Question

The hydrolysis of sucrose (C12H22011) into glucose and fructose in acidic solution is a first-order reaction with a rate constant of 1.8 x 10-45-1 at 25°C. Determine the mass (g) of sucrose that is consumed when 2.15 L of a 0.223 M sucrose solution is allowed to react for 282 minutes. Enter your answer as an integer. Previous Next Not saved Submit Qu.

Answer 1

Answer : The mass of sucrose consumed is 156.1 grams.

Explanation :

The expression for first order reaction is:

$[C_t]=[C_o]e^{-kt}$

where,

$[C_t]$ = concentration of sucrose at time 't'

$[C_o]$ = concentration of sucrose at time '0' = 0.223 M

k = rate constant = $1.8\times 10^{-4}s^{-1}$

t = time = 282 min = 16920 s    (1 min = 60 s)

Now put all the given values in the above expression, we get:

$[C_t]=(0.223)\times e^{-(1.8\times 10^{-4})\times (16920)}$

$[C_t]=0.0106M$

Now we have to calculate the initial and final moles of sucrose.

$n_o=[C_o]\times V=0.223M\times 2.15L=0.479moles$

$n_t=[C_t]\times V=0.0106M\times 2.15L=0.0228moles$

Number of moles of sucrose hydrolysed = $n_o-n_t$

Number of moles of sucrose hydrolysed = $0.479-0.0228=0.456mole$

Now we have to calculate the mass of sucrose used.

$\text{ Mass of sucrose}=\text{ Moles of sucrose}\times \text{ Molar mass of sucrose}$

$\text{ Mass of sucrose}=(0.456moles)\times (342.3g/mole)=156.1g$

Therefore, the mass of sucrose consumed is 156.1 grams.