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* 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)* e^{-(1.8* 10^(-4))* (16920)}`

`[C_t]=0.0106M`

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

`n_o=[C_o]* V=0.223M* 2.15L=0.479moles`

`n_t=[C_t]* V=0.0106M* 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}* \text{ Molar mass of sucrose}`

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

Therefore, the mass of sucrose consumed is 156.1 grams.