Problem: The hydrolysis of the sugar sucrose to the sugars glucose and fructose, C12H22O11 + H2O ⟶ C6H12O6 + C6H12O6 follows a first-order rate equation for the disappearance of sucrose: Rate = k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)(a) In neutral solution, k = 2.1 × 10−11 s −1 at 27 °C and 8.5 × 10−11 s −1 at 37 °C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 °C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature).

FREE Expert Solution

We’re being asked to determine the activation energy, the frequency factor, and the rate constant for this equation at 47 °C.


We’re given the rate constant at another temperature and the activation energy of the reaction. This means we need to use the two-point form of the Arrhenius Equation:

ln k2k1=-EaR[1T2-1T1]

where k1 = rate constant at T1
k2 = rate constant at T2
Ea = activation energy (in J/mol)
R = gas constant (8.314 J/mol•K)
T1 and T2 = temperature (in K)


Let's first calculate the activation energy:

T1 = 27°C + 273.15 300.15 K
T2 = 37°C + 273.15 310.15 K

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Problem Details

The hydrolysis of the sugar sucrose to the sugars glucose and fructose, C12H22O11 + H2O ⟶ C6H12O6 + C6H12O6 follows a first-order rate equation for the disappearance of sucrose: Rate = k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)

(a) In neutral solution, k = 2.1 × 10−11 s −1 at 27 °C and 8.5 × 10−11 s −1 at 37 °C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 °C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature).

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