Concepts.for.GATE

  Equation of State for the Real Gases (van der Waals Equation) To explain the behaviour of real gases, J .D. van der Waals, in 1873, modified the ideal gas equation applying appropriate corrections so as to take into account The volume of the gas molecules The forces of attraction between the gas molecules He put forward the modified equation, known after him as van der Waals equation. The equation is For 1 mole of the gas, For n moles of the gas, Where ‘a’ and ‘b’ van der Waals constant.There values depend upon nature of gas. Significance of Van der Waals Constants Van der Waals constant ‘a’:  Its value is a measure of the magnitude of the attractive forces among the molecules of the gas. There would be large intermolecular forces of attraction if the value ‘a’, is large. Van der Waals constant ‘b’:  Its value is a measure of the effective size of the gas molecules. Its value is equal to four times the actual volume of the gas molecules. It is called  Excluded Volume  or  Co-volume .

  Significance of compressibility factor The significance of compressibility factor can be further understood from the following derivation: If the gas shows ideal behaviour, Substituting this value of nRT/P in eqn. (1), we get Thus, compressibility factor is defined as the ratio of the actual molar volume of the gas ( For Example:  experimentally observed value) to the calculated molar volume (considering it as an ideal gas) at the same temperature and pressure. Causes of Deviation from Ideal Behaviour As stated above, the real gases obey ideal gas equation (PV = nRT) only if the pressure is low the temperature is high. However, if the pressure is high or the temperature is low, the real gases show marked deviations from ideal behaviour. The reasons for such a behaviour shown by the real gases have been found to be as follows: The derivation of the gas laws (and hence of the ideal gas equation) is based upon the Kinetic Theory of Gases which in turn is based upon certain assumptions.

  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 H 2  and He, PV increases continuously with increase of pressure whereas for gases like CO, CH 4  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

  Ideal and Real Gases A gas which obeys the ideal gas equation, PV = nRT under all conditions of temperature and pressure is called an ‘ ideal gas ’.However, there is no gas which obeys the ideal gas equation under all conditions of temperature and pressure. Hence, the concept of ideal gas is only theoretical or hypothetical. The gases are found to obey the gas laws fairly well if the pressure is low or the temperature is high. Such gases are, therefore, known as ‘ Real gases .’ All gases are real gases. However, it is found that gases which are soluble in water or are easily liquefiable, e. g. CO 2 , SO 2 , NH 3  etc. show larger deviations than the gases like H 2 , O 2 , N 2  etc. Differences between Ideal Gas and Real Gas Ideal Gases Real Gases Ideal Gases obey all gas laws under all conditions of temperature and pressure. Real Gases obey gas laws only at low pressures and high temperature. The volume occupied by the molecules is negligible as compared to the total volume occupied