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:
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
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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