question_answer 63)

  The relation between pressure exerted by an ideal gas\[({{p}_{deal}})\] and observed pressure \[({{p}_{real}})\] is given by the equation : \[{{p}_{ideal}}={{p}_{real}}+\frac{a{{n}^{2}}}{{{V}^{2}}}\] If pressure is taken in\[N{{m}^{-2}}\], number of moles in mol and volume in\[{{m}^{3}}\]. Calculate the unit of ?a'. What will be the unit of ?a' when pressure is in atmosphere and volume in \[d{{m}^{3}}\]?

Answer:

  (i) Unit of \['a'=\frac{({{p}_{ideal}}-{{p}_{real}}){{V}^{2}}}{{{n}^{2}}}=\frac{N{{m}^{-2}}\times {{m}^{6}}}{mo{{l}^{2}}}\] \[=N{{m}^{4}}mo{{l}^{-1}}\] (iii) Unit of \['a'=\frac{atm\times d{{m}^{6}}}{mo{{l}^{2}}}=atmd{{m}^{6}}mo{{l}^{-2}}\]