by what factor is the rate of detoxification changed if a liver enzyme lowers the activation energy of the reaction by 5 kJ/mol at 37 degree celsius?

Question

by what factor is the rate of detoxification changed if a liver enzyme lowers the activation energy of the reaction by 5 kJ/mol at 37 degree celsius?

Answer 1

The rate of detoxification would be increased by a factor of e^(5/RT), where R is the gas constant (8.314 J/mol K) and T is the temperature in Kelvin (310 K). Therefore, the rate of detoxification would be increased by a factor of e^(5/2442) = 1.0021.

Answer 2

To calculate the factor by which the rate of detoxification is changed, we need to use the Arrhenius equation:

k = Ae^(-Ea/RT)

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

Since the activation energy is reduced by 5 kJ/mol, we need to convert it to Joules by multiplying by 1000:

Ea = 5 kJ/mol x 1000 J/kJ = 5000 J/mol

The temperature is given as 37 degrees Celsius, so we need to convert it to Kelvin:

T = 37 + 273.15 = 310.15 K

Now, we can calculate the factor by which the rate changes. We'll compare the rate constant at the original activation energy (Ea) and the reduced activation energy (Ea - 5000 J/mol).

Let's denote the rate constant at the original activation energy as k1, and at the reduced activation energy as k2.

The factor by which the rate changes can be calculated as:

Factor = (k2/k1)

Now, let's calculate k1 and k2.

For k1, we can plug in the original activation energy (Ea) into the Arrhenius equation:

k1 = Ae^(-Ea/RT)

For k2, we will use the reduced activation energy (Ea - 5000 J/mol):

k2 = Ae^(-(Ea - 5000)/RT)

Finally, we can find the factor by dividing k2 by k1:

Factor = (k2/k1)

I will now perform the calculations.

Answer 3

To determine the factor by which the rate of detoxification changes, we need to use the Arrhenius equation, which relates the rate constant (k) to the activation energy (ΔEa), the temperature (T), and the rate constant at a reference temperature (k_ref).

The Arrhenius equation is given by:

k = A * e^(-ΔEa / (R * T))

Where:
- k is the rate constant at a specific temperature
- A is the pre-exponential factor
- ΔEa is the activation energy of the reaction
- R is the gas constant (8.314 J/(mol*K))
- T is the absolute temperature in Kelvin

To calculate the factor by which the rate changes, we can compare the rate constants at two different temperatures. Let's assume the reference temperature is 298 K (25°C). We need to find the rate constant at 37°C (310 K) considering a decrease in activation energy by 5 kJ/mol.

First, we convert the activation energy to Joules/mol:

ΔEa = 5 kJ/mol = 5000 J/mol

Let's assume the rate constant at 298 K is k_ref.

Now, we can rearrange the Arrhenius equation to solve for k:

k = A * e^(-ΔEa / (R * T))

k_ref = A * e^(-ΔEa / (R * T_ref))

To find the factor by which the rate changes, we divide the rate constant at 37°C (k_37) by the rate constant at 298 K (k_ref):

Factor = k_37 / k_ref

Now, let's calculate the factor by following these steps:

1. Calculate k_ref:
k_ref = A * e^(-ΔEa / (R * T_ref))

2. Calculate k_37:
k_37 = A * e^(-ΔEa / (R * T_37))

3. Calculate the factor:
Factor = k_37 / k_ref

Note that we still need to know the pre-exponential factor (A) in order to calculate the actual factors. Without that value, we cannot provide the specific factor by which the rate changes.