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 2.45 L of a 0.170 M sucrose solution is allowed to react for 195 min.

Explanation:

k = 1.8 x 10⁻⁴ s⁻¹

no of moles initially = 2.45 x .17 = .4165 moles

initial moles a = .4165

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

a is initial moles , x is moles reacted .

a is initial moles , x is moles reacted .

time t = 195 min = 11700 s

1.8 x 10⁻⁴ = 1 / 11700 x ln .4165 /( .4165 - x )

2.106 = ln .4165 /( .4165 - x )

.4165 /( .4165 - x ) = e²°¹⁰⁶ = 8.215

.4165 = 3.42 - 8.215 x

8.215 x = 3.0035

x = .3656

moles of sucrose hydrolysed = .3656 moles.