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Write the Van der Waals equation for a real gas. Explain the correction term for pressure and volume. |
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Answer» Solution :The vander equation for a real gas is `(P+(an^(2))/(V^(2)))(V-nb)=nRT` Pressure correction : the pressure of a gas is directly proportional to the FORCE created by the bombardment of molecules on the walls ofthe container. The speed of a molecule moving towards the wallof the container is REDUCED by the attractive Force EXERTED by is neighbours. Hence , the MEASURED gas pressure is lower than the ideal pressure of the gas. Hence, van der waals introduced a correction term to this effect .  Van der Waal' s found out the forces of attraction experienced by a molecule near the wall are directly proportional to the square of the the density of the gas `P'" a "r^(2)` `rho=n/V` When n is the number of moles of gas and V is the volume of the container `impliesP'alpha(n^(2))/(V^(2))` `P'=(an^(2))/(V^(2))` Where a is proportionality. Constant and depends on the natural of gas Therefore , `P_("ideal")=P+(an^(2))/(V^(2))` Volume correction: As very individual molecule of a gas occupies a certain volume. The actual volume is less than the volume of the container, V Van der waals introduced acorrection factorV ' to this effect . LET uscalculate the correction term by. Considering gas molecules as spheres.  V = excluded volume Excluded volume for two molecules `4/3pi(2r)^(3)` `=8(4/3pir^(3))=8v_(m)` Where v is a volume of a single molecule Excluded volume for single molecule `(8V_(m))/(2)=4V_(m)` Excluded volume for n molecule= `n(4V_(m))=nb` Where b is van der waals constant which is equal to `4V_(m)` `impliesV=nb` `V_("ideal")=V-nb` Replacing the corrected pressure and volume in the ideal gas equation of state for real gases as below. `(P+(an^(2))/(V^(2)))(V-nb)=nRT` The constants a and b are van der waals constants and their values vary with the natural of the gas. It is an appointment formula for the non- ideal gas. |
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