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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
The mass of sucrose is 96.96g.
Given:
The reaction is first order.
Time, t= 190min
Unit conversion:
t = 190 * 60 = 11400 s (since, 1 min=60 secs)
The value of rate constant, [tex]k = 1.8 * 10^-4 s^{-2}[/tex]
To find:
Mass=?
A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant.
From equation of first order kinetics:
[tex]ln[A] - ln[A]_0 = - kt\\\\ln[A] = - kt + ln[A]_0\\\\ln[A] = - ( 1.8 * 10^{-4} * 11400) + ln (0.130)\\\\ln[A] = - 2.052 - 2.04\\\\\text{[A]} = 0.0167M\\[/tex]
- 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
[tex]\text{Mass} = 0.28325 * 342.30 g/mol \\\\\text{Mass}= 96.96g[/tex]
Thus, the mass of sucrose that is hydrolyzed will be 96.9grams.
Find more information about "First order kinetics" here:
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