The inversion of cane sugar proceeds with half-life of 500 min at pH = 5 for any concentration of sugar. However, if pH = 6, the half-life changes to 50 min.Expression for the rate law for sugar inversion is

At, pH = 5, the half-life is 500 min for all concentration of sugar, i.e. t1/2∝[ sugar ]. Thus, the reaction is of first order with respect to sugar.Now,           rate =k[ sugar ]1H+mAlso for         H+t1/2∝H+1−m                 ∴ 500∝10−51−m              …….(i)                          50∝10−61−m                …….(ii)∴ 10=(10)(1−m) or (1−m)=1          m=1−1=0     rate =k[ sugar ]1H+0