Assuming the reaction is first order in sucrose, determine the mass of sucrose that is hydrolyzed when 2.50 L of a 0.130 M sucrose solution is allowed to react for 190 min.

Full Question:

The hydrolysis of sucrose C12H22O11 into glucose and fructose in acidic water has a rate constant of 1.8 x 10^-4 s^-2 at 25 C.

Assuming the reaction is first order in sucrose, determine the mass of sucrose that is hydrolyzed when 2.50 L of a 0.130 M sucrose solution is allowed to react for 190 minutes.

Answer:

96.96g

Explanation:

t = 190 x 60 = 11400 s (upon conversion to seconds)

k = 1.8 x 10^-4 s^-2

ln[A] - ln[A]o = - kt

ln[A] = - kt + ln[A]o

ln[A] = - (1.8 x 10^-4 * 11400) + ln (0.130)

ln[A] = - 2.052 - 2.04

[A] = 0.0167M

initial moles = 2.50 x 0.130 = 0.325

moles after 190 min = 0.0167 x 2.50 = 0.04175

moles hydrolyzed = 0.325 - 0.04175 = 0.28325

mass = 0.28325 x 342.30 g/mol = 96.96g