Real Vs Ideal Gases 2
Study of Deviations
To understand the deviations from ideal behaviour, let us first see how the real gases show deviations from Boyle’s law. According to Boyle’s law, PV = constant, at constant temperature. Hence, at constant temperature, plot of PV vs. P has to be a straight line which is parallel to x-axis. However, the real gases do not show such a behaviour as shown in figure no. 1 below.
Fig No. 1 PV vs P for Real and Ideal Gas
From the plots, we observe that for gases like H2 and He, PV increases continuously with increase of pressure whereas for gases like CO, CH4 etc. PV first decreases with increase of pressure and reaches a minimum value and then increases continuously with increase of pressure. Similarly, if we plot experimental values of pressure versus volume at constant temperature (that is, for real gas) and theoretically calculated values from Boyle’s law (that is,for ideal gas) the two curves do not coincide as shown in figure no. 2.
Fig. No. 2 Pressure vs Volume for Real and Ideal Gas
From above graphs, we observe that at higher pressure, volume which is observed is higher than that of calculated volume. At lower pressures, the observed and the calculated volumes approach each other.
Alternatively, upto what extent a real gas deviates from ideal behaviour can be studied using the terms of a quantity ‘Z’ which is known as the compressibility factor, and defined as:
(i) For an ideal gas, as PV = nRT, Z = 1
(ii) For a real gas, as PV ≠ nRT, Z ≠ 1.
Hence, two cases arise:
(a) When Z < 1, (For Example: for CH4, CO2 etc.) The gas is said to show negative deviation. Therefore gas will show more compression than expected from ideal behaviour.
This is caused by predominance of attractive forces among the molecules of these gases.
(b) When Z > 1, the gas is said to show positive deviation. This implies that the gas will show less compression than expected from ideal behaviour.
This is caused by the predominance of the strong repulsive forces among the molecules. Greater the departure in the value of Z from unity, greater are the deviations from ideal behaviour.
At the same temperature and pressure, the extent of deviation depends upon the nature of the gas, as shown in figure no. 3 Thus, at intermediate pressures, CO2 shows much larger negative deviation than H2 or N2.
Fig. No. 3 Z vs P for Different Gases
For the same gas, at a particular pressure, the extent of deviation depends upon temperature, as shown in figure no. 4 for the case of N2 gas.
Fig. No. 4 Z vs P for N2 gas at different temperatures
Plots in fig. no. 4 show that as the temperature increases, the minimum in the curve shifts upwards. Ultimately, a temperature is reached at which the value of Z remains close to 1 over an appreciable range of pressure. For Example, in case of N2, at 323 K, the value of Z remains close to 1 upto nearly 100 atmospheres.
The temperature at which a real gas behaves like an ideal gas over an appreciable pressure range is called Boyle temperature or Boyle point.
Further, from the plots shown in figure no. 3 and 4, it may be seen that at ordinary pressures (1-10 atm), Z is very near to 1, that is, the deviations from ideal behaviour are so small that the ideal gas laws can be applied.
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