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. Assuming the reaction is first order in sucrose, determine the mass of sucrose that is hydrolyzed when 2.40 L of a 0.180 M sucrose solution is allowed to react for 200 minutes.

Answer 1

we have relation for 1st order

t = ( 1/k) ln ( a/a-x)

where t = time = 200 min = 200 x 60 sec = 12000 s

k = 1.8 x 10^ -4 s-1 ,

a = initial concentration = 0.18 , we find a-x = final conc after t = 200 min

hence now 12000 = ( 1/1.8x10^-4) ln ( 0.18 / a-x)

a-x = 0.02076 M

Moles of sucrose = M x V = 0.02076 x 2.4 =0.04982

Mass of sucrose left = moles x molar mass of sucrose = 0.04982 x 342.3 = 17.05 g

Initial mass of sucrose = initial moles x molar mass = ( 0.18x2.4) x 342.3 = 147.874 g

sucrose hydrolysed = 147.874-17.05 = 130.8 g