Structure of Liquids The structure of liquids is less well established than that of gases or solids. To understand the structure of liquids, we will consider the theories of liquid state and other various approaches. 1.  Vacancy Theory of Liquids A Liquid is generally less dense than the corresponding solid; \(\implies\) intermolecular space in a … Read more
 liquefaction of gases For liquefaction of gases having fairly high critical temperature e.g. ammonia, chlorine, sulphur dioxide and carbon dioxide, the application of a suitable pressure alone is sufficient. For liquefaction of permanent gases which have very low critical temperature e.g. hydrogen, oxygen, nitrogen, helium etc. application of pressure alone will not bring liquefaction but … Read more
Critical Compressibility Factor (\({Z}_c\)) The critical Compressibility factor \({Z}_c\) of a van der Walls gas is given by, \({Z}_c=\frac{{P}_c{V}_c}{R{T}_c}\)Â Â Â Â Â Â Â Â Â Â Â (1)Â Â Â Â Â As we know, $${P}_c=\frac{a}{27{b}^2}$$ $${V}_c=3b$$ $${T}_c=\frac{8a}{27Rb}$$ By putting the value of \({P}_c, {V}_c\) and \({T}_c\)Â in equation 1 : $$\Rightarrow{Z}_c=\frac{(\frac{a}{27{b}^2})(3b)}{{R}[\frac{8a}{27Rb}]}$$ $$\Rightarrow{{Z}_c=\frac{3}{8}}$$ $$\Rightarrow\fbox{\({Z}_c\)=0.375}$$ Note- We can test whether a gas behaves as a van der Waals gas … Read more
Relationship Between Critical Constants And Vander Waal’s Constants Vanderwaals equation for one mole of gas is, \( \left( {P + \frac{{a}}{{V^2 }}} \right)\left( {V – n} \right) = RT \) \(PV+\frac{a}{V}-Pb-\frac{ab}{V^2}=RT\) Multiplying both sides by \(\frac{V^2}{P}\) and arranging the obtained equation in decreasing powers of V, we get \(V^3-(b+\frac{RT}{P})V^2 +\frac{aV}{P} -\frac{ab}{P}=0\tag1\\\) viz., a cubic equation … Read more
The Isotherms of van der Wall’s Equation As we know, the Vanderwaals equation for one mole of gas is, \( \left( {P + \frac{{a}}{{V^2 }}} \right)\left( {V – b} \right) = RT \) ⇒\(PV+\frac{a}{V}-Pb-\frac{ab}{V^2}=RT\) Multiplying both sides by \(\frac{V^2}{P}\) and arranging the obtained equation in decreasing powers of V, we get \(\fbox{\(V^3-(b+\frac{RT}{P})V^2 +\frac{aV}{P} -\frac{ab}{P}=0\)}\) viz., … Read more
 CONTINUITY OF STATE At the critical temperature, the gaseous \(C{O}_2\) cannot be distinguished from liquid carbon dioxide which indicates that the conversion of \(C{O}_2\) gas into liquid \(C{O}_2\) or vice versa is not a sharp or discontinuous process but is a continuous process. As shown in the figure, if the ends of the horizontal portions … Read more
 PV ISOTHERM OF REAL GASES The plots of pressure vs volume at a given temperature of real gases are called P-V isotherms In 1869, Thomas Andrews studied the critical phenomenon in detail. He measured the variation of volume of \(C{O}_2\) with pressure at different temperatures. The first complete data on P-V isotherms of \(C{O}_2\) was … Read more
Critical Temperature Critical Pressure Critical Volume and their Determination THE CRITICAL PHENOMENON • According to kinetic theory of gases, the gas molecules are constantly moving. ∴ the gas molecules possess kinetic energy. • average kinetic energy of the molecules is directly proportional to the absolute temperature. • Average K.E \(\propto\) absolute temperature. i.e., As the temperature decreases, the kinetic … Read more
Explanation of Behaviour of Real Gases Using Vander Waal’s Equation As we know the Van der Walls equation for n moles of a real gas is, \( \left( {P + \frac{{an^2 }}{{V^2 }}} \right)\left( {V – bn} \right) = nRT \) For one mole of gas, put n=1, \( \left( {P + \frac{{a}}{{V^2 }}} \right)\left( … Read more
Application of Vanderwaals Equation in Calculation of Boyle’s temperature Consider the Z vs P plots of nitrogen at different temperatures varying between – 70°C and 50 °C • The graph shows that as the temperature is raised, the dip in the curve becomes smaller and smaller. At 50°C the curve is almost horizontal for an … Read more
