Question

The hydrolysis of sucrose (C12H22O11) into glucose and fructose in acidic water has a rate constant of 1.8×10−4s−1 at 25 ∘C.

1) Assuming the reaction is first order in sucrose, determine the mass of sucrose that is hydrolyzed when 2.75 L of a 0.160 M sucrose solution is allowed to react for 195 minutes.

Answer 1

For first order reaction in aqueous medium, the equation relating conversion (XA), time(t) and rate constant k is given by

-ln (1-XA)= kt      (1)

XA= 1-CA/CAO

given k= 1.8*10-4/s and t= 195 minutes=195*60 sec=11700 sec

at t= 11700 sec -ln (1-XA)= 1.8*10^-4*11700=2.106

1- XA= exp(-2.106)= 0.1217= CA/CAO where CA= concentration at time t =11700 sec and CAO = initial concentration= 0.16M

CA/CAO= 0.1217 CA=0.1217*0.16= 0.019472

Intialm moles of sucrose= 0.16*2.75=0.44 moles, final moles = 0.019472*2.75= 0.003116 M

Molecular weight of sucrsoe (C12H22O11)= 12*12+22+16*11=342

Mass of sucrose hydrolyzed = (0.44-0.003116)* Molecular weight of sucrose = 149.41 gms