In the thermal decomposition of a gaseous substance, the time taken for the decomposition of half of the reactants was 105 minutes when the initial pressure was 750 mm and 950 minutes when the initial pressure was 250 mm. Find the order of reaction.

Explanation

`(t_(1//2)) _1 = 105` minutes
`p_1 = 750 mm (t_(1//2))_2 = 950 ` minutes `: p_2 = 250 mm`
For a reaction of nth order,
`((t_(1//2))_1)/( (t_(1//2))_2)= ((a_2)/(a_1))^(n-1) = ((P_2)/(p_1))^(n-1) or (105 )/(950 )= ((250 )/(750 ))^(n-1)`
` or log"" (105)/(950 ) = log "" ((250 ) /(750 ))^(n-1) = (n-1) log ""((250 )/(750 ))`
` or (n-1) = (log"" (105)/(950 ))/(log"" (250 )/(750 )) = ( -0.9565 )/(-0.4771 )`
` or (n-1) =2.00 or n=2 +1=3`
hence , the reaction is of third order .