propane involved in the combustion are at 25°C and that the combustion goes to completion. 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

Note that in Example 5.6 the final step involved calculation of the volume of gas from the number of moles. Since the conditions were specified as STP, we were able to use the molar volume of a gas at STP. If the conditions of a problem are different from STP, the ideal gas law must be used to calculate the volume. 

An equation of state relates the molar quantity and volume of a gas to temperature and pressure. The simplest and most widely used of these relationships is the ideal gas equation of state (the familiar PV = nRT), which, while approximate, is adequate for many engineering calculations involving gases at low pressures. However, some gases deviate from ideal behavior at nearly all conditions and all gases deviate substantially at certain conditions (notably at high pressures and/or low temperatures). In such cases it is necessary to use more complex equations of state for PVT calculations. 

Here TJ and v are the energy and the volume of a monatomic gas consisting of N molecules. is a constant independent of the energy and the volume, but involving the number and mass of the molecules, and also depending on the manner in which the probabihty w is calculated. 

There are ways other than density to include volume in stoichiometry problems. For example, if a substance in the problem is a gas at standard temperature and pressure (STP), use the molar volume of a gas to change directly between volume of the gas and moles. The molar volume of a gas is 22.41 L/mol for any gas at STP. Also, if a substance in the problem is in aqueous solution, then use the concentration of the solution to convert the volume of the solution to the moles of the substance dissolved. This procedure is especially useful when you perform calculations involving the reaction between an acid and a base. Of course, even in these problems, the basic process remains the same change to moles, use the mole ratio, and change to the desired units. 

The ideal gas law relates amount of gaseous substance in moles, n, with the other gas variables pressure, volume, and temperature. Now that you have learned how to use the ideal gas law, an equation that relates the number of moles of gas to its volume, you can use it in calculations involving gases that react. 

Boyle s, Charles s, and Gay-Lussac s laws are brought together in the combined gas law, which permits calculations involving changes in the three gas variables of pressure, volume, and temperature. 

Use the ideal gas law to relate pressure, volume, temperature, and nnmber of moles of an ideal gas and to do stoichiometric calculations involving gases (Section 9.3, Problems 19-32). 

This is slightly above typical room temperature. Notice that these thermodynamic standard conditions are not the same as the standard temperature and pressure (STP) that we used in gas calculations involving standard molar volume (Chapter 12). 

The combined gas law provides a convenient expression for performing gas law calculations involving the most common variables pressure, volume, and temperature. 

The basic calculation involves a determination of the maximum error in moles adsorbed due to uncontrolled fluctuations in system pressure, temperature, and volume and a comparison of the weight of adsorbent or catalyst necessary to adsorb the number of moles of gas which would exactly compensate for the maximum error fluctuation (also expressed in moles). 

To understand how the pressure and volume of a gas are related To do calculations involving Boyle s law To learn about absolute zero... 

Describes how to perform chemical calculations, involving masses and gas volumes using moles... 

To learn about absolute zero. To learn about the law relating the volume and temperature of a sample of gas at constant moles and pressure, and to do calculations involving that law. 

Hence in the calculation of energy changes for processes in a perfect gas one can ignore any effect due to a change in volume. This greatly simplifies the calculations involved because one can drop the first term of eqn 2.40 and need wwk only with dU = Cy dT. In a more sensitive apparatus. Joule would have observed a small temperature change upon expansion of the real gas. Joule s result holds exactly only in the limit of zero pressure where all gases can be considered perfect... 

Be aware that the definition of pH just shown, and indeed aU the calculations involving solution concentrations (expressed either as molarity or molality) discussed in previous chapters, are subject to error because we have implicitly assumed ideal behavior, hi reality, ion-pair formation and other types of intermolecular interactions may affect the actual concentrations of species in solution. The situation is analogous to the relationships between ideal gas behavior and the behavior of real gases discussed in Chapter 5. Depending on temperature, volume, and amount and type of gas present. 

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