Answer:
Step-by-step explanation:
The relationship between the rate constant of a chemical reaction (k) and the activation energy (Ea) is described by the Arrhenius equation:
k = A * exp(-Ea / (R * T))
where A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin.
If an enzyme lowers the activation energy (Ea) by 2.0 kJ/mol at 37°C (which is 310 Kelvin), we can calculate the new rate constant (k') using the modified activation energy (Ea') as:
k' = A * exp(-Ea' / (R * T))
where Ea' = Ea - 2.0 kJ/mol.
Substituting the values into the equation, we get:
k' = A * exp(-((Ea - 2.0) / (R * T)))
k' = A * exp(-Ea / (R * T)) * exp(2.0 / (R * T))
The ratio of the new rate constant (k') to the original rate constant (k) is:
k' / k = (A * exp(-Ea / (R * T)) * exp(2.0 / (R * T))) / (A * exp(-Ea / (R * T)))
k' / k = exp(2.0 / (R * T))
Plugging in the values of R and T, we get:
k' / k = exp(2.0 / (8.3145 J/(mol*K) * 310 K))
k' / k = exp(0.965)
k' / k = 2.62
Therefore, the rate of the reaction is increased by a factor of approximately 2.62 if an enzyme lowers the activation energy by 2.0 kJ/mol at 37°C.