The gas phase decomposition of COCl2, …

The order of reaction representing rate law  as  ,

Rate  =   k  [ COCl₂ ]^3/2   is  1.5

$\therefore$The unit for the rate constant  is   M ^-0.5 s^-1 

(where M represents  mole per litre or Molarity of the reactant ) 

   * It should  be noted that even though it is a gas phase reaction , where the change in pressure is conveniently measured during the course of a reaction , but still the rate constant is expressed in terms of change in concentration of the reactant  ( as per rate law ) in terms of moles per Litre (ie .M or molarity ) / unit of time .  The reason being that pressure is temperature as well as  unit dependent , where as concentration or molarity is always in moles per litre .

** The concentration of the reactant is easily calculated using  the relation  PV  =  nRT , or P  = ( n/V ) RT  

ie .   P  =  C RT     

 Explanation : 

THe unit for rate constant of a reaction is derived through dimensional analysis .

In this case since ,

 k  = Rate / [ A ] ⁿ 

(where ,  n  represents the order of reaction  

 k =Rate / [ COCl₂ ]^3/2

or,=  Rate /  [ COCl₂ ]^1.5

= ( concentration / time )  x  1 / (  concentration )^1.5 

= ( mol L^-1 ) s^-1 x  1 / ( mol L^-1 )^1.5 

=  [ ( mol L^-1 / { mol L^-1  ) x ( 1 / mol L^-1 )^0.5  }s^-1 

={ ( 1 / M )^0.5 } s ^-1 

or , =  M ^-0.5 s^-1 

[  where , mol L ^-1  , represents  molarity (M) of the reactant ]