Ideal gases, real versus

Kinetic-Molecular Theory and Ideal Versus Real Gases Postulates of the Model Real Gases and Limitations... 

At the Boyle temperature the Z versus p curve is tangent to the curve for the ideal gas at p = 0 and rises above the ideal gas curve only very slowly. In Eq. (3.8) the second term drops out at 7, and the remaining terms are small until the pressure becomes very high. Thus at the Boyle temperature the real gas behaves ideally over a wide range of pressures, because the effects of size and of intermolecular forces roughly compensate. This is also shown in Fig. 3.4. The Boyle temperatures for several different gases are given in Table 3.2. 

We will examine the experimentally observed behavior of real gases by measuring the pressure, volume, temperature, and number of moles for a gas and noting how the quantity PV/nRT depends on pressure. Plots of PV/nRT versus P are shown for several gases in Fig. 5.22. For an ideal gas PV/nRT equals 1 under all conditions, but notice that for real gases PV/nRT approaches 1 only at low pressures (typically 1 atm). To illustrate the effect of temperature, we have plotted PV/nRT versus P for nitrogen gas at several temperatures in Fig. 5.23. Notice that the behavior of the gas appears to become more nearly ideal as the temperature is increased. The most important conclusion to be drawn from these plots is that a real gas typically exhibits behavior that is closest to ideal behavior at low pressures and high temperatures. 

No gas is truly ideal, but many gases follow the predictions of the ideal gas law at normal temperature and pressure (1.013 bar, 0°C) within 5% deviation. At lower temperatures or higher pressures, the behavior of a real gas may significantly deviate from that of an ideal gas, as shown in Figure 3.1.1 for the example of CO2 by the plot of p Vrnoi versus p. The ideal gas equation predicts that this plot should give horizontal lines that only depend on temperature, but we see by the experimental data that this is not the case (see also Example 3.1.1). 

A FIGURE 5.26 Real versus Ideal Behavior For 1 mol of an ideal gas, PV/RT is equal to 1. The combined effects of the volume of gas particles and the interactions among them cause each real gas to deviate from ideal behavior in a slightly different way. These curves were calculated at a temperature of 500 K. 

It should be quite obvious that, although the model provided in the form of the ideal gas law does a reasonable job at lower pressures, it rapidly deviates as the pressure increases and the volume decreases. We can see this more clearly in Figure 2.5, where we compare the real data with that derived from the ideal gas law in a scatter plot of p versus 1/v. We can see from our plot that the experimental data, shown as solid circles, are modelled reasonably well by a linear (straight line) function, but only for pressures less than 50 atm. The Boyle model is clearly of limited applicability in this case. 

We will examine the experimentally observed behavior of real gases by measuring the pressure, volume, temperature, and number of moles for a gas and noting how the quantity PV/nRT depends on pressure. Plots of PV/nRT versus P are shown for several gases in Fig. 5.22. For an ideal gas PV/nRT equals 1 under all conditions, but notice that for real gases PV/nRT approach -... 

Real versus ideal gases What does the term ideal gas mean An ideal gas is one whose particles take up no space and have no intermolecular attractive forces. An ideal gas follows the gas laws under all conditions of temperature and pressure. 

FIGURE5.19 Plot of PV/RT versus P of 1 mole of a gas at CPC. For 1 mole of an ideal gas, PV/RT is equal to I, no matter what the pressure of the gas is. For real gases, we observe various deviations from ideality at high pressures. At very low pressures, all gases exhibit ideal behavior that is, their PV/RT values all converge to I as P approaches zero. 

Figure 38.5 Graphs of gas) o(reaigas)j] versus f for real gases and of [( weaigas) oodeaigas)] versus P for ideal gases superimposed. Also when 0 = 1, ln0 = 0 and f = P (Figure 38.4) ...

Plot P= i< versus Hl and on the same graph plot P < versus Hv. This will give the vapor-liquid boundary. To add isotherms, first tabulate H at various pressures. Start at a pressure close to the ideal-gas state and calculate the enthalpy. If the compressibility equation has three real roots, use the largest one, since the calculation is done for the vapor. Increase the pressure in small steps and repeat the calculation until you reach P-. Past P = P use the smallest root, since the calculation is now done for the liquid. The isotherm is obtained by plotting the results of this calculation as P versus H. 

The phenomena that cause slight deviations under standard conditions exert more influence as the temperature deaeases and pressure increases. Figure 5.21 shows a plot of PV/RT versus external pressure (P xt) for 1 iriol of several real gases and an ideal gas. The values on the horizontal axis are the external pressures at which the PV/RT ratios were calculated. The PV/RT values range from normal (at P xt = 1 atm, PV/RT = 1) to very high (at P xt 10(X) atm, PV/RT == 1.6 to 2.3). For the ideal gas, PV/RT is 1 at any P xf... 

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