Given the activation energy for hydrolysis of sucrose is 108*10'3kj/mol compare rate constant of this reaction at 37degree c (t1) with the rate constant of same reaction at 27degree c

Question

Given the activation energy for hydrolysis of sucrose is 108*10'3kj/mol compare rate constant of this reaction at 37degree c (t1) with the rate constant of same reaction at 27degree c

Answer 1

USE THE ARRHENIUS EQUATION. Post your work if you have trouble.

Answer 2

To compare the rate constants of a reaction at different temperatures, we can use the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea), temperature (T), and the gas constant (R).

The Arrhenius equation is given by:

k = A * exp(-Ea / (R * T))

Where:
k = rate constant
A = pre-exponential factor (frequency factor)
Ea = activation energy
R = gas constant (8.314 J/(mol*K))
T = temperature (in Kelvin)

Let's solve this step-by-step for the two given temperatures:

1. Convert the temperatures to Kelvin:
T1 = 37 degrees C + 273.15 = 310.15 K
T2 = 27 degrees C + 273.15 = 300.15 K

2. Plug the values into the equation to find the rate constants:
k1 = A * exp(-Ea / (R * T1))
k2 = A * exp(-Ea / (R * T2))

3. Since the pre-exponential factor (A) is not given, we can assume that it is the same for both temperatures. Therefore, we can compare the rate constants using the ratio:

k1 / k2 = (A * exp(-Ea / (R * T1))) / (A * exp(-Ea / (R * T2)))
= exp(-Ea / (R * T1)) / exp(-Ea / (R * T2))

4. Simplify the ratio by canceling out the A and rearranging the terms:
k1 / k2 = exp(-Ea / (R * T1) + Ea / (R * T2))

5. Combine the terms inside the exponent:
k1 / k2 = exp((-Ea * (T2 - T1)) / (R * T1 * T2))

6. Multiply the numerator and denominator by T1 * T2 to simplify further:
k1 / k2 = exp((-Ea * (T2 - T1)) / (R * T1 * T2)) * (T1 * T2) / (T1 * T2)
= exp((-Ea * (T2 - T1)) / (R * T1 * T2)) * (T1 * T2) / (T2 - T1)

Now you can substitute the values of Ea, R, T1, and T2 into the equation and calculate k1 / k2.

Answer 3

To compare the rate constants of the hydrolysis of sucrose at two different temperatures, we will use the Arrhenius equation:

k = Ae^(-Ea/RT)

Where:
k = rate constant
A = pre-exponential factor (also known as frequency factor)
Ea = activation energy
R = gas constant (8.314 J/mol·K)
T = temperature in Kelvin

First, let's convert the temperatures from Celsius to Kelvin:

t1 = 37°C = 37 + 273 = 310 K
t2 = 27°C = 27 + 273 = 300 K

Now we can compare the rate constants. Since we have the activation energy, we only need to compare the exponential term (e^(-Ea/RT)) for the two temperatures:

At 37°C (t1):
k1 = Ae^(-Ea/RT1)

At 27°C (t2):
k2 = Ae^(-Ea/RT2)

To compare the rate constants k1 and k2, we can divide k1 by k2:

k1 / k2 = (Ae^(-Ea/RT1)) / (Ae^(-Ea/RT2))

The pre-exponential factor (A) cancels out:

k1 / k2 = e^(-Ea/RT1) / e^(-Ea/RT2)

To simplify further, we can use the properties of exponents:

k1 / k2 = e^(-Ea/RT1 + Ea/RT2)

Taking the exponential term on the right side under a common denominator:

k1 / k2 = e^((-EaRT2 + EaRT1) / (RT1RT2))

Now we can substitute the values into the equation:

k1 / k2 = e^((-Ea * R * 300 + Ea * R * 310) / (8.314 * 300 * 310))

Using the given activation energy (Ea = 108 * 10^3 kJ/mol) and the value for the gas constant (R = 8.314 J/mol·K), we can calculate the value by plugging in the numbers:

k1/k2 = e^((-108 * 10^3 * 8.314 * 300 + 108 * 10^3 * 8.314 * 310) / (8.314 * 300 * 310))

Evaluating this expression will give you the ratio of the rate constants at 37°C (t1) and 27°C (t2).