Enzymes in the liver catalyze a large number of reactions that degrade ingested toxic chemicals . By what factor is the rate of detoxification reaction changed if a liver enzyme lowers the activation energy of the reaction by 5 kj / mol at 37 celcius ?

Question

Enzymes in the liver catalyze a large number of reactions that degrade ingested toxic chemicals . By what factor is the rate of detoxification reaction changed if a liver enzyme lowers the activation energy of the reaction by 5 kj / mol at 37 celcius ?

Answer 1

Why can't you use the Arrhenius equation and calculate k1/k2.

Answer 2

To determine the factor by which the rate of the detoxification reaction is changed, we need to use the Arrhenius equation. The Arrhenius equation relates the rate constant of a reaction to the activation energy, temperature, and a factor called the frequency factor or pre-exponential factor.

The Arrhenius equation is given as:

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

Where:
- k is the rate constant of the reaction
- 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

In this case, we want to determine the factor by which the rate is changed when the activation energy is reduced by 5 kJ/mol at 37 degrees Celsius.

First, we need to convert the temperature from Celsius to Kelvin:
T (Kelvin) = 37 + 273.15

Next, we substitute the given values into the equation. Let's assume the pre-exponential factor remains constant:
k1 = A * exp(-Ea1 / (R * T))
k2 = A * exp(-Ea2 / (R * T))

We know that activation energy, Ea2 = Ea1 - 5 kJ/mol.

So, the factor by which the rate changes can be calculated using the ratio of the rate constants:

Rate factor = k2 / k1 = (A * exp(-Ea2 / (R * T))) / (A * exp(-Ea1 / (R * T)))
= exp((-Ea2 + Ea1) / (R * T))

Substituting the values, we have:
Rate factor = exp((-Ea1 + (Ea1 - 5)) / (R * T))
= exp(-5 / (R * T))

Now, we can calculate the rate factor using the given values for temperature and the gas constant.

Note: The given activation energy is in kJ/mol, so we need to convert it to Joules/mol by multiplying by 1000.

Rate factor = exp(-5000 / (8.314 * (37 + 273.15)))

Calculating this expression will give you the factor by which the rate of the detoxification reaction changes when the activation energy is lowered by 5 kJ/mol at 37 degrees Celsius.