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# 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

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a
r=k[ sugar ]1H+0
b
r=k[ sugar ]0H+1
c
r=k[ sugar ]2H+0
d
r=k[ sugar ]1H+1

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detailed solution

Correct option is A

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

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Following data is given for the reaction,$\mathrm{X}+\mathrm{Y}\to \mathrm{P}$