Question

The relation between pressure exerted by an ideal gas (P_ideal) and observed pressure (P_real) is given by the equation

P_ideal = P_real + `(an^2)/V^2`

If pressure is taken in Nm^–2, number of moles in mol and volume in m³, Calculate the unit of ‘a’. What will be the unit of ‘a’ when pressure is in atmosphere and volume in dm3?

Answer 1

P_ideal = P_real + `(an^2)/V^2`

Unit of ‘P’ = Nm^–2

∴ Unit of ‘a’ =  Nm^–2 × (m³)²/(mol)²

= Nm⁴ mol^–2

Unit of ‘a’ when pressure is in atm, and volume in dm3 

Unit of ‘P’ = atm

∴ Unit of ‘a’ = atm × (dm³)²/(mol)²

= atm(dm⁶) mol^–2